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| <h1 id="develop-a-neural-network-with-mxnet-in-five-minutes">Develop a Neural Network with MXNet in Five Minutes</h1> |
| |
| <p>This tutorial is designed for new users of the <code>mxnet</code> package for R. It shows how to construct a neural network to do regression in 5 minutes. It shows how to perform classification and regression tasks, respectively. The data we use is in the <code>mlbench</code> package. Instructions to install R and MXNet's R package in different environments can be found <a href="/get_started?version=master&platform=linux&language=r&environ=pip&processor=cpu">here</a>.</p> |
| |
| <h2 id="classification">Classification</h2> |
| <div class="highlight"><pre><code class="language-" data-lang=""> ## Loading required package: mlbench |
| </code></pre></div><div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">require</span><span class="p">(</span><span class="n">mlbench</span><span class="p">))</span><span class="w"> </span><span class="p">{</span><span class="w"> |
| </span><span class="n">install.packages</span><span class="p">(</span><span class="s1">'mlbench'</span><span class="p">)</span><span class="w"> |
| </span><span class="p">}</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang=""> ## Loading required package: mxnet |
| </code></pre></div><div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="n">require</span><span class="p">(</span><span class="n">mxnet</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang=""> ## Loading required datasets |
| </code></pre></div><div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="n">data</span><span class="p">(</span><span class="n">Sonar</span><span class="p">,</span><span class="w"> </span><span class="n">package</span><span class="o">=</span><span class="s2">"mlbench"</span><span class="p">)</span><span class="w"> |
| |
| </span><span class="n">Sonar</span><span class="p">[,</span><span class="m">61</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nf">as.numeric</span><span class="p">(</span><span class="n">Sonar</span><span class="p">[,</span><span class="m">61</span><span class="p">])</span><span class="m">-1</span><span class="w"> |
| </span><span class="n">train.ind</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nf">c</span><span class="p">(</span><span class="m">1</span><span class="o">:</span><span class="m">50</span><span class="p">,</span><span class="w"> </span><span class="m">100</span><span class="o">:</span><span class="m">150</span><span class="p">)</span><span class="w"> |
| </span><span class="n">train.x</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">data.matrix</span><span class="p">(</span><span class="n">Sonar</span><span class="p">[</span><span class="n">train.ind</span><span class="p">,</span><span class="w"> </span><span class="m">1</span><span class="o">:</span><span class="m">60</span><span class="p">])</span><span class="w"> |
| </span><span class="n">train.y</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Sonar</span><span class="p">[</span><span class="n">train.ind</span><span class="p">,</span><span class="w"> </span><span class="m">61</span><span class="p">]</span><span class="w"> |
| </span><span class="n">test.x</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">data.matrix</span><span class="p">(</span><span class="n">Sonar</span><span class="p">[</span><span class="o">-</span><span class="n">train.ind</span><span class="p">,</span><span class="w"> </span><span class="m">1</span><span class="o">:</span><span class="m">60</span><span class="p">])</span><span class="w"> |
| </span><span class="n">test.y</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Sonar</span><span class="p">[</span><span class="o">-</span><span class="n">train.ind</span><span class="p">,</span><span class="w"> </span><span class="m">61</span><span class="p">]</span><span class="w"> |
| </span></code></pre></div> |
| <p>We are going to use a multi-layer perceptron as our classifier. In <code>mxnet</code>, we have a function called <code>mx.mlp</code> for building a general multi-layer neural network to do classification or regression.</p> |
| |
| <p><code>mx.mlp</code> requires the following parameters:</p> |
| |
| <ul> |
| <li>Training data and label</li> |
| <li>Number of hidden nodes in each hidden layer</li> |
| <li>Number of nodes in the output layer</li> |
| <li>Type of the activation</li> |
| <li>Type of the output loss</li> |
| <li>The device to train (GPU or CPU)</li> |
| <li>Other parameters for <code>mx.model.FeedForward.create</code></li> |
| </ul> |
| |
