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| <h1 id="handwritten-digits-classification-competition">Handwritten Digits Classification Competition</h1> |
| |
| <p><a href="http://yann.lecun.com/exdb/mnist/">MNIST</a> is a handwritten digits image data set created by Yann LeCun. Every digit is represented by a 28 x 28 pixel image. It's become a standard data set for testing classifiers on simple image input. A neural network is a strong model for image classification tasks. There's a <a href="https://www.kaggle.com/c/digit-recognizer">long-term hosted competition</a> on Kaggle using this data set. |
| This tutorial shows how to use <a href="https://github.com/apache/mxnet/tree/v1.x/R-package">MXNet</a> to compete in this challenge.</p> |
| |
| <h2 id="loading-the-data">Loading the Data</h2> |
| |
| <p>First, let's download the data from <a href="https://www.kaggle.com/c/digit-recognizer/data">Kaggle</a> and put it in the <code>data/</code> folder in your working directory.</p> |
| |
| <p>Now we can read it in R and convert it to matrices:</p> |
| <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 package: mxnet |
| ## Loading required package: methods |
| </code></pre></div><div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="n">train</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">read.csv</span><span class="p">(</span><span class="s1">'data/train.csv'</span><span class="p">,</span><span class="w"> </span><span class="n">header</span><span class="o">=</span><span class="kc">TRUE</span><span class="p">)</span><span class="w"> |
| </span><span class="n">test</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">read.csv</span><span class="p">(</span><span class="s1">'data/test.csv'</span><span class="p">,</span><span class="w"> </span><span class="n">header</span><span class="o">=</span><span class="kc">TRUE</span><span class="p">)</span><span class="w"> |
| </span><span class="n">train</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">train</span><span class="p">)</span><span class="w"> |
| </span><span class="n">test</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">test</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">train</span><span class="p">[,</span><span class="m">-1</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">train</span><span class="p">[,</span><span class="m">1</span><span class="p">]</span><span class="w"> |
| </span></code></pre></div> |
| <p>Every image is represented as a single row in train/test. The greyscale of each image falls in the range [0, 255]. Linearly transform it into [0,1] by using the following command:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><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">t</span><span class="p">(</span><span class="n">train.x</span><span class="o">/</span><span class="m">255</span><span class="p">)</span><span class="w"> |
| </span><span class="n">test</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">t</span><span class="p">(</span><span class="n">test</span><span class="o">/</span><span class="m">255</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div> |
| <p>Transpose the input matrix to npixel x nexamples, which is the major format for columns accