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<li class="toctree-l1"><a class="reference internal" href="../../../tutorials/index.html">Python Tutorials</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../../../tutorials/getting-started/index.html">Getting Started</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/index.html">Crash Course</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/0-introduction.html">Introduction</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/1-nparray.html">Step 1: Manipulate data with NP on MXNet</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/2-create-nn.html">Step 2: Create a neural network</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/3-autograd.html">Step 3: Automatic differentiation with autograd</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/4-components.html">Step 4: Necessary components that are not in the network</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/5-datasets.html">Step 5: <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-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/5-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-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/5-datasets.html#Using-your-own-data-with-custom-Datasets">Using your own data with custom <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/5-datasets.html#New-in-MXNet-2.0:-faster-C++-backend-dataloaders">New in MXNet 2.0: faster C++ backend dataloaders</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/6-train-nn.html">Step 6: Train a Neural Network</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/7-use-gpus.html">Step 7: Load and Run a NN using GPU</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/getting-started/to-mxnet/index.html">Moving to MXNet from Other Frameworks</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/to-mxnet/pytorch.html">PyTorch vs Apache MXNet</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/getting-started/logistic_regression_explained.html">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>
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<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/blocks/custom-layer.html">Custom Layers</a></li>
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<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/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="../../../tutorials/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="../../../tutorials/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="../../../tutorials/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>
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<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/image/mnist.html">Handwritten Digit Recognition</a></li>
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<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/loss/kl_divergence.html">Kullback-Leibler (KL) Divergence</a></li>
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<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/training/fit_api_tutorial.html">MXNet Gluon Fit API</a></li>
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<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/training/learning_rates/index.html">Learning Rates</a><ul>
<li class="toctree-l6"><a class="reference internal" href="../../../tutorials/packages/gluon/training/learning_rates/learning_rate_finder.html">Learning Rate Finder</a></li>
<li class="toctree-l6"><a class="reference internal" href="../../../tutorials/packages/gluon/training/learning_rates/learning_rate_schedules.html">Learning Rate Schedules</a></li>
<li class="toctree-l6"><a class="reference internal" href="../../../tutorials/packages/gluon/training/learning_rates/learning_rate_schedules_advanced.html">Advanced Learning Rate Schedules</a></li>
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<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/training/normalization/index.html">Normalization Blocks</a></li>
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<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/legacy/ndarray/01-ndarray-intro.html">An Intro: Manipulate Data the MXNet Way with NDArray</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/legacy/ndarray/02-ndarray-operations.html">NDArray Operations</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/legacy/ndarray/03-ndarray-contexts.html">NDArray Contexts</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/legacy/ndarray/gotchas_numpy_in_mxnet.html">Gotchas using NumPy in Apache MXNet</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/legacy/ndarray/sparse/index.html">Tutorials</a><ul>
<li class="toctree-l6"><a class="reference internal" href="../../../tutorials/packages/legacy/ndarray/sparse/csr.html">CSRNDArray - NDArray in Compressed Sparse Row Storage Format</a></li>
<li class="toctree-l6"><a class="reference internal" href="../../../tutorials/packages/legacy/ndarray/sparse/row_sparse.html">RowSparseNDArray - NDArray for Sparse Gradient Updates</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/packages/np/index.html">What is NP on MXNet</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/packages/np/cheat-sheet.html">The NP on MXNet cheat sheet</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/packages/np/np-vs-numpy.html">Differences between NP on MXNet and NumPy</a></li>
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<span class="mdl-layout-title toc">Table Of Contents</span>
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<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="../../../tutorials/index.html">Python Tutorials</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../../../tutorials/getting-started/index.html">Getting Started</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/index.html">Crash Course</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/0-introduction.html">Introduction</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/1-nparray.html">Step 1: Manipulate data with NP on MXNet</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/2-create-nn.html">Step 2: Create a neural network</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/3-autograd.html">Step 3: Automatic differentiation with autograd</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/4-components.html">Step 4: Necessary components that are not in the network</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/5-datasets.html">Step 5: <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-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/5-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-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/5-datasets.html#Using-your-own-data-with-custom-Datasets">Using your own data with custom <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/5-datasets.html#New-in-MXNet-2.0:-faster-C++-backend-dataloaders">New in MXNet 2.0: faster C++ backend dataloaders</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/6-train-nn.html">Step 6: Train a Neural Network</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/crash-course/7-use-gpus.html">Step 7: Load and Run a NN using GPU</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/getting-started/to-mxnet/index.html">Moving to MXNet from Other Frameworks</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/getting-started/to-mxnet/pytorch.html">PyTorch vs Apache MXNet</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/getting-started/gluon_from_experiment_to_deployment.html">Gluon: from experiment to deployment</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/getting-started/gluon_migration_guide.html">Gluon2.0: Migration Guide</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/getting-started/logistic_regression_explained.html">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="../../../tutorials/packages/index.html">Packages</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/packages/autograd/index.html">Automatic Differentiation</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/packages/gluon/index.html">Gluon</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/packages/gluon/blocks/index.html">Blocks</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/blocks/custom-layer.html">Custom Layers</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/blocks/hybridize.html">Hybridize</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/blocks/init.html">Initialization</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/blocks/naming.html">Parameter and Block Naming</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/blocks/nn.html">Layers and Blocks</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/blocks/parameters.html">Parameter Management</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/blocks/save_load_params.html">Saving and Loading Gluon Models</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/blocks/activations/activations.html">Activation Blocks</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/packages/gluon/data/index.html">Data Tutorials</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/data/data_augmentation.html">Image Augmentation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/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="../../../tutorials/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="../../../tutorials/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="../../../tutorials/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="../../../tutorials/packages/gluon/image/index.html">Image Tutorials</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/image/info_gan.html">Image similarity search with InfoGAN</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/image/mnist.html">Handwritten Digit Recognition</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/packages/gluon/loss/index.html">Losses</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/loss/custom-loss.html">Custom Loss Blocks</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/loss/kl_divergence.html">Kullback-Leibler (KL) Divergence</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/loss/loss.html">Loss functions</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/packages/gluon/text/index.html">Text Tutorials</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/text/gnmt.html">Google Neural Machine Translation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/text/transformer.html">Machine Translation with Transformer</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/packages/gluon/training/index.html">Training</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/training/fit_api_tutorial.html">MXNet Gluon Fit API</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/training/trainer.html">Trainer</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/gluon/training/learning_rates/index.html">Learning Rates</a><ul>
<li class="toctree-l6"><a class="reference internal" href="../../../tutorials/packages/gluon/training/learning_rates/learning_rate_finder.html">Learning Rate Finder</a></li>
<li class="toctree-l6"><a class="reference internal" href="../../../tutorials/packages/gluon/training/learning_rates/learning_rate_schedules.html">Learning Rate Schedules</a></li>
<li class="toctree-l6"><a class="reference internal" href="../../../tutorials/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="../../../tutorials/packages/gluon/training/normalization/index.html">Normalization Blocks</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/packages/kvstore/index.html">KVStore</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/packages/kvstore/kvstore.html">Distributed Key-Value Store</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/packages/legacy/index.html">Legacy</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/packages/legacy/ndarray/index.html">NDArray</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/legacy/ndarray/01-ndarray-intro.html">An Intro: Manipulate Data the MXNet Way with NDArray</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/legacy/ndarray/02-ndarray-operations.html">NDArray Operations</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/legacy/ndarray/03-ndarray-contexts.html">NDArray Contexts</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/legacy/ndarray/gotchas_numpy_in_mxnet.html">Gotchas using NumPy in Apache MXNet</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/packages/legacy/ndarray/sparse/index.html">Tutorials</a><ul>
<li class="toctree-l6"><a class="reference internal" href="../../../tutorials/packages/legacy/ndarray/sparse/csr.html">CSRNDArray - NDArray in Compressed Sparse Row Storage Format</a></li>
<li class="toctree-l6"><a class="reference internal" href="../../../tutorials/packages/legacy/ndarray/sparse/row_sparse.html">RowSparseNDArray - NDArray for Sparse Gradient Updates</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/packages/np/index.html">What is NP on MXNet</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/packages/np/cheat-sheet.html">The NP on MXNet cheat sheet</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/packages/np/np-vs-numpy.html">Differences between NP on MXNet and NumPy</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/packages/onnx/index.html">ONNX</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/packages/onnx/fine_tuning_gluon.html">Fine-tuning an ONNX model</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/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 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="../../../tutorials/packages/optimizer/index.html">Optimizers</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/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>
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<li class="toctree-l2"><a class="reference internal" href="../../../tutorials/performance/index.html">Performance</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/performance/compression/index.html">Compression</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/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>
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<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/performance/backend/index.html">Accelerated Backend Tools</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/performance/backend/dnnl/index.html">oneDNN</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/performance/backend/dnnl/dnnl_readme.html">Install MXNet with oneDNN</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/performance/backend/dnnl/dnnl_quantization.html">oneDNN Quantization</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../tutorials/performance/backend/dnnl/dnnl_quantization_inc.html">Improving accuracy with Intel® Neural Compressor</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/performance/backend/tvm.html">Use TVM</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/performance/backend/profiler.html">Profiling MXNet Models</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/performance/backend/amp.html">Using AMP: Automatic Mixed Precision</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../../../tutorials/deploy/index.html">Deployment</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/deploy/export/index.html">Export</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/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>
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<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/deploy/inference/index.html">Inference</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/deploy/inference/cpp.html">Deploy into C++</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/deploy/inference/image_classification_jetson.html">Image Classication using pretrained ResNet-50 model on Jetson module</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/deploy/run-on-aws/index.html">Run on AWS</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/deploy/run-on-aws/use_ec2.html">Run on an EC2 Instance</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/deploy/run-on-aws/use_sagemaker.html">Run on Amazon SageMaker</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../tutorials/deploy/run-on-aws/cloud.html">MXNet on the Cloud</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../../tutorials/extend/index.html">Extend</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../../tutorials/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>
<li class="toctree-l3"><a class="reference external" href="https://mxnet.apache.org/api/faq/using_rtc">Using RTC for CUDA kernels</a></li>
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<li class="toctree-l4"><a class="reference internal" href="../arrays.indexing.html">Indexing</a></li>
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<div class="section" id="mxnet-np-histogram-bin-edges">