| <p>The following code shows an example usage of <code>mx.mlp</code>:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="n">mx.set.seed</span><span class="p">(</span><span class="m">0</span><span class="p">)</span><span class="w"> |
| </span><span class="n">model</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.mlp</span><span class="p">(</span><span class="n">train.x</span><span class="p">,</span><span class="w"> </span><span class="n">train.y</span><span class="p">,</span><span class="w"> </span><span class="n">hidden_node</span><span class="o">=</span><span class="m">10</span><span class="p">,</span><span class="w"> </span><span class="n">out_node</span><span class="o">=</span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="n">out_activation</span><span class="o">=</span><span class="s2">"softmax"</span><span class="p">,</span><span class="w"> |
| </span><span class="n">num.round</span><span class="o">=</span><span class="m">20</span><span class="p">,</span><span class="w"> </span><span class="n">array.batch.size</span><span class="o">=</span><span class="m">15</span><span class="p">,</span><span class="w"> </span><span class="n">learning.rate</span><span class="o">=</span><span class="m">0.07</span><span class="p">,</span><span class="w"> </span><span class="n">momentum</span><span class="o">=</span><span class="m">0.9</span><span class="p">,</span><span class="w"> |
| </span><span class="n">eval.metric</span><span class="o">=</span><span class="n">mx.metric.accuracy</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang=""> ## Auto detect layout of input matrix, use rowmajor.. |
| ## Start training with 1 devices |
| ## [1] Train-accuracy=0.488888888888889 |
| ## [2] Train-accuracy=0.514285714285714 |
| ## [3] Train-accuracy=0.514285714285714 |
| ## [4] Train-accuracy=0.514285714285714 |
| ## [5] Train-accuracy=0.514285714285714 |
| ## [6] Train-accuracy=0.523809523809524 |
| ## [7] Train-accuracy=0.619047619047619 |
| ## [8] Train-accuracy=0.695238095238095 |
| ## [9] Train-accuracy=0.695238095238095 |
| ## [10] Train-accuracy=0.761904761904762 |
| ## [11] Train-accuracy=0.828571428571429 |
| ## [12] Train-accuracy=0.771428571428571 |
| ## [13] Train-accuracy=0.742857142857143 |
| ## [14] Train-accuracy=0.733333333333333 |
| ## [15] Train-accuracy=0.771428571428571 |
| ## [16] Train-accuracy=0.847619047619048 |
| ## [17] Train-accuracy=0.857142857142857 |
| ## [18] Train-accuracy=0.838095238095238 |
| ## [19] Train-accuracy=0.838095238095238 |
| ## [20] Train-accuracy=0.838095238095238 |
| </code></pre></div> |
| <p>Note that <code>mx.set.seed</code> controls the random process in <code>mxnet</code>. You can see the accuracy in each round during training. It's also easy to make predictions and evaluate.</p> |
| |
| <p>To get an idea of what is happening, view the computation graph from R:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="n">graph.viz</span><span class="p">(</span><span class="n">model</span><span class="o">$</span><span class="n">symbol</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div> |
| <p><a href="https://github.com/apache/mxnet"><img src="https://raw.githubusercontent.com/dmlc/web-data/master/mxnet/knitr/graph.computation.png"></a></p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="n">preds</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">predict</span><span class="p">(</span><span class="n">model</span><span class="p">,</span><span class="w"> </span><span class="n">test.x</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang=""> ## Auto detect layout of input matrix, use rowmajor. |
| </code></pre></div><div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="n">pred.label</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max.col</span><span class="p">(</span><span class="n">t</span><span class="p">(</span><span class="n">preds</span><span class="p">))</span><span class="m">-1</span><span class="w"> |
| </span><span class="n">table</span><span class="p">(</span><span class="n">pred.label</span><span class="p">,</span><span class="w"> </span><span class="n">test.y</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang=""> ## test.y |
| ## pred.label 0 1 |
| ## 0 24 14 |
| ## 1 36 33 |
| </code></pre></div> |
| <p>Note for that for multi-class predictions, mxnet outputs <code>nclass</code> x <code>nexamples</code>, with each row corresponding to the probability of the class.</p> |
| |
| <h2 id="regression">Regression</h2> |
| |
