Google Git
Sign in
apache / mxnet-site / d5c5a235eef72f64ccaf224b834a20ef3287469b / . / versions / 1.9.1 / api / python / docs / tutorials / getting-started / logistic_regression_explained.html
blob: 1935d251b5015baaa809eef29fd04bd33c2d0018 [file] [log] [blame]
<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
<meta http-equiv="x-ua-compatible" content="ie=edge">
<style>
.dropdown {
position: relative;
display: inline-block;
}
.dropdown-content {
display: none;
position: absolute;
background-color: #f9f9f9;
min-width: 160px;
box-shadow: 0px 8px 16px 0px rgba(0,0,0,0.2);
padding: 12px 16px;
z-index: 1;
text-align: left;
}
.dropdown:hover .dropdown-content {
display: block;
}
.dropdown-option:hover {
color: #FF4500;
}
.dropdown-option-active {
color: #FF4500;
font-weight: lighter;
}
.dropdown-option {
color: #000000;
font-weight: lighter;
}
.dropdown-header {
color: #FFFFFF;
display: inline-flex;
}
.dropdown-caret {
width: 18px;
}
.dropdown-caret-path {
fill: #FFFFFF;
}
</style>
<title>Logistic regression explained &#8212; Apache MXNet documentation</title>
<link rel="stylesheet" href="../../_static/basic.css" type="text/css" />
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
<link rel="stylesheet" type="text/css" href="../../_static/mxnet.css" />
<link rel="stylesheet" href="../../_static/material-design-lite-1.3.0/material.blue-deep_orange.min.css" type="text/css" />
<link rel="stylesheet" href="../../_static/sphinx_materialdesign_theme.css" type="text/css" />
<link rel="stylesheet" href="../../_static/fontawesome/all.css" type="text/css" />
<link rel="stylesheet" href="../../_static/fonts.css" type="text/css" />
<link rel="stylesheet" href="../../_static/feedback.css" type="text/css" />
<script id="documentation_options" data-url_root="../../" src="../../_static/documentation_options.js"></script>
<script src="../../_static/jquery.js"></script>
<script src="../../_static/underscore.js"></script>
<script src="../../_static/doctools.js"></script>
<script src="../../_static/language_data.js"></script>
<script src="../../_static/matomo_analytics.js"></script>
<script src="../../_static/autodoc.js"></script>
<script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
<script async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-AMS-MML_HTMLorMML"></script>
<script type="text/x-mathjax-config">MathJax.Hub.Config({"tex2jax": {"inlineMath": [["$", "$"], ["\\(", "\\)"]], "processEscapes": true, "ignoreClass": "document", "processClass": "math|output_area"}})</script>
<link rel="shortcut icon" href="../../_static/mxnet-icon.png"/>
<link rel="index" title="Index" href="../../genindex.html" />
<link rel="search" title="Search" href="../../search.html" />
<link rel="next" title="Packages" href="../packages/index.html" />
<link rel="prev" title="Gluon: from experiment to deployment" href="gluon_from_experiment_to_deployment.html" />
</head>
<body><header class="site-header" role="banner">
<div class="wrapper">
<a class="site-title" rel="author" href="/versions/1.9.1/"><img
src="../../_static/mxnet_logo.png" class="site-header-logo"></a>
<nav class="site-nav">
<input type="checkbox" id="nav-trigger" class="nav-trigger"/>
<label for="nav-trigger">
<span class="menu-icon">
<svg viewBox="0 0 18 15" width="18px" height="15px">
<path d="M18,1.484c0,0.82-0.665,1.484-1.484,1.484H1.484C0.665,2.969,0,2.304,0,1.484l0,0C0,0.665,0.665,0,1.484,0 h15.032C17.335,0,18,0.665,18,1.484L18,1.484z M18,7.516C18,8.335,17.335,9,16.516,9H1.484C0.665,9,0,8.335,0,7.516l0,0 c0-0.82,0.665-1.484,1.484-1.484h15.032C17.335,6.031,18,6.696,18,7.516L18,7.516z M18,13.516C18,14.335,17.335,15,16.516,15H1.484 C0.665,15,0,14.335,0,13.516l0,0c0-0.82,0.665-1.483,1.484-1.483h15.032C17.335,12.031,18,12.695,18,13.516L18,13.516z"/>
</svg>
</span>
</label>
<div class="trigger">
<a class="page-link" href="/versions/1.9.1/get_started">Get Started</a>
<a class="page-link" href="/versions/1.9.1/features">Features</a>
<a class="page-link" href="/versions/1.9.1/ecosystem">Ecosystem</a>
<a class="page-link page-current" href="/versions/1.9.1/api">Docs & Tutorials</a>
<a class="page-link" href="/versions/1.9.1/trusted_by">Trusted By</a>
<a class="page-link" href="https://github.com/apache/mxnet">GitHub</a>
<div class="dropdown" style="min-width:100px">
<span class="dropdown-header">Apache
<svg class="dropdown-caret" viewBox="0 0 32 32" class="icon icon-caret-bottom" aria-hidden="true"><path class="dropdown-caret-path" d="M24 11.305l-7.997 11.39L8 11.305z"></path></svg>
</span>
<div class="dropdown-content" style="min-width:250px">
<a href="https://www.apache.org/foundation/">Apache Software Foundation</a>
<a href="https://incubator.apache.org/">Apache Incubator</a>
<a href="https://www.apache.org/licenses/">License</a>
<a href="/versions/1.9.1/api/faq/security.html">Security</a>
<a href="https://privacy.apache.org/policies/privacy-policy-public.html">Privacy</a>
<a href="https://www.apache.org/events/current-event">Events</a>
<a href="https://www.apache.org/foundation/sponsorship.html">Sponsorship</a>
<a href="https://www.apache.org/foundation/thanks.html">Thanks</a>
</div>
</div>
<div class="dropdown">
<span class="dropdown-header">1.9.1
<svg class="dropdown-caret" viewBox="0 0 32 32" class="icon icon-caret-bottom" aria-hidden="true"><path class="dropdown-caret-path" d="M24 11.305l-7.997 11.39L8 11.305z"></path></svg>
</span>
<div class="dropdown-content">
<a class="dropdown-option" href="/">master</a><br>
<a class="dropdown-option-active" href="/versions/1.9.1/">1.9.1</a><br>
<a class="dropdown-option" href="/versions/1.8.0/">1.8.0</a><br>
<a class="dropdown-option" href="/versions/1.7.0/">1.7.0</a><br>
<a class="dropdown-option" href="/versions/1.6.0/">1.6.0</a><br>
<a class="dropdown-option" href="/versions/1.5.0/">1.5.0</a><br>
<a class="dropdown-option" href="/versions/1.4.1/">1.4.1</a><br>
<a class="dropdown-option" href="/versions/1.3.1/">1.3.1</a><br>
<a class="dropdown-option" href="/versions/1.2.1/">1.2.1</a><br>
<a class="dropdown-option" href="/versions/1.1.0/">1.1.0</a><br>
<a class="dropdown-option" href="/versions/1.0.0/">1.0.0</a><br>
<a class="dropdown-option" href="/versions/0.12.1/">0.12.1</a><br>
<a class="dropdown-option" href="/versions/0.11.0/">0.11.0</a>
</div>
</div>
</div>
</nav>
</div>
</header>
<div class="mdl-layout mdl-js-layout mdl-layout--fixed-header mdl-layout--fixed-drawer"><header class="mdl-layout__header mdl-layout__header--waterfall ">
<div class="mdl-layout__header-row">
<nav class="mdl-navigation breadcrumb">
<a class="mdl-navigation__link" href="../index.html">Python Tutorials</a><i class="material-icons">navigate_next</i>
<a class="mdl-navigation__link" href="index.html">Getting Started</a><i class="material-icons">navigate_next</i>
<a class="mdl-navigation__link is-active">Logistic regression explained</a>
</nav>
<div class="mdl-layout-spacer"></div>
<nav class="mdl-navigation">
<form class="form-inline pull-sm-right" action="../../search.html" method="get">
<div class="mdl-textfield mdl-js-textfield mdl-textfield--expandable mdl-textfield--floating-label mdl-textfield--align-right">
<label id="quick-search-icon" class="mdl-button mdl-js-button mdl-button--icon" for="waterfall-exp">
<i class="material-icons">search</i>
</label>
<div class="mdl-textfield__expandable-holder">
<input class="mdl-textfield__input" type="text" name="q" id="waterfall-exp" placeholder="Search" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</div>
</div>
<div class="mdl-tooltip" data-mdl-for="quick-search-icon">
Quick search
</div>
</form>
<a id="button-show-source"
class="mdl-button mdl-js-button mdl-button--icon"
href="../../_sources/tutorials/getting-started/logistic_regression_explained.ipynb" rel="nofollow">
<i class="material-icons">code</i>
</a>
<div class="mdl-tooltip" data-mdl-for="button-show-source">
Show Source
</div>
</nav>
</div>
<div class="mdl-layout__header-row header-links">
<div class="mdl-layout-spacer"></div>
<nav class="mdl-navigation">
</nav>
</div>
</header><header class="mdl-layout__drawer">
<div class="globaltoc">
<span class="mdl-layout-title toc">Table Of Contents</span>
<nav class="mdl-navigation">
<ul class="current">
<li class="toctree-l1 current"><a class="reference internal" href="../index.html">Python Tutorials</a><ul class="current">
<li class="toctree-l2 current"><a class="reference internal" href="index.html">Getting Started</a><ul class="current">
<li class="toctree-l3"><a class="reference internal" href="crash-course/index.html">Crash Course</a><ul>
<li class="toctree-l4"><a class="reference internal" href="crash-course/1-ndarray.html">Manipulate data with <code class="docutils literal notranslate"><span class="pre">ndarray</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="crash-course/2-nn.html">Create a neural network</a></li>
<li class="toctree-l4"><a class="reference internal" href="crash-course/3-autograd.html">Automatic differentiation with <code class="docutils literal notranslate"><span class="pre">autograd</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="crash-course/4-train.html">Train the neural network</a></li>
<li class="toctree-l4"><a class="reference internal" href="crash-course/5-predict.html">Predict with a pre-trained model</a></li>
<li class="toctree-l4"><a class="reference internal" href="crash-course/6-use_gpus.html">Use GPUs</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="to-mxnet/index.html">Moving to MXNet from Other Frameworks</a><ul>
<li class="toctree-l4"><a class="reference internal" href="to-mxnet/pytorch.html">PyTorch vs Apache MXNet</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="gluon_from_experiment_to_deployment.html">Gluon: from experiment to deployment</a></li>
<li class="toctree-l3 current"><a class="current reference internal" href="#">Logistic regression explained</a></li>
<li class="toctree-l3"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/packages/gluon/image/mnist.html">MNIST</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../packages/index.html">Packages</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../packages/autograd/index.html">Automatic Differentiation</a></li>
<li class="toctree-l3"><a class="reference internal" href="../packages/gluon/index.html">Gluon</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../packages/gluon/blocks/index.html">Blocks</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/blocks/custom-layer.html">Custom Layers</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/blocks/custom_layer_beginners.html">Customer Layers (Beginners)</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/blocks/hybridize.html">Hybridize</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/blocks/init.html">Initialization</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/blocks/naming.html">Parameter and Block Naming</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/blocks/nn.html">Layers and Blocks</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/blocks/parameters.html">Parameter Management</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/blocks/save_load_params.html">Saving and Loading Gluon Models</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/blocks/activations/activations.html">Activation Blocks</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../packages/gluon/data/index.html">Data Tutorials</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/data/data_augmentation.html">Image Augmentation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/data/data_augmentation.html#Spatial-Augmentation">Spatial Augmentation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/data/data_augmentation.html#Color-Augmentation">Color Augmentation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/data/data_augmentation.html#Composed-Augmentations">Composed Augmentations</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/data/datasets.html">Gluon <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s and <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/data/datasets.html#Using-own-data-with-included-Datasets">Using own data with included <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/data/datasets.html#Using-own-data-with-custom-Datasets">Using own data with custom <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/data/datasets.html#Appendix:-Upgrading-from-Module-DataIter-to-Gluon-DataLoader">Appendix: Upgrading from Module <code class="docutils literal notranslate"><span class="pre">DataIter</span></code> to Gluon <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../packages/gluon/image/index.html">Image Tutorials</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/image/image-augmentation.html">Image Augmentation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/image/info_gan.html">Image similarity search with InfoGAN</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/image/mnist.html">Handwritten Digit Recognition</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/image/pretrained_models.html">Using pre-trained models in MXNet</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../packages/gluon/loss/index.html">Losses</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/loss/custom-loss.html">Custom Loss Blocks</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/loss/kl_divergence.html">Kullback-Leibler (KL) Divergence</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/loss/loss.html">Loss functions</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../packages/gluon/text/index.html">Text Tutorials</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/text/gnmt.html">Google Neural Machine Translation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/text/transformer.html">Machine Translation with Transformer</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../packages/gluon/training/index.html">Training</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/training/fit_api_tutorial.html">MXNet Gluon Fit API</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/training/trainer.html">Trainer</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/training/learning_rates/index.html">Learning Rates</a><ul>
<li class="toctree-l6"><a class="reference internal" href="../packages/gluon/training/learning_rates/learning_rate_finder.html">Learning Rate Finder</a></li>
<li class="toctree-l6"><a class="reference internal" href="../packages/gluon/training/learning_rates/learning_rate_schedules.html">Learning Rate Schedules</a></li>
<li class="toctree-l6"><a class="reference internal" href="../packages/gluon/training/learning_rates/learning_rate_schedules_advanced.html">Advanced Learning Rate Schedules</a></li>
</ul>
</li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/training/normalization/index.html">Normalization Blocks</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../packages/kvstore/index.html">KVStore</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../packages/kvstore/kvstore.html">Distributed Key-Value Store</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../packages/ndarray/index.html">NDArray</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../packages/ndarray/01-ndarray-intro.html">An Intro: Manipulate Data the MXNet Way with NDArray</a></li>
<li class="toctree-l4"><a class="reference internal" href="../packages/ndarray/02-ndarray-operations.html">NDArray Operations</a></li>
<li class="toctree-l4"><a class="reference internal" href="../packages/ndarray/03-ndarray-contexts.html">NDArray Contexts</a></li>
<li class="toctree-l4"><a class="reference internal" href="../packages/ndarray/gotchas_numpy_in_mxnet.html">Gotchas using NumPy in Apache MXNet</a></li>
<li class="toctree-l4"><a class="reference internal" href="../packages/ndarray/sparse/index.html">Tutorials</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../packages/ndarray/sparse/csr.html">CSRNDArray - NDArray in Compressed Sparse Row Storage Format</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/ndarray/sparse/row_sparse.html">RowSparseNDArray - NDArray for Sparse Gradient Updates</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/ndarray/sparse/train.html">Train a Linear Regression Model with Sparse Symbols</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/ndarray/sparse/train_gluon.html">Sparse NDArrays with Gluon</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../packages/onnx/index.html">ONNX</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../packages/onnx/fine_tuning_gluon.html">Fine-tuning an ONNX model</a></li>
<li class="toctree-l4"><a class="reference internal" href="../packages/onnx/inference_on_onnx_model.html">Running inference on MXNet/Gluon from an ONNX model</a></li>
<li class="toctree-l4"><a class="reference internal" href="../packages/onnx/super_resolution.html">Importing an ONNX model into MXNet</a></li>
<li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/deploy/export/onnx.html">Export ONNX Models</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../packages/optimizer/index.html">Optimizers</a></li>
<li class="toctree-l3"><a class="reference internal" href="../packages/viz/index.html">Visualization</a><ul>
<li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/faq/visualize_graph">Visualize networks</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../performance/index.html">Performance</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../performance/compression/index.html">Compression</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../performance/compression/int8.html">Deploy with int-8</a></li>
<li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/faq/float16">Float16</a></li>
<li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/faq/gradient_compression">Gradient Compression</a></li>
<li class="toctree-l4"><a class="reference external" href="https://gluon-cv.mxnet.io/build/examples_deployment/int8_inference.html">GluonCV with Quantized Models</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../performance/backend/index.html">Accelerated Backend Tools</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../performance/backend/mkldnn/index.html">Intel MKL-DNN</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../performance/backend/mkldnn/mkldnn_quantization.html">Quantize with MKL-DNN backend</a></li>
<li class="toctree-l5"><a class="reference internal" href="../performance/backend/mkldnn/mkldnn_quantization.html#Improving-accuracy-with-Intel®-Neural-Compressor">Improving accuracy with Intel® Neural Compressor</a></li>
<li class="toctree-l5"><a class="reference internal" href="../performance/backend/mkldnn/mkldnn_readme.html">Install MXNet with MKL-DNN</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../performance/backend/tensorrt/index.html">TensorRT</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../performance/backend/tensorrt/tensorrt.html">Optimizing Deep Learning Computation Graphs with TensorRT</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../performance/backend/tvm.html">Use TVM</a></li>
<li class="toctree-l4"><a class="reference internal" href="../performance/backend/profiler.html">Profiling MXNet Models</a></li>
<li class="toctree-l4"><a class="reference internal" href="../performance/backend/amp.html">Using AMP: Automatic Mixed Precision</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../deploy/index.html">Deployment</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../deploy/export/index.html">Export</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../deploy/export/onnx.html">Exporting to ONNX format</a></li>
<li class="toctree-l4"><a class="reference external" href="https://gluon-cv.mxnet.io/build/examples_deployment/export_network.html">Export Gluon CV Models</a></li>
<li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/packages/gluon/blocks/save_load_params.html">Save / Load Parameters</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../deploy/inference/index.html">Inference</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../deploy/inference/cpp.html">Deploy into C++</a></li>
<li class="toctree-l4"><a class="reference internal" href="../deploy/inference/image_classification_jetson.html">Image Classication using pretrained ResNet-50 model on Jetson module</a></li>
<li class="toctree-l4"><a class="reference internal" href="../deploy/inference/scala.html">Deploy into a Java or Scala Environment</a></li>
<li class="toctree-l4"><a class="reference internal" href="../deploy/inference/wine_detector.html">Real-time Object Detection with MXNet On The Raspberry Pi</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../deploy/run-on-aws/index.html">Run on AWS</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../deploy/run-on-aws/use_ec2.html">Run on an EC2 Instance</a></li>
<li class="toctree-l4"><a class="reference internal" href="../deploy/run-on-aws/use_sagemaker.html">Run on Amazon SageMaker</a></li>
<li class="toctree-l4"><a class="reference internal" href="../deploy/run-on-aws/cloud.html">MXNet on the Cloud</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../extend/index.html">Extend</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../extend/custom_layer.html">Custom Layers</a></li>
<li class="toctree-l3"><a class="reference internal" href="../extend/customop.html">Custom Numpy Operators</a></li>
<li class="toctree-l3"><a class="reference external" href="https://mxnet.apache.org/api/faq/new_op">New Operator Creation</a></li>
<li class="toctree-l3"><a class="reference external" href="https://mxnet.apache.org/api/faq/add_op_in_backend">New Operator in MXNet Backend</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../../api/index.html">Python API</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../../api/ndarray/index.html">mxnet.ndarray</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../api/ndarray/ndarray.html">ndarray</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/ndarray/contrib/index.html">ndarray.contrib</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/ndarray/image/index.html">ndarray.image</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/ndarray/linalg/index.html">ndarray.linalg</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/ndarray/op/index.html">ndarray.op</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/ndarray/random/index.html">ndarray.random</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/ndarray/register/index.html">ndarray.register</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/ndarray/sparse/index.html">ndarray.sparse</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/ndarray/utils/index.html">ndarray.utils</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../../api/gluon/index.html">mxnet.gluon</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/block.html">gluon.Block</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/hybrid_block.html">gluon.HybridBlock</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/symbol_block.html">gluon.SymbolBlock</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/constant.html">gluon.Constant</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/parameter.html">gluon.Parameter</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/parameter_dict.html">gluon.ParameterDict</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/trainer.html">gluon.Trainer</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/contrib/index.html">gluon.contrib</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/data/index.html">gluon.data</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../api/gluon/data/vision/index.html">data.vision</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../api/gluon/data/vision/datasets/index.html">vision.datasets</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../api/gluon/data/vision/transforms/index.html">vision.transforms</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/loss/index.html">gluon.loss</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/model_zoo/index.html">gluon.model_zoo.vision</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/nn/index.html">gluon.nn</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/rnn/index.html">gluon.rnn</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/utils/index.html">gluon.utils</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../../api/autograd/index.html">mxnet.autograd</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../api/initializer/index.html">mxnet.initializer</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../api/optimizer/index.html">mxnet.optimizer</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../api/lr_scheduler/index.html">mxnet.lr_scheduler</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../api/metric/index.html">mxnet.metric</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../api/kvstore/index.html">mxnet.kvstore</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../api/symbol/index.html">mxnet.symbol</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../api/symbol/symbol.html">symbol</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/symbol/contrib/index.html">symbol.contrib</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/symbol/image/index.html">symbol.image</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/symbol/linalg/index.html">symbol.linalg</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/symbol/op/index.html">symbol.op</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/symbol/random/index.html">symbol.random</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/symbol/register/index.html">symbol.register</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/symbol/sparse/index.html">symbol.sparse</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../../api/module/index.html">mxnet.module</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../api/contrib/index.html">mxnet.contrib</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../api/contrib/autograd/index.html">contrib.autograd</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/contrib/io/index.html">contrib.io</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/contrib/ndarray/index.html">contrib.ndarray</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/contrib/onnx/index.html">contrib.onnx</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/contrib/quantization/index.html">contrib.quantization</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/contrib/symbol/index.html">contrib.symbol</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/contrib/tensorboard/index.html">contrib.tensorboard</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/contrib/tensorrt/index.html">contrib.tensorrt</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/contrib/text/index.html">contrib.text</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../../api/mxnet/index.html">mxnet</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/attribute/index.html">mxnet.attribute</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/base/index.html">mxnet.base</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/callback/index.html">mxnet.callback</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/context/index.html">mxnet.context</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/engine/index.html">mxnet.engine</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/executor/index.html">mxnet.executor</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/executor_manager/index.html">mxnet.executor_manager</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/image/index.html">mxnet.image</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/io/index.html">mxnet.io</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/kvstore_server/index.html">mxnet.kvstore_server</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/libinfo/index.html">mxnet.libinfo</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/log/index.html">mxnet.log</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/model/index.html">mxnet.model</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/monitor/index.html">mxnet.monitor</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/name/index.html">mxnet.name</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/notebook/index.html">mxnet.notebook</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/operator/index.html">mxnet.operator</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/profiler/index.html">mxnet.profiler</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/random/index.html">mxnet.random</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/recordio/index.html">mxnet.recordio</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/registry/index.html">mxnet.registry</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/rtc/index.html">mxnet.rtc</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/runtime/index.html">mxnet.runtime</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/test_utils/index.html">mxnet.test_utils</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/torch/index.html">mxnet.torch</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/util/index.html">mxnet.util</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/visualization/index.html">mxnet.visualization</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</nav>
</div>
</header>
<main class="mdl-layout__content" tabIndex="0">
<script type="text/javascript" src="../../_static/sphinx_materialdesign_theme.js "></script>
<script type="text/javascript" src="../../_static/feedback.js"></script>
<header class="mdl-layout__drawer">
<div class="globaltoc">
<span class="mdl-layout-title toc">Table Of Contents</span>
<nav class="mdl-navigation">
<ul class="current">
<li class="toctree-l1 current"><a class="reference internal" href="../index.html">Python Tutorials</a><ul class="current">
<li class="toctree-l2 current"><a class="reference internal" href="index.html">Getting Started</a><ul class="current">
<li class="toctree-l3"><a class="reference internal" href="crash-course/index.html">Crash Course</a><ul>
<li class="toctree-l4"><a class="reference internal" href="crash-course/1-ndarray.html">Manipulate data with <code class="docutils literal notranslate"><span class="pre">ndarray</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="crash-course/2-nn.html">Create a neural network</a></li>
<li class="toctree-l4"><a class="reference internal" href="crash-course/3-autograd.html">Automatic differentiation with <code class="docutils literal notranslate"><span class="pre">autograd</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="crash-course/4-train.html">Train the neural network</a></li>
<li class="toctree-l4"><a class="reference internal" href="crash-course/5-predict.html">Predict with a pre-trained model</a></li>
<li class="toctree-l4"><a class="reference internal" href="crash-course/6-use_gpus.html">Use GPUs</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="to-mxnet/index.html">Moving to MXNet from Other Frameworks</a><ul>
<li class="toctree-l4"><a class="reference internal" href="to-mxnet/pytorch.html">PyTorch vs Apache MXNet</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="gluon_from_experiment_to_deployment.html">Gluon: from experiment to deployment</a></li>
<li class="toctree-l3 current"><a class="current reference internal" href="#">Logistic regression explained</a></li>
<li class="toctree-l3"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/packages/gluon/image/mnist.html">MNIST</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../packages/index.html">Packages</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../packages/autograd/index.html">Automatic Differentiation</a></li>