<h1>mxnet.np.histogram_bin_edges<a class="headerlink" href="#mxnet-np-histogram-bin-edges" title="Permalink to this headline"></a></h1>
<dl class="function">
<dt id="mxnet.np.histogram_bin_edges">
<code class="sig-name descname">histogram_bin_edges</code><span class="sig-paren">(</span><em class="sig-param">a</em>, <em class="sig-param">bins=10</em>, <em class="sig-param">range=None</em>, <em class="sig-param">weights=None</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.np.histogram_bin_edges" title="Permalink to this definition"></a></dt>
<dd><p>Function to calculate only the edges of the bins used by the <cite>histogram</cite>
function.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>a</strong> (<em>array_like</em>) – Input data. The histogram is computed over the flattened array.</p></li>
<li><p><strong>bins</strong> (<em>int</em><em> or </em><em>sequence of scalars</em><em> or </em><em>str</em><em>, </em><em>optional</em>) – <p>If <cite>bins</cite> is an int, it defines the number of equal-width
bins in the given range (10, by default). If <cite>bins</cite> is a
sequence, it defines the bin edges, including the rightmost
edge, allowing for non-uniform bin widths.</p>
<p>If <cite>bins</cite> is a string from the list below, <cite>histogram_bin_edges</cite> will use
the method chosen to calculate the optimal bin width and
consequently the number of bins (see <cite>Notes</cite> for more detail on
the estimators) from the data that falls within the requested
range. While the bin width will be optimal for the actual data
in the range, the number of bins will be computed to fill the
entire range, including the empty portions. For visualisation,
using the ‘auto’ option is suggested. Weighted data is not
supported for automated bin size selection.</p>
<dl class="simple">
<dt>’auto’</dt><dd><p>Maximum of the ‘sturges’ and ‘fd’ estimators. Provides good
all around performance.</p>
</dd>
<dt>’fd’ (Freedman Diaconis Estimator)</dt><dd><p>Robust (resilient to outliers) estimator that takes into
account data variability and data size.</p>
</dd>
<dt>’doane’</dt><dd><p>An improved version of Sturges’ estimator that works better
with non-normal datasets.</p>
</dd>
<dt>’scott’</dt><dd><p>Less robust estimator that that takes into account data
variability and data size.</p>
</dd>
<dt>’stone’</dt><dd><p>Estimator based on leave-one-out cross-validation estimate of
the integrated squared error. Can be regarded as a generalization
of Scott’s rule.</p>
</dd>
<dt>’rice’</dt><dd><p>Estimator does not take variability into account, only data
size. Commonly overestimates number of bins required.</p>
</dd>
<dt>’sturges’</dt><dd><p>R’s default method, only accounts for data size. Only
optimal for gaussian data and underestimates number of bins
for large non-gaussian datasets.</p>
</dd>
<dt>’sqrt’</dt><dd><p>Square root (of data size) estimator, used by Excel and
other programs for its speed and simplicity.</p>
</dd>
</dl>
</p></li>
<li><p><strong>range</strong> (<em>(</em><em>float</em><em>, </em><em>float</em><em>)</em><em>, </em><em>optional</em>) – The lower and upper range of the bins. If not provided, range
is simply <code class="docutils literal notranslate"><span class="pre">(a.min(),</span> <span class="pre">a.max())</span></code>. Values outside the range are
ignored. The first element of the range must be less than or
equal to the second. <cite>range</cite> affects the automatic bin
computation as well. While bin width is computed to be optimal
based on the actual data within <cite>range</cite>, the bin count will fill
the entire range including portions containing no data.</p></li>
<li><p><strong>weights</strong> (<em>array_like</em><em>, </em><em>optional</em>) – An array of weights, of the same shape as <cite>a</cite>. Each value in
<cite>a</cite> only contributes its associated weight towards the bin count
(instead of 1). This is currently not used by any of the bin estimators,
but may be in the future.</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p><strong>bin_edges</strong> – The edges to pass into <cite>histogram</cite></p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>array of dtype float</p>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="mxnet.np.histogram.html#mxnet.np.histogram" title="mxnet.np.histogram"><code class="xref py py-func docutils literal notranslate"><span class="pre">histogram()</span></code></a></p>
</div>
<p class="rubric">Notes</p>
<p>The methods to estimate the optimal number of bins are well founded
in literature, and are inspired by the choices R provides for
histogram visualisation. Note that having the number of bins
proportional to <span class="math notranslate nohighlight">\(n^{1/3}\)</span> is asymptotically optimal, which is
why it appears in most estimators. These are simply plug-in methods
that give good starting points for number of bins. In the equations
below, <span class="math notranslate nohighlight">\(h\)</span> is the binwidth and <span class="math notranslate nohighlight">\(n_h\)</span> is the number of
bins. All estimators that compute bin counts are recast to bin width
using the <cite>ptp</cite> of the data. The final bin count is obtained from
<code class="docutils literal notranslate"><span class="pre">np.round(np.ceil(range</span> <span class="pre">/</span> <span class="pre">h))</span></code>.</p>
<dl>
<dt>‘auto’ (maximum of the ‘sturges’ and ‘fd’ estimators)</dt><dd><p>A compromise to get a good value. For small datasets the Sturges
value will usually be chosen, while larger datasets will usually
default to FD. Avoids the overly conservative behaviour of FD
and Sturges for small and large datasets respectively.