| <p>Again, let us preprocess the data:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="n">data</span><span class="p">(</span><span class="n">BostonHousing</span><span class="p">,</span><span class="w"> </span><span class="n">package</span><span class="o">=</span><span class="s2">"mlbench"</span><span class="p">)</span><span class="w"> |
| |
| </span><span class="n">train.ind</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">seq</span><span class="p">(</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">506</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">)</span><span class="w"> |
| </span><span class="n">train.x</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">data.matrix</span><span class="p">(</span><span class="n">BostonHousing</span><span class="p">[</span><span class="n">train.ind</span><span class="p">,</span><span class="w"> </span><span class="m">-14</span><span class="p">])</span><span class="w"> |
| </span><span class="n">train.y</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BostonHousing</span><span class="p">[</span><span class="n">train.ind</span><span class="p">,</span><span class="w"> </span><span class="m">14</span><span class="p">]</span><span class="w"> |
| </span><span class="n">test.x</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">data.matrix</span><span class="p">(</span><span class="n">BostonHousing</span><span class="p">[</span><span class="o">-</span><span class="n">train.ind</span><span class="p">,</span><span class="w"> </span><span class="m">-14</span><span class="p">])</span><span class="w"> |
| </span><span class="n">test.y</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BostonHousing</span><span class="p">[</span><span class="o">-</span><span class="n">train.ind</span><span class="p">,</span><span class="w"> </span><span class="m">14</span><span class="p">]</span><span class="w"> |
| </span></code></pre></div> |
| <p>Although we can use <code>mx.mlp</code> again to do regression by changing the <code>out_activation</code>, this time we are going to introduce a flexible way to configure neural networks in <code>mxnet</code>. Configuration is done by the "Symbol" system in <code>mxnet</code>. The Symbol system takes care of the links among nodes, activation, dropout ratio, etc. Configure a multi-layer neural network as follows:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="c1"># Define the input data</span><span class="w"> |
| </span><span class="n">data</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Variable</span><span class="p">(</span><span class="s2">"data"</span><span class="p">)</span><span class="w"> |
| </span><span class="c1"># A fully connected hidden layer</span><span class="w"> |
| </span><span class="c1"># data: input source</span><span class="w"> |
| </span><span class="c1"># num_hidden: number of neurons in this hidden layer</span><span class="w"> |
| </span><span class="n">fc1</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.FullyConnected</span><span class="p">(</span><span class="n">data</span><span class="p">,</span><span class="w"> </span><span class="n">num_hidden</span><span class="o">=</span><span class="m">1</span><span class="p">)</span><span class="w"> |
| |
| </span><span class="c1"># Use linear regression for the output layer</span><span class="w"> |
| </span><span class="n">lro</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.LinearRegressionOutput</span><span class="p">(</span><span class="n">fc1</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div> |
| <p>What matters for a regression task is mainly the last function. It enables the new network to optimize for squared loss. Now let's train on this simple data set. In this configuration, we dropped the hidden layer so that the input layer is directly connected to the output layer.</p> |
| |
| <p>Next, make prediction with this structure and other parameters with <code>mx.model.FeedForward.create</code>:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="n">mx.set.seed</span><span class="p">(</span><span class="m">0</span><span class="p">)</span><span class="w"> |
| </span><span class="n">model</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.model.FeedForward.create</span><span class="p">(</span><span class="n">lro</span><span class="p">,</span><span class="w"> </span><span class="n">X</span><span class="o">=</span><span class="n">train.x</span><span class="p">,</span><span class="w"> </span><span class="n">y</span><span class="o">=</span><span class="n">train.y</span><span class="p">,</span><span class="w"> |