<li class="toctree-l3"><a class="reference internal" href="../packages/gluon/index.html">Gluon</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../packages/gluon/blocks/index.html">Blocks</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/blocks/custom-layer.html">Custom Layers</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/blocks/custom_layer_beginners.html">Customer Layers (Beginners)</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/blocks/hybridize.html">Hybridize</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/blocks/init.html">Initialization</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/blocks/naming.html">Parameter and Block Naming</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/blocks/nn.html">Layers and Blocks</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/blocks/parameters.html">Parameter Management</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/blocks/save_load_params.html">Saving and Loading Gluon Models</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/blocks/activations/activations.html">Activation Blocks</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../packages/gluon/data/index.html">Data Tutorials</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/data/data_augmentation.html">Image Augmentation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/data/data_augmentation.html#Spatial-Augmentation">Spatial Augmentation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/data/data_augmentation.html#Color-Augmentation">Color Augmentation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/data/data_augmentation.html#Composed-Augmentations">Composed Augmentations</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/data/datasets.html">Gluon <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s and <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/data/datasets.html#Using-own-data-with-included-Datasets">Using own data with included <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/data/datasets.html#Using-own-data-with-custom-Datasets">Using own data with custom <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/data/datasets.html#Appendix:-Upgrading-from-Module-DataIter-to-Gluon-DataLoader">Appendix: Upgrading from Module <code class="docutils literal notranslate"><span class="pre">DataIter</span></code> to Gluon <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../packages/gluon/image/index.html">Image Tutorials</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/image/image-augmentation.html">Image Augmentation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/image/info_gan.html">Image similarity search with InfoGAN</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/image/mnist.html">Handwritten Digit Recognition</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/image/pretrained_models.html">Using pre-trained models in MXNet</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../packages/gluon/loss/index.html">Losses</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/loss/custom-loss.html">Custom Loss Blocks</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/loss/kl_divergence.html">Kullback-Leibler (KL) Divergence</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/loss/loss.html">Loss functions</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../packages/gluon/text/index.html">Text Tutorials</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/text/gnmt.html">Google Neural Machine Translation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/text/transformer.html">Machine Translation with Transformer</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../packages/gluon/training/index.html">Training</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/training/fit_api_tutorial.html">MXNet Gluon Fit API</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/training/trainer.html">Trainer</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/training/learning_rates/index.html">Learning Rates</a><ul>
<li class="toctree-l6"><a class="reference internal" href="../packages/gluon/training/learning_rates/learning_rate_finder.html">Learning Rate Finder</a></li>
<li class="toctree-l6"><a class="reference internal" href="../packages/gluon/training/learning_rates/learning_rate_schedules.html">Learning Rate Schedules</a></li>
<li class="toctree-l6"><a class="reference internal" href="../packages/gluon/training/learning_rates/learning_rate_schedules_advanced.html">Advanced Learning Rate Schedules</a></li>
</ul>
</li>
<li class="toctree-l5"><a class="reference internal" href="../packages/gluon/training/normalization/index.html">Normalization Blocks</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../packages/kvstore/index.html">KVStore</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../packages/kvstore/kvstore.html">Distributed Key-Value Store</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../packages/ndarray/index.html">NDArray</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../packages/ndarray/01-ndarray-intro.html">An Intro: Manipulate Data the MXNet Way with NDArray</a></li>
<li class="toctree-l4"><a class="reference internal" href="../packages/ndarray/02-ndarray-operations.html">NDArray Operations</a></li>
<li class="toctree-l4"><a class="reference internal" href="../packages/ndarray/03-ndarray-contexts.html">NDArray Contexts</a></li>
<li class="toctree-l4"><a class="reference internal" href="../packages/ndarray/gotchas_numpy_in_mxnet.html">Gotchas using NumPy in Apache MXNet</a></li>
<li class="toctree-l4"><a class="reference internal" href="../packages/ndarray/sparse/index.html">Tutorials</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../packages/ndarray/sparse/csr.html">CSRNDArray - NDArray in Compressed Sparse Row Storage Format</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/ndarray/sparse/row_sparse.html">RowSparseNDArray - NDArray for Sparse Gradient Updates</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/ndarray/sparse/train.html">Train a Linear Regression Model with Sparse Symbols</a></li>
<li class="toctree-l5"><a class="reference internal" href="../packages/ndarray/sparse/train_gluon.html">Sparse NDArrays with Gluon</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../packages/onnx/index.html">ONNX</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../packages/onnx/fine_tuning_gluon.html">Fine-tuning an ONNX model</a></li>
<li class="toctree-l4"><a class="reference internal" href="../packages/onnx/inference_on_onnx_model.html">Running inference on MXNet/Gluon from an ONNX model</a></li>
<li class="toctree-l4"><a class="reference internal" href="../packages/onnx/super_resolution.html">Importing an ONNX model into MXNet</a></li>
<li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/deploy/export/onnx.html">Export ONNX Models</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../packages/optimizer/index.html">Optimizers</a></li>
<li class="toctree-l3"><a class="reference internal" href="../packages/viz/index.html">Visualization</a><ul>
<li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/faq/visualize_graph">Visualize networks</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../performance/index.html">Performance</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../performance/compression/index.html">Compression</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../performance/compression/int8.html">Deploy with int-8</a></li>
<li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/faq/float16">Float16</a></li>
<li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/faq/gradient_compression">Gradient Compression</a></li>
<li class="toctree-l4"><a class="reference external" href="https://gluon-cv.mxnet.io/build/examples_deployment/int8_inference.html">GluonCV with Quantized Models</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../performance/backend/index.html">Accelerated Backend Tools</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../performance/backend/mkldnn/index.html">Intel MKL-DNN</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../performance/backend/mkldnn/mkldnn_quantization.html">Quantize with MKL-DNN backend</a></li>
<li class="toctree-l5"><a class="reference internal" href="../performance/backend/mkldnn/mkldnn_quantization.html#Improving-accuracy-with-Intel®-Neural-Compressor">Improving accuracy with Intel® Neural Compressor</a></li>
<li class="toctree-l5"><a class="reference internal" href="../performance/backend/mkldnn/mkldnn_readme.html">Install MXNet with MKL-DNN</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../performance/backend/tensorrt/index.html">TensorRT</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../performance/backend/tensorrt/tensorrt.html">Optimizing Deep Learning Computation Graphs with TensorRT</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../performance/backend/tvm.html">Use TVM</a></li>
<li class="toctree-l4"><a class="reference internal" href="../performance/backend/profiler.html">Profiling MXNet Models</a></li>
<li class="toctree-l4"><a class="reference internal" href="../performance/backend/amp.html">Using AMP: Automatic Mixed Precision</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../deploy/index.html">Deployment</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../deploy/export/index.html">Export</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../deploy/export/onnx.html">Exporting to ONNX format</a></li>
<li class="toctree-l4"><a class="reference external" href="https://gluon-cv.mxnet.io/build/examples_deployment/export_network.html">Export Gluon CV Models</a></li>
<li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/packages/gluon/blocks/save_load_params.html">Save / Load Parameters</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../deploy/inference/index.html">Inference</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../deploy/inference/cpp.html">Deploy into C++</a></li>
<li class="toctree-l4"><a class="reference internal" href="../deploy/inference/image_classification_jetson.html">Image Classication using pretrained ResNet-50 model on Jetson module</a></li>
<li class="toctree-l4"><a class="reference internal" href="../deploy/inference/scala.html">Deploy into a Java or Scala Environment</a></li>
<li class="toctree-l4"><a class="reference internal" href="../deploy/inference/wine_detector.html">Real-time Object Detection with MXNet On The Raspberry Pi</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../deploy/run-on-aws/index.html">Run on AWS</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../deploy/run-on-aws/use_ec2.html">Run on an EC2 Instance</a></li>
<li class="toctree-l4"><a class="reference internal" href="../deploy/run-on-aws/use_sagemaker.html">Run on Amazon SageMaker</a></li>
<li class="toctree-l4"><a class="reference internal" href="../deploy/run-on-aws/cloud.html">MXNet on the Cloud</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../extend/index.html">Extend</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../extend/custom_layer.html">Custom Layers</a></li>
<li class="toctree-l3"><a class="reference internal" href="../extend/customop.html">Custom Numpy Operators</a></li>
<li class="toctree-l3"><a class="reference external" href="https://mxnet.apache.org/api/faq/new_op">New Operator Creation</a></li>