Switchover point is usually <span class="math notranslate nohighlight">\(a.size \approx 1000\)</span>.</p>
</dd>
<dt>‘fd’ (Freedman Diaconis Estimator)</dt><dd><div class="math notranslate nohighlight">
\[h = 2 \frac{IQR}{n^{1/3}}\]</div>
<p>The binwidth is proportional to the interquartile range (IQR)
and inversely proportional to cube root of a.size. Can be too
conservative for small datasets, but is quite good for large
datasets. The IQR is very robust to outliers.</p>
</dd>
<dt>‘scott’</dt><dd><div class="math notranslate nohighlight">
\[h = \sigma \sqrt[3]{\frac{24 * \sqrt{\pi}}{n}}\]</div>
<p>The binwidth is proportional to the standard deviation of the
data and inversely proportional to cube root of <code class="docutils literal notranslate"><span class="pre">x.size</span></code>. Can
be too conservative for small datasets, but is quite good for
large datasets. The standard deviation is not very robust to
outliers. Values are very similar to the Freedman-Diaconis
estimator in the absence of outliers.</p>
</dd>
<dt>‘rice’</dt><dd><div class="math notranslate nohighlight">
\[n_h = 2n^{1/3}\]</div>
<p>The number of bins is only proportional to cube root of
<code class="docutils literal notranslate"><span class="pre">a.size</span></code>. It tends to overestimate the number of bins and it
does not take into account data variability.</p>
</dd>
<dt>‘sturges’</dt><dd><div class="math notranslate nohighlight">
\[n_h = \log _{2}n+1\]</div>
<p>The number of bins is the base 2 log of <code class="docutils literal notranslate"><span class="pre">a.size</span></code>. This
estimator assumes normality of data and is too conservative for
larger, non-normal datasets. This is the default method in R’s
<code class="docutils literal notranslate"><span class="pre">hist</span></code> method.</p>
</dd>
<dt>‘doane’</dt><dd><div class="math notranslate nohighlight">
\[ \begin{align}\begin{aligned}n_h = 1 + \log_{2}(n) +
\log_{2}(1 + \frac{|g_1|}{\sigma_{g_1}})\\g_1 = mean[(\frac{x - \mu}{\sigma})^3]\\\sigma_{g_1} = \sqrt{\frac{6(n - 2)}{(n + 1)(n + 3)}}\end{aligned}\end{align} \]</div>
<p>An improved version of Sturges’ formula that produces better
estimates for non-normal datasets. This estimator attempts to
account for the skew of the data.</p>
</dd>
<dt>‘sqrt’</dt><dd><div class="math notranslate nohighlight">
\[n_h = \sqrt n\]</div>
<p>The simplest and fastest estimator. Only takes into account the
data size.</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">arr</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</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="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">histogram_bin_edges</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="s1">&#39;auto&#39;</span><span class="p">,</span> <span class="nb">range</span><span class="o">=</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="go">array([0. , 0.25, 0.5 , 0.75, 1. ])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">histogram_bin_edges</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="go">array([0. , 2.5, 5. ])</span>
</pre></div>
</div>
<p>For consistency with histogram, an array of pre-computed bins is
passed through unmodified:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">histogram_bin_edges</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="go">array([1, 2])</span>
</pre></div>
</div>
<p>This function allows one set of bins to be computed, and reused across
multiple histograms:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">shared_bins</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">histogram_bin_edges</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="s1">&#39;auto&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">shared_bins</span>
<span class="go">array([0., 1., 2., 3., 4., 5.])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">group_id</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</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="mi">1</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="mi">1</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="mi">1</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">hist_0</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">histogram</span><span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="n">group_id</span> <span class="o">==</span> <span class="mi">0</span><span class="p">],</span> <span class="n">bins</span><span class="o">=</span><span class="n">shared_bins</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">hist_1</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">histogram</span><span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="n">group_id</span> <span class="o">==</span> <span class="mi">1</span><span class="p">],</span> <span class="n">bins</span><span class="o">=</span><span class="n">shared_bins</span><span class="p">)</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">hist_0</span><span class="p">;</span> <span class="n">hist_1</span>
<span class="go">array([1, 1, 0, 1, 0])</span>
<span class="go">array([2, 0, 1, 1, 2])</span>
</pre></div>
</div>
<p>Which gives more easily comparable results than using separate bins for
each histogram:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">hist_0</span><span class="p">,</span> <span class="n">bins_0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">histogram</span><span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="n">group_id</span> <span class="o">==</span> <span class="mi">0</span><span class="p">],</span> <span class="n">bins</span><span class="o">=</span><span class="s1">&#39;auto&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">hist_1</span><span class="p">,</span> <span class="n">bins_1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">histogram</span><span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="n">group_id</span> <span class="o">==</span> <span class="mi">1</span><span class="p">],</span> <span class="n">bins</span><span class="o">=</span><span class="s1">&#39;auto&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">hist_0</span><span class="p">;</span> <span class="n">hist_1</span>
<span class="go">array([1, 1, 1])</span>
<span class="go">array([2, 1, 1, 2])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">bins_0</span><span class="p">;</span> <span class="n">bins_1</span>
<span class="go">array([0., 1., 2., 3.])</span>
<span class="go">array([0. , 1.25, 2.5 , 3.75, 5. ])</span>
</pre></div>
</div>
</dd></dl>
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