| </span><span class="n">ctx</span><span class="o">=</span><span class="n">mx.cpu</span><span class="p">(),</span><span class="w"> </span><span class="n">num.round</span><span class="o">=</span><span class="m">50</span><span class="p">,</span><span class="w"> </span><span class="n">array.batch.size</span><span class="o">=</span><span class="m">20</span><span class="p">,</span><span class="w"> |
| </span><span class="n">learning.rate</span><span class="o">=</span><span class="m">2e-6</span><span class="p">,</span><span class="w"> </span><span class="n">momentum</span><span class="o">=</span><span class="m">0.9</span><span class="p">,</span><span class="w"> </span><span class="n">eval.metric</span><span class="o">=</span><span class="n">mx.metric.rmse</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang=""> ## Auto detect layout of input matrix, use rowmajor. |
| ## Start training with 1 devices |
| ## [1] Train-rmse=16.063282524034 |
| ## [2] Train-rmse=12.2792375712573 |
| ## [3] Train-rmse=11.1984634005885 |
| ## [4] Train-rmse=10.2645236892904 |
| ## [5] Train-rmse=9.49711005504284 |
| ## [6] Train-rmse=9.07733734175182 |
| ## [7] Train-rmse=9.07884450847991 |
| ## [8] Train-rmse=9.10463850277417 |
| ## [9] Train-rmse=9.03977049028532 |
| ## [10] Train-rmse=8.96870685004475 |
| ## [11] Train-rmse=8.93113287361574 |
| ## [12] Train-rmse=8.89937257821847 |
| ## [13] Train-rmse=8.87182096922953 |
| ## [14] Train-rmse=8.84476075083586 |
| ## [15] Train-rmse=8.81464673014974 |
| ## [16] Train-rmse=8.78672567900196 |
| ## [17] Train-rmse=8.76265872846474 |
| ## [18] Train-rmse=8.73946101419974 |
| ## [19] Train-rmse=8.71651926303267 |
| ## [20] Train-rmse=8.69457600919277 |
| ## [21] Train-rmse=8.67354928674563 |
| ## [22] Train-rmse=8.65328755392436 |
| ## [23] Train-rmse=8.63378039680078 |
| ## [24] Train-rmse=8.61488162586984 |
| ## [25] Train-rmse=8.5965105183022 |
| ## [26] Train-rmse=8.57868133563275 |
| ## [27] Train-rmse=8.56135851937663 |
| ## [28] Train-rmse=8.5444819772098 |
| ## [29] Train-rmse=8.52802114610432 |
| ## [30] Train-rmse=8.5119504512622 |
| ## [31] Train-rmse=8.49624261719241 |
| ## [32] Train-rmse=8.48087453238701 |
| ## [33] Train-rmse=8.46582689119887 |
| ## [34] Train-rmse=8.45107881002491 |
| ## [35] Train-rmse=8.43661331401712 |
| ## [36] Train-rmse=8.42241575909639 |
| ## [37] Train-rmse=8.40847217331365 |
| ## [38] Train-rmse=8.39476931796395 |
| ## [39] Train-rmse=8.38129658373974 |
| ## [40] Train-rmse=8.36804269059018 |
| ## [41] Train-rmse=8.35499817678397 |
| ## [42] Train-rmse=8.34215505742154 |
| ## [43] Train-rmse=8.32950441908131 |
| ## [44] Train-rmse=8.31703985777311 |
| ## [45] Train-rmse=8.30475363906755 |
| ## [46] Train-rmse=8.29264031506106 |
| ## [47] Train-rmse=8.28069372820073 |
| ## [48] Train-rmse=8.26890902770415 |
| ## [49] Train-rmse=8.25728089053853 |
| ## [50] Train-rmse=8.24580511500735 |
| </code></pre></div> |
| <p>It's also easy to make a prediction and evaluate it:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="n">preds</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">predict</span><span class="p">(</span><span class="n">model</span><span class="p">,</span><span class="w"> </span><span class="n">test.x</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang=""> ## Auto detect layout of input matrix, use rowmajor.. |
| </code></pre></div><div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="nf">sqrt</span><span class="p">(</span><span class="n">mean</span><span class="p">((</span><span class="n">preds</span><span class="o">-</span><span class="n">test.y</span><span class="p">)</span><span class="o">^</span><span class="m">2</span><span class="p">))</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang=""> ## [1] 7.800502 |
| </code></pre></div> |
| <p>Currently, we have four predefined metrics: "accuracy", "rmse", "mae", and "rmsle". MXNet provides the interface for defining your own metrics:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="n">demo.metric.mae</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.metric.custom</span><span class="p">(</span><span class="s2">"mae"</span><span class="p">,</span><span class="w"> </span><span class="k">function</span><span class="p">(</span><span class="n">label</span><span class="p">,</span><span class="w"> </span><span class="n">pred</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> |
| </span><span class="n">pred</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.nd.reshape</span><span class="p">(</span><span class="n">pred</span><span class="p">,</span><span class="w"> </span><span class="n">shape</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> |