<li class="toctree-l3"><a class="reference external" href="https://mxnet.apache.org/api/faq/add_op_in_backend">New Operator in MXNet Backend</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../../api/index.html">Python API</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../../api/ndarray/index.html">mxnet.ndarray</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../api/ndarray/ndarray.html">ndarray</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/ndarray/contrib/index.html">ndarray.contrib</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/ndarray/image/index.html">ndarray.image</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/ndarray/linalg/index.html">ndarray.linalg</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/ndarray/op/index.html">ndarray.op</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/ndarray/random/index.html">ndarray.random</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/ndarray/register/index.html">ndarray.register</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/ndarray/sparse/index.html">ndarray.sparse</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/ndarray/utils/index.html">ndarray.utils</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../../api/gluon/index.html">mxnet.gluon</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/block.html">gluon.Block</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/hybrid_block.html">gluon.HybridBlock</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/symbol_block.html">gluon.SymbolBlock</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/constant.html">gluon.Constant</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/parameter.html">gluon.Parameter</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/parameter_dict.html">gluon.ParameterDict</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/trainer.html">gluon.Trainer</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/contrib/index.html">gluon.contrib</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/data/index.html">gluon.data</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../api/gluon/data/vision/index.html">data.vision</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../api/gluon/data/vision/datasets/index.html">vision.datasets</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../api/gluon/data/vision/transforms/index.html">vision.transforms</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/loss/index.html">gluon.loss</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/model_zoo/index.html">gluon.model_zoo.vision</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/nn/index.html">gluon.nn</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/rnn/index.html">gluon.rnn</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/gluon/utils/index.html">gluon.utils</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../../api/autograd/index.html">mxnet.autograd</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../api/initializer/index.html">mxnet.initializer</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../api/optimizer/index.html">mxnet.optimizer</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../api/lr_scheduler/index.html">mxnet.lr_scheduler</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../api/metric/index.html">mxnet.metric</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../api/kvstore/index.html">mxnet.kvstore</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../api/symbol/index.html">mxnet.symbol</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../api/symbol/symbol.html">symbol</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/symbol/contrib/index.html">symbol.contrib</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/symbol/image/index.html">symbol.image</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/symbol/linalg/index.html">symbol.linalg</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/symbol/op/index.html">symbol.op</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/symbol/random/index.html">symbol.random</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/symbol/register/index.html">symbol.register</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/symbol/sparse/index.html">symbol.sparse</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../../api/module/index.html">mxnet.module</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../api/contrib/index.html">mxnet.contrib</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../api/contrib/autograd/index.html">contrib.autograd</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/contrib/io/index.html">contrib.io</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/contrib/ndarray/index.html">contrib.ndarray</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/contrib/onnx/index.html">contrib.onnx</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/contrib/quantization/index.html">contrib.quantization</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/contrib/symbol/index.html">contrib.symbol</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/contrib/tensorboard/index.html">contrib.tensorboard</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/contrib/tensorrt/index.html">contrib.tensorrt</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/contrib/text/index.html">contrib.text</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../../api/mxnet/index.html">mxnet</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/attribute/index.html">mxnet.attribute</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/base/index.html">mxnet.base</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/callback/index.html">mxnet.callback</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/context/index.html">mxnet.context</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/engine/index.html">mxnet.engine</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/executor/index.html">mxnet.executor</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/executor_manager/index.html">mxnet.executor_manager</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/image/index.html">mxnet.image</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/io/index.html">mxnet.io</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/kvstore_server/index.html">mxnet.kvstore_server</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/libinfo/index.html">mxnet.libinfo</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/log/index.html">mxnet.log</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/model/index.html">mxnet.model</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/monitor/index.html">mxnet.monitor</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/name/index.html">mxnet.name</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/notebook/index.html">mxnet.notebook</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/operator/index.html">mxnet.operator</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/profiler/index.html">mxnet.profiler</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/random/index.html">mxnet.random</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/recordio/index.html">mxnet.recordio</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/registry/index.html">mxnet.registry</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/rtc/index.html">mxnet.rtc</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/runtime/index.html">mxnet.runtime</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/test_utils/index.html">mxnet.test_utils</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/torch/index.html">mxnet.torch</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/util/index.html">mxnet.util</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/mxnet/visualization/index.html">mxnet.visualization</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</nav>
</div>
</header>
<div class="document">
<div class="page-content" role="main">
<!--- Licensed to the Apache Software Foundation (ASF) under one --><!--- or more contributor license agreements. See the NOTICE file --><!--- distributed with this work for additional information --><!--- regarding copyright ownership. The ASF licenses this file --><!--- to you under the Apache License, Version 2.0 (the --><!--- "License"); you may not use this file except in compliance --><!--- with the License. You may obtain a copy of the License at --><!--- http://www.apache.org/licenses/LICENSE-2.0 --><!--- Unless required by applicable law or agreed to in writing, --><!--- software distributed under the License is distributed on an --><!--- "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY --><!--- KIND, either express or implied. See the License for the --><!--- specific language governing permissions and limitations --><!--- under the License. --><div class="section" id="Logistic-regression-explained">
<h1>Logistic regression explained<a class="headerlink" href="#Logistic-regression-explained" title="Permalink to this headline"></a></h1>
<p>Logistic Regression is one of the first models newcomers to Deep Learning are implementing. The focus of this tutorial is to show how to do logistic regression using Gluon API.</p>
<p>Before anything else, let’s import required packages for this tutorial.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">mxnet</span> <span class="k">as</span> <span class="nn">mx</span>
<span class="kn">from</span> <span class="nn">mxnet</span> <span class="kn">import</span> <span class="n">nd</span><span class="p">,</span> <span class="n">autograd</span><span class="p">,</span> <span class="n">gluon</span>
<span class="kn">from</span> <span class="nn">mxnet.gluon</span> <span class="kn">import</span> <span class="n">nn</span><span class="p">,</span> <span class="n">Trainer</span>
<span class="kn">from</span> <span class="nn">mxnet.gluon.data</span> <span class="kn">import</span> <span class="n">DataLoader</span><span class="p">,</span> <span class="n">ArrayDataset</span>
<span class="n">mx</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">12345</span><span class="p">)</span> <span class="c1"># Added for reproducibility</span>
</pre></div>
</div>
<p>In this tutorial we will use fake dataset, which contains 10 features drawn from a normal distribution with mean equals to 0 and standard deviation equals to 1, and a class label, which can be either 0 or 1. The size of the dataset is an arbitrary value. The function below helps us to generate a dataset. Class label <code class="docutils literal notranslate"><span class="pre">y</span></code> is generated via a non-random logic, so the network would have a pattern to look for. Boundary of 3 is selected to make sure that number of positive examples smaller than
negative, but not too small</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">get_random_data</span><span class="p">(</span><span class="n">size</span><span class="p">,</span> <span class="n">ctx</span><span class="p">):</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">nd</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="n">size</span><span class="p">,</span> <span class="mi">10</span><span class="p">),</span> <span class="n">ctx</span><span class="o">=</span><span class="n">ctx</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">3</span>
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span>
</pre></div>
</div>
<p>Also, let’s define a set of hyperparameters, that we are going to use later. Since our model is simple and dataset is small, we are going to use CPU for calculations. Feel free to change it to GPU for a more advanced scenario.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">ctx</span> <span class="o">=</span> <span class="n">mx</span><span class="o">.</span><span class="n">cpu</span><span class="p">()</span>
<span class="n">train_data_size</span> <span class="o">=</span> <span class="mi">1000</span>
<span class="n">val_data_size</span> <span class="o">=</span> <span class="mi">100</span>
<span class="n">batch_size</span> <span class="o">=</span> <span class="mi">10</span>
</pre></div>
</div>
<div class="section" id="Working-with-data">
<h2>Working with data<a class="headerlink" href="#Working-with-data" title="Permalink to this headline"></a></h2>
<p>To work with data, Apache MXNet provides <a class="reference external" href="https://mxnet.apache.org/api/python/gluon/data.html#mxnet.gluon.data.Dataset">Dataset</a> and <a class="reference external" href="https://mxnet.apache.org/api/python/gluon/data.html#mxnet.gluon.data.DataLoader">DataLoader</a> classes. The former is used to provide an indexed access to the data, the latter is used to shuffle and batchify the data. To learn more about working with data in Gluon, please refer to <a class="reference external" href="/api/python/docs/api/gluon/data/index.html">Gluon Datasets and Dataloaders</a>.</p>
<p>Below we define training and validation datasets, which we are going to use in the tutorial.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">train_x</span><span class="p">,</span> <span class="n">train_ground_truth_class</span> <span class="o">=</span> <span class="n">get_random_data</span><span class="p">(</span><span class="n">train_data_size</span><span class="p">,</span> <span class="n">ctx</span><span class="p">)</span>
<span class="n">train_dataset</span> <span class="o">=</span> <span class="n">ArrayDataset</span><span class="p">(</span><span class="n">train_x</span><span class="p">,</span> <span class="n">train_ground_truth_class</span><span class="p">)</span>
<span class="n">train_dataloader</span> <span class="o">=</span> <span class="n">DataLoader</span><span class="p">(</span><span class="n">train_dataset</span><span class="p">,</span> <span class="n">batch_size</span><span class="o">=</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">shuffle</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">val_x</span><span class="p">,</span> <span class="n">val_ground_truth_class</span> <span class="o">=</span> <span class="n">get_random_data</span><span class="p">(</span><span class="n">val_data_size</span><span class="p">,</span> <span class="n">ctx</span><span class="p">)</span>
<span class="n">val_dataset</span> <span class="o">=</span> <span class="n">ArrayDataset</span><span class="p">(</span><span class="n">val_x</span><span class="p">,</span> <span class="n">val_ground_truth_class</span><span class="p">)</span>
<span class="n">val_dataloader</span> <span class="o">=</span> <span class="n">DataLoader</span><span class="p">(</span><span class="n">val_dataset</span><span class="p">,</span> <span class="n">batch_size</span><span class="o">=</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">shuffle</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="section" id="Defining-and-training-the-model">
<h2>Defining and training the model<a class="headerlink" href="#Defining-and-training-the-model" title="Permalink to this headline"></a></h2>
<p>The only requirement for the logistic regression is that the last layer of the network must be a single neuron. Apache MXNet allows us to do so by using <a class="reference external" href="https://mxnet.apache.org/api/python/gluon/nn.html#mxnet.gluon.nn.Dense">Dense</a> layer and specifying the number of units to 1. The rest of the network can be arbitrarily complex.</p>
<p>Below, we define a model which has an input layer of 10 neurons, a couple of inner layers of 10 neurons each, and output layer of 1 neuron. We stack the layers using <a class="reference external" href="https://mxnet.apache.org/api/python/gluon/gluon.html#mxnet.gluon.nn.HybridSequential">HybridSequential</a> block and initialize parameters of the network using <a class="reference external" href="https://mxnet.apache.org/api/python/optimization/optimization.html#mxnet.initializer.Xavier">Xavier</a> initialization.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">net</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">HybridSequential</span><span class="p">()</span>
<span class="k">with</span> <span class="n">net</span><span class="o">.</span><span class="n">name_scope</span><span class="p">():</span>
<span class="n">net</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">Dense</span><span class="p">(</span><span class="n">units</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">activation</span><span class="o">=</span><span class="s1">&#39;relu&#39;</span><span class="p">))</span> <span class="c1"># input layer</span>
<span class="n">net</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">Dense</span><span class="p">(</span><span class="n">units</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">activation</span><span class="o">=</span><span class="s1">&#39;relu&#39;</span><span class="p">))</span> <span class="c1"># inner layer 1</span>
<span class="n">net</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">Dense</span><span class="p">(</span><span class="n">units</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">activation</span><span class="o">=</span><span class="s1">&#39;relu&#39;</span><span class="p">))</span> <span class="c1"># inner layer 2</span>
<span class="n">net</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">Dense</span><span class="p">(</span><span class="n">units</span><span class="o">=</span><span class="mi">1</span><span class="p">))</span> <span class="c1"># output layer: notice, it must have only 1 neuron</span>
<span class="n">net</span><span class="o">.</span><span class="n">initialize</span><span class="p">(</span><span class="n">mx</span><span class="o">.</span><span class="n">init</span><span class="o">.</span><span class="n">Xavier</span><span class="p">())</span>
</pre></div>
</div>
<p>After defining the model, we need to define a few more things: our loss, our trainer and our metric.</p>
<p>Loss function is used to calculate how the output of the network differs from the ground truth. Because classes of the logistic regression are either 0 or 1, we are using <a class="reference external" href="https://mxnet.apache.org/api/python/gluon/loss.html#mxnet.gluon.loss.SigmoidBinaryCrossEntropyLoss">SigmoidBinaryCrossEntropyLoss</a>. Notice that we do not specify <code class="docutils literal notranslate"><span class="pre">from_sigmoid</span></code> attribute in the code, which means that the output of the neuron doesn’t need to go through sigmoid, but at inference we’d have to pass it through
sigmoid. You can learn more about cross entropy on <a class="reference external" href="https://en.wikipedia.org/wiki/Cross_entropy">wikipedia</a>.</p>
<p>Trainer object allows to specify the method of training to be used. For our tutorial we use <a class="reference external" href="https://mxnet.apache.org/api/python/optimization/optimization.html#mxnet.optimizer.SGD">Stochastic Gradient Descent (SGD)</a>. For more information on SGD refer to <a class="reference external" href="https://gluon.mxnet.io/chapter06_optimization/gd-sgd-scratch.html">the following tutorial</a>. We also need to parametrize it with learning rate value, which defines the weight updates, and weight decay, which is used for regularization.</p>
<p>Metric helps us to estimate how good our model is in terms of a problem we are trying to solve. Where loss function has more importance for the training process, a metric is usually the thing we are trying to improve and reach maximum value. We also can use more than one metric, to measure various aspects of our model. In our example, we are using <a class="reference external" href="https://mxnet.apache.org/api/python/metric/metric.html?highlight=metric.acc#mxnet.metric.Accuracy">Accuracy</a> and <a class="reference external" href="http://mxnet.apache.org/api/python/metric/metric.html?highlight=metric.f1#mxnet.metric.F1">F1
score</a> as measurements of success of our model.</p>
<p>Below we define these objects.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">loss</span> <span class="o">=</span> <span class="n">gluon</span><span class="o">.</span><span class="n">loss</span><span class="o">.</span><span class="n">SigmoidBinaryCrossEntropyLoss</span><span class="p">()</span>
<span class="n">trainer</span> <span class="o">=</span> <span class="n">Trainer</span><span class="p">(</span><span class="n">params</span><span class="o">=</span><span class="n">net</span><span class="o">.</span><span class="n">collect_params</span><span class="p">(),</span> <span class="n">optimizer</span><span class="o">=</span><span class="s1">&#39;sgd&#39;</span><span class="p">,</span>
<span class="n">optimizer_params</span><span class="o">=</span><span class="p">{</span><span class="s1">&#39;learning_rate&#39;</span><span class="p">:</span> <span class="mf">0.1</span><span class="p">})</span>
<span class="n">accuracy</span> <span class="o">=</span> <span class="n">mx</span><span class="o">.</span><span class="n">metric</span><span class="o">.</span><span class="n">Accuracy</span><span class="p">()</span>
<span class="n">f1</span> <span class="o">=</span> <span class="n">mx</span><span class="o">.</span><span class="n">metric</span><span class="o">.</span><span class="n">F1</span><span class="p">()</span>
</pre></div>
</div>
<p>The next step is to define the training function in which we iterate over all batches of training data, execute the forward pass on each batch and calculate training loss. On line 19, we sum losses of every batch per epoch into a single variable, because we calculate loss per single batch, but want to display it per epoch.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">train_model</span><span class="p">():</span>
<span class="n">cumulative_train_loss</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">label</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">train_dataloader</span><span class="p">):</span>
<span class="k">with</span> <span class="n">autograd</span><span class="o">.</span><span class="n">record</span><span class="p">():</span>
<span class="c1"># Do forward pass on a batch of training data</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">net</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="c1"># Calculate loss for the training data batch</span>
<span class="n">loss_result</span> <span class="o">=</span> <span class="n">loss</span><span class="p">(</span><span class="n">output</span><span class="p">,</span> <span class="n">label</span><span class="p">)</span>
<span class="c1"># Calculate gradients</span>
<span class="n">loss_result</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
<span class="c1"># Update parameters of the network</span>
<span class="n">trainer</span><span class="o">.</span><span class="n">step</span><span class="p">(</span><span class="n">batch_size</span><span class="p">)</span>
<span class="c1"># sum losses of every batch</span>
<span class="n">cumulative_train_loss</span> <span class="o">+=</span> <span class="n">nd</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">loss_result</span><span class="p">)</span><span class="o">.</span><span class="n">asscalar</span><span class="p">()</span>
<span class="k">return</span> <span class="n">cumulative_train_loss</span>
</pre></div>
</div>
</div>
<div class="section" id="Validating-the-model">
<h2>Validating the model<a class="headerlink" href="#Validating-the-model" title="Permalink to this headline"></a></h2>
<p>Our validation function is very similar to the training one. The main difference is that we want to calculate accuracy of the model. We use <a class="reference external" href="https://mxnet.apache.org/api/python/metric/metric.html?highlight=metric.acc#mxnet.metric.Accuracy">Accuracy metric</a> to do so.</p>
<p><code class="docutils literal notranslate"><span class="pre">Accuracy</span></code> metric requires 2 arguments: 1) a vector of ground-truth classes and 2) A vector or matrix of predictions. When predictions are of the same shape as the vector of ground-truth classes, <code class="docutils literal notranslate"><span class="pre">Accuracy</span></code> class assumes that prediction vector contains predicted classes. So, it converts the vector to <code class="docutils literal notranslate"><span class="pre">Int32</span></code> and compare each item of ground-truth classes to prediction vector.</p>
<p>Because of the behaviour above, you will get an unexpected result if you just apply <a class="reference external" href="https://mxnet.apache.org/api/python/ndarray/ndarray.html#mxnet.ndarray.sigmoid">Sigmoid</a> function to the network result and pass it to <code class="docutils literal notranslate"><span class="pre">Accuracy</span></code> metric. As mentioned before, we need to apply <code class="docutils literal notranslate"><span class="pre">Sigmoid</span></code> function to the output of the neuron to get a probability of belonging to the class 1. But <code class="docutils literal notranslate"><span class="pre">Sigmoid</span></code> function produces output in range [0; 1], and all numbers in that range are going to be casted to 0,
even if it is as high as 0.99. To avoid this we write a custom bit of code on line 12, that:</p>
<ol class="arabic simple">
<li><p>Calculates sigmoid using <code class="docutils literal notranslate"><span class="pre">Sigmoid</span></code> function</p></li>
<li><p>Subtracts a threshold from the original sigmoid output. Usually, the threshold is equal to 0.5, but it can be higher, if you want to increase certainty of an item to belong to class 1.</p></li>
<li><p>Uses <a class="reference external" href="https://mxnet.apache.org/api/python/ndarray/ndarray.html#mxnet.ndarray.ceil">mx.nd.ceil</a> function, which converts all negative values to 0 and all positive values to 1</p></li>
</ol>
<p>After these transformations we can pass the result to <code class="docutils literal notranslate"><span class="pre">Accuracy.update()</span></code> method and expect it to behave in a proper way.</p>
<p>For <code class="docutils literal notranslate"><span class="pre">F1</span></code> metric to work, instead of one number per class, we must pass probabilities of belonging to both classes. Because of that, on lines 21-22 we:</p>
<ol class="arabic simple">
<li><p>Reshape predictions to a single vector</p></li>
<li><p>We stack together two vectors: probabilities of belonging to class 0 (1 - <code class="docutils literal notranslate"><span class="pre">prediction</span></code>) and probabilities of belonging to class 1.</p></li>
</ol>
<p>Then we pass this stacked matrix to <code class="docutils literal notranslate"><span class="pre">F1</span></code> score.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">validate_model</span><span class="p">(</span><span class="n">threshold</span><span class="p">):</span>
<span class="n">cumulative_val_loss</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="p">(</span><span class="n">val_data</span><span class="p">,</span> <span class="n">val_ground_truth_class</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">val_dataloader</span><span class="p">):</span>
<span class="c1"># Do forward pass on a batch of validation data</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">net</span><span class="p">(</span><span class="n">val_data</span><span class="p">)</span>
<span class="c1"># Similar to cumulative training loss, calculate cumulative validation loss</span>
<span class="n">cumulative_val_loss</span> <span class="o">+=</span> <span class="n">nd</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">loss</span><span class="p">(</span><span class="n">output</span><span class="p">,</span> <span class="n">val_ground_truth_class</span><span class="p">))</span><span class="o">.</span><span class="n">asscalar</span><span class="p">()</span>
<span class="c1"># getting prediction as a sigmoid</span>
<span class="n">prediction</span> <span class="o">=</span> <span class="n">net</span><span class="p">(</span><span class="n">val_data</span><span class="p">)</span><span class="o">.</span><span class="n">sigmoid</span><span class="p">()</span>
<span class="c1"># Converting neuron outputs to classes</span>
<span class="n">predicted_classes</span> <span class="o">=</span> <span class="n">mx</span><span class="o">.</span><span class="n">nd</span><span class="o">.</span><span class="n">ceil</span><span class="p">(</span><span class="n">prediction</span> <span class="o">-</span> <span class="n">threshold</span><span class="p">)</span>
<span class="c1"># Update validation accuracy</span>
<span class="n">accuracy</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">val_ground_truth_class</span><span class="p">,</span> <span class="n">predicted_classes</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span>
<span class="c1"># calculate probabilities of belonging to different classes. F1 metric works only with this notation</span>
<span class="n">prediction</span> <span class="o">=</span> <span class="n">prediction</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="n">probabilities</span> <span class="o">=</span> <span class="n">mx</span><span class="o">.</span><span class="n">nd</span><span class="o">.</span><span class="n">stack</span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">prediction</span><span class="p">,</span> <span class="n">prediction</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">f1</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">val_ground_truth_class</span><span class="p">,</span> <span class="n">probabilities</span><span class="p">)</span>
<span class="k">return</span> <span class="n">cumulative_val_loss</span>
</pre></div>
</div>
</div>
<div class="section" id="Putting-it-all-together">
<h2>Putting it all together<a class="headerlink" href="#Putting-it-all-together" title="Permalink to this headline"></a></h2>
<p>By using the defined above functions, we can finally write our main training loop.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">epochs</span> <span class="o">=</span> <span class="mi">10</span>
<span class="n">threshold</span> <span class="o">=</span> <span class="mf">0.5</span>
<span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">epochs</span><span class="p">):</span>
<span class="n">avg_train_loss</span> <span class="o">=</span> <span class="n">train_model</span><span class="p">()</span> <span class="o">/</span> <span class="n">train_data_size</span>
<span class="n">avg_val_loss</span> <span class="o">=</span> <span class="n">validate_model</span><span class="p">(</span><span class="n">threshold</span><span class="p">)</span> <span class="o">/</span> <span class="n">val_data_size</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Epoch: </span><span class="si">%s</span><span class="s2">, Training loss: </span><span class="si">%.2f</span><span class="s2">, Validation loss: </span><span class="si">%.2f</span><span class="s2">, Validation accuracy: </span><span class="si">%.2f</span><span class="s2">, F1 score: </span><span class="si">%.2f</span><span class="s2">&quot;</span> <span class="o">%</span>
<span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">avg_train_loss</span><span class="p">,</span> <span class="n">avg_val_loss</span><span class="p">,</span> <span class="n">accuracy</span><span class="o">.</span><span class="n">get</span><span class="p">()[</span><span class="mi">1</span><span class="p">],</span> <span class="n">f1</span><span class="o">.</span><span class="n">get</span><span class="p">()[</span><span class="mi">1</span><span class="p">]))</span>
<span class="c1"># we reset accuracy, so the new epoch&#39;s accuracy would be calculated from the blank state</span>
<span class="n">accuracy</span><span class="o">.</span><span class="n">reset</span><span class="p">()</span>
</pre></div>
</div>
<p>Output:</p>
<div class="highlight-bash notranslate"><div class="highlight"><pre><span></span>Epoch:<span class="w"> </span><span class="m">0</span>,<span class="w"> </span>Training<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.43,<span class="w"> </span>Validation<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.36,<span class="w"> </span>Validation<span class="w"> </span>accuracy:<span class="w"> </span><span class="m">0</span>.85,<span class="w"> </span>F1<span class="w"> </span>score:<span class="w"> </span><span class="m">0</span>.00<span class="w"> </span>&lt;!--notebook-skip-line--&gt;
Epoch:<span class="w"> </span><span class="m">1</span>,<span class="w"> </span>Training<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.22,<span class="w"> </span>Validation<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.14,<span class="w"> </span>Validation<span class="w"> </span>accuracy:<span class="w"> </span><span class="m">0</span>.96,<span class="w"> </span>F1<span class="w"> </span>score:<span class="w"> </span><span class="m">0</span>.35<span class="w"> </span>&lt;!--notebook-skip-line--&gt;
Epoch:<span class="w"> </span><span class="m">2</span>,<span class="w"> </span>Training<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.09,<span class="w"> </span>Validation<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.11,<span class="w"> </span>Validation<span class="w"> </span>accuracy:<span class="w"> </span><span class="m">0</span>.97,<span class="w"> </span>F1<span class="w"> </span>score:<span class="w"> </span><span class="m">0</span>.48<span class="w"> </span>&lt;!--notebook-skip-line--&gt;
Epoch:<span class="w"> </span><span class="m">3</span>,<span class="w"> </span>Training<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.07,<span class="w"> </span>Validation<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.09,<span class="w"> </span>Validation<span class="w"> </span>accuracy:<span class="w"> </span><span class="m">0</span>.96,<span class="w"> </span>F1<span class="w"> </span>score:<span class="w"> </span><span class="m">0</span>.53<span class="w"> </span>&lt;!--notebook-skip-line--&gt;