| </span><span class="n">res</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.nd.mean</span><span class="p">(</span><span class="n">mx.nd.abs</span><span class="p">(</span><span class="n">label</span><span class="o">-</span><span class="n">pred</span><span class="p">))</span><span class="w"> |
| </span><span class="nf">return</span><span class="p">(</span><span class="n">res</span><span class="p">)</span><span class="w"> |
| </span><span class="p">})</span><span class="w"> |
| </span></code></pre></div> |
| <p>This is an example of the mean absolute error metric. Simply plug it into the training function:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="n">mx.set.seed</span><span class="p">(</span><span class="m">0</span><span class="p">)</span><span class="w"> |
| </span><span class="n">model</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.model.FeedForward.create</span><span class="p">(</span><span class="n">lro</span><span class="p">,</span><span class="w"> </span><span class="n">X</span><span class="o">=</span><span class="n">train.x</span><span class="p">,</span><span class="w"> </span><span class="n">y</span><span class="o">=</span><span class="n">train.y</span><span class="p">,</span><span class="w"> |
| </span><span class="n">ctx</span><span class="o">=</span><span class="n">mx.cpu</span><span class="p">(),</span><span class="w"> </span><span class="n">num.round</span><span class="o">=</span><span class="m">50</span><span class="p">,</span><span class="w"> </span><span class="n">array.batch.size</span><span class="o">=</span><span class="m">20</span><span class="p">,</span><span class="w"> |
| </span><span class="n">learning.rate</span><span class="o">=</span><span class="m">2e-6</span><span class="p">,</span><span class="w"> </span><span class="n">momentum</span><span class="o">=</span><span class="m">0.9</span><span class="p">,</span><span class="w"> </span><span class="n">eval.metric</span><span class="o">=</span><span class="n">demo.metric.mae</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang=""> ## Auto detect layout of input matrix, use rowmajor. |
| ## Start training with 1 devices |
| ## [1] Train-mae=14.953625731998 |
| ## [2] Train-mae=11.4802955521478 |
| ## [3] Train-mae=8.50700579749213 |
| ## [4] Train-mae=7.30591265360514 |
| ## [5] Train-mae=7.38049803839789 |
| ## [6] Train-mae=7.36036252975464 |
| ## [7] Train-mae=7.06519222259521 |
| ## [8] Train-mae=6.9962231847975 |
| ## [9] Train-mae=6.96296903822157 |
| ## [10] Train-mae=6.9046172036065 |
| ## [11] Train-mae=6.87867620256212 |
| ## [12] Train-mae=6.85872554779053 |
| ## [13] Train-mae=6.81936407089233 |
| ## [14] Train-mae=6.79135354359945 |
| ## [15] Train-mae=6.77438741260105 |
| ## [16] Train-mae=6.75365140702989 |
| ## [17] Train-mae=6.73369296391805 |
| ## [18] Train-mae=6.71600982877943 |
| ## [19] Train-mae=6.69932826360067 |
| ## [20] Train-mae=6.6852519777086 |
| ## [21] Train-mae=6.67343420452542 |
| ## [22] Train-mae=6.66315894656711 |
| ## [23] Train-mae=6.65314838621351 |
| ## [24] Train-mae=6.64388704299927 |
| ## [25] Train-mae=6.63480265935262 |
| ## [26] Train-mae=6.62583245171441 |
| ## [27] Train-mae=6.61697626113892 |
| ## [28] Train-mae=6.60842116673787 |
| ## [29] Train-mae=6.60040124257406 |
| ## [30] Train-mae=6.59264140658908 |
| ## [31] Train-mae=6.58551020092434 |
| ## [32] Train-mae=6.57864215638902 |
| ## [33] Train-mae=6.57178926467896 |
| ## [34] Train-mae=6.56495311525133 |
| ## [35] Train-mae=6.55813185373942 |
| ## [36] Train-mae=6.5513252152337 |
| ## [37] Train-mae=6.54453214009603 |
| ## [38] Train-mae=6.53775374094645 |
| ## [39] Train-mae=6.53098879920112 |
| ## [40] Train-mae=6.52423816257053 |
| ## [41] Train-mae=6.51764053768582 |
| ## [42] Train-mae=6.51121346155802 |
| ## [43] Train-mae=6.5047902001275 |
| ## [44] Train-mae=6.49837123023139 |
| ## [45] Train-mae=6.49216641320123 |
| ## [46] Train-mae=6.48598252402412 |
| ## [47] Train-mae=6.4798010720147 |
| ## [48] Train-mae=6.47362396452162 |
| ## [49] Train-mae=6.46745183732775 |
| ## [50] Train-mae=6.46128723356459 |
| </code></pre></div> |
| <p>Congratulations! You've learned the basics for using MXNet in R. To learn how to use MXNet's advanced features, see the other tutorials.</p> |
| |
| <h2 id="next-steps">Next Steps</h2> |
| |
| <ul> |
| <li><a href="https://mxnet.io/tutorials/r/classifyRealImageWithPretrainedModel.html">Classify Real-World Images with Pre-trained Model</a></li> |
| <li><a href="https://mxnet.io/tutorials/r/mnistCompetition.html">Handwritten Digits Classification Competition</a></li> |
| <li><a href="https://mxnet.io/tutorials/r/charRnnModel.html">Character Language Model using RNN</a></li> |
| </ul> |
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