Epoch:<span class="w"> </span><span class="m">4</span>,<span class="w"> </span>Training<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.06,<span class="w"> </span>Validation<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.09,<span class="w"> </span>Validation<span class="w"> </span>accuracy:<span class="w"> </span><span class="m">0</span>.97,<span class="w"> </span>F1<span class="w"> </span>score:<span class="w"> </span><span class="m">0</span>.58<span class="w"> </span>&lt;!--notebook-skip-line--&gt;
Epoch:<span class="w"> </span><span class="m">5</span>,<span class="w"> </span>Training<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.04,<span class="w"> </span>Validation<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.12,<span class="w"> </span>Validation<span class="w"> </span>accuracy:<span class="w"> </span><span class="m">0</span>.97,<span class="w"> </span>F1<span class="w"> </span>score:<span class="w"> </span><span class="m">0</span>.59<span class="w"> </span>&lt;!--notebook-skip-line--&gt;
Epoch:<span class="w"> </span><span class="m">6</span>,<span class="w"> </span>Training<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.05,<span class="w"> </span>Validation<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.09,<span class="w"> </span>Validation<span class="w"> </span>accuracy:<span class="w"> </span><span class="m">0</span>.99,<span class="w"> </span>F1<span class="w"> </span>score:<span class="w"> </span><span class="m">0</span>.62<span class="w"> </span>&lt;!--notebook-skip-line--&gt;
Epoch:<span class="w"> </span><span class="m">7</span>,<span class="w"> </span>Training<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.05,<span class="w"> </span>Validation<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.10,<span class="w"> </span>Validation<span class="w"> </span>accuracy:<span class="w"> </span><span class="m">0</span>.97,<span class="w"> </span>F1<span class="w"> </span>score:<span class="w"> </span><span class="m">0</span>.62<span class="w"> </span>&lt;!--notebook-skip-line--&gt;
Epoch:<span class="w"> </span><span class="m">8</span>,<span class="w"> </span>Training<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.05,<span class="w"> </span>Validation<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.12,<span class="w"> </span>Validation<span class="w"> </span>accuracy:<span class="w"> </span><span class="m">0</span>.95,<span class="w"> </span>F1<span class="w"> </span>score:<span class="w"> </span><span class="m">0</span>.63<span class="w"> </span>&lt;!--notebook-skip-line--&gt;
Epoch:<span class="w"> </span><span class="m">9</span>,<span class="w"> </span>Training<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.04,<span class="w"> </span>Validation<span class="w"> </span>loss:<span class="w"> </span><span class="m">0</span>.09,<span class="w"> </span>Validation<span class="w"> </span>accuracy:<span class="w"> </span><span class="m">0</span>.98,<span class="w"> </span>F1<span class="w"> </span>score:<span class="w"> </span><span class="m">0</span>.65<span class="w"> </span>&lt;!--notebook-skip-line--&gt;
</pre></div>
</div>
<p>In our case we hit the accuracy of 0.98 and F1 score of 0.65.</p>
</div>
<div class="section" id="Tip-1:-Use-only-one-neuron-in-the-output-layer">
<h2>Tip 1: Use only one neuron in the output layer<a class="headerlink" href="#Tip-1:-Use-only-one-neuron-in-the-output-layer" title="Permalink to this headline"></a></h2>
<p>Despite that there are 2 classes, there should be only one output neuron, because <code class="docutils literal notranslate"><span class="pre">SigmoidBinaryCrossEntropyLoss</span></code> accepts only one feature as an input.</p>
</div>
<div class="section" id="Tip-2:-Encode-classes-as-0-and-1">
<h2>Tip 2: Encode classes as 0 and 1<a class="headerlink" href="#Tip-2:-Encode-classes-as-0-and-1" title="Permalink to this headline"></a></h2>
<p>For <code class="docutils literal notranslate"><span class="pre">SigmoidBinaryCrossEntropyLoss</span></code> to work it is required that classes were encoded as 0 and 1. In some datasets the class encoding might be different, like -1 and 1 or 1 and 2. If this is how your dataset looks like, then you need to re-encode the data before using <code class="docutils literal notranslate"><span class="pre">SigmoidBinaryCrossEntropyLoss</span></code>.</p>
</div>
<div class="section" id="Tip-3:-Use-SigmoidBinaryCrossEntropyLoss-instead-of-LogisticRegressionOutput">
<h2>Tip 3: Use SigmoidBinaryCrossEntropyLoss instead of LogisticRegressionOutput<a class="headerlink" href="#Tip-3:-Use-SigmoidBinaryCrossEntropyLoss-instead-of-LogisticRegressionOutput" title="Permalink to this headline"></a></h2>
<p>NDArray API has two options to calculate logistic regression loss: <a class="reference external" href="https://mxnet.apache.org/api/python/gluon/loss.html#mxnet.gluon.loss.SigmoidBinaryCrossEntropyLoss">SigmoidBinaryCrossEntropyLoss</a> and <a class="reference external" href="https://mxnet.apache.org/api/python/ndarray/ndarray.html#mxnet.ndarray.LogisticRegressionOutput">LogisticRegressionOutput</a>. <code class="docutils literal notranslate"><span class="pre">LogisticRegressionOutput</span></code> is designed to be an output layer when using the Module API, and is not supposed to be used when using Gluon API.</p>
</div>
<div class="section" id="Conclusion">
<h2>Conclusion<a class="headerlink" href="#Conclusion" title="Permalink to this headline"></a></h2>
<p>In this tutorial I explained some potential pitfalls to be aware of. When doing logistic regression using Gluon API remember to: 1. Use only one neuron in the output layer 1. Encode class labels as 0 or 1 1. Use <code class="docutils literal notranslate"><span class="pre">SigmoidBinaryCrossEntropyLoss</span></code> 1. Convert probabilities to classes before calculating Accuracy</p>
</div>
</div>
<hr class="feedback-hr-top" />
<div class="feedback-container">
<div class="feedback-question">Did this page help you?</div>
<div class="feedback-answer-container">
<div class="feedback-answer yes-link" data-response="yes">Yes</div>
<div class="feedback-answer no-link" data-response="no">No</div>
</div>
<div class="feedback-thank-you">Thanks for your feedback!</div>
</div>
<hr class="feedback-hr-bottom" />
</div>
<div class="side-doc-outline">
<div class="side-doc-outline--content">
<div class="localtoc">
<p class="caption">
<span class="caption-text">Table Of Contents</span>
</p>
<ul>
<li><a class="reference internal" href="#">Logistic regression explained</a><ul>
<li><a class="reference internal" href="#Working-with-data">Working with data</a></li>
<li><a class="reference internal" href="#Defining-and-training-the-model">Defining and training the model</a></li>
<li><a class="reference internal" href="#Validating-the-model">Validating the model</a></li>
<li><a class="reference internal" href="#Putting-it-all-together">Putting it all together</a></li>
<li><a class="reference internal" href="#Tip-1:-Use-only-one-neuron-in-the-output-layer">Tip 1: Use only one neuron in the output layer</a></li>
<li><a class="reference internal" href="#Tip-2:-Encode-classes-as-0-and-1">Tip 2: Encode classes as 0 and 1</a></li>
<li><a class="reference internal" href="#Tip-3:-Use-SigmoidBinaryCrossEntropyLoss-instead-of-LogisticRegressionOutput">Tip 3: Use SigmoidBinaryCrossEntropyLoss instead of LogisticRegressionOutput</a></li>
<li><a class="reference internal" href="#Conclusion">Conclusion</a></li>
</ul>
</li>
</ul>
</div>
</div>
</div>
<div class="clearer"></div>
</div><div class="pagenation">
<a id="button-prev" href="gluon_from_experiment_to_deployment.html" class="mdl-button mdl-js-button mdl-js-ripple-effect mdl-button--colored" role="botton" accesskey="P">
<i class="pagenation-arrow-L fas fa-arrow-left fa-lg"></i>
<div class="pagenation-text">
<span class="pagenation-direction">Previous</span>
<div>Gluon: from experiment to deployment</div>
</div>
</a>
<a id="button-next" href="../packages/index.html" class="mdl-button mdl-js-button mdl-js-ripple-effect mdl-button--colored" role="botton" accesskey="N">
<i class="pagenation-arrow-R fas fa-arrow-right fa-lg"></i>
<div class="pagenation-text">
<span class="pagenation-direction">Next</span>
<div>Packages</div>
</div>
</a>
</div>
<footer class="site-footer h-card">
<div class="wrapper">
<div class="row">
<div class="col-4">
<h4 class="footer-category-title">Resources</h4>
<ul class="contact-list">
<li><a class="u-email" href="mailto:dev@mxnet.apache.org">Dev list</a></li>
<li><a class="u-email" href="mailto:user@mxnet.apache.org">User mailing list</a></li>
<li><a href="https://cwiki.apache.org/confluence/display/MXNET/Apache+MXNet+Home">Developer Wiki</a></li>
<li><a href="https://issues.apache.org/jira/projects/MXNET/issues">Jira Tracker</a></li>
<li><a href="https://github.com/apache/mxnet/labels/Roadmap">Github Roadmap</a></li>
<li><a href="https://medium.com/apache-mxnet">Blog</a></li>
<li><a href="https://discuss.mxnet.io">Forum</a></li>
<li><a href="/community/contribute">Contribute</a></li>
</ul>
</div>
<div class="col-4"><ul class="social-media-list"><li><a href="https://github.com/apache/mxnet"><svg class="svg-icon"><use xlink:href="../../_static/minima-social-icons.svg#github"></use></svg> <span class="username">apache/mxnet</span></a></li><li><a href="https://www.twitter.com/apachemxnet"><svg class="svg-icon"><use xlink:href="../../_static/minima-social-icons.svg#twitter"></use></svg> <span class="username">apachemxnet</span></a></li><li><a href="https://youtube.com/apachemxnet"><svg class="svg-icon"><use xlink:href="../../_static/minima-social-icons.svg#youtube"></use></svg> <span class="username">apachemxnet</span></a></li></ul>
</div>
<div class="col-4 footer-text">
<p>A flexible and efficient library for deep learning.</p>
</div>
</div>
</div>
</footer>
<footer class="site-footer2">
<div class="wrapper">
<div class="row">
<div class="col-3">
<img src="../../_static/apache_incubator_logo.png" class="footer-logo col-2">
</div>
<div class="footer-bottom-warning col-9">
<p>Apache MXNet is an effort undergoing incubation at <a href="http://www.apache.org/">The Apache Software Foundation</a> (ASF), <span style="font-weight:bold">sponsored by the <i>Apache Incubator</i></span>. Incubation is required
of all newly accepted projects until a further review indicates that the infrastructure,
communications, and decision making process have stabilized in a manner consistent with other
successful ASF projects. While incubation status is not necessarily a reflection of the completeness
or stability of the code, it does indicate that the project has yet to be fully endorsed by the ASF.
</p><p>"Copyright © 2017-2018, The Apache Software Foundation Apache MXNet, MXNet, Apache, the Apache
feather, and the Apache MXNet project logo are either registered trademarks or trademarks of the
Apache Software Foundation."</p>
</div>
</div>
</div>
</footer>
</body>
</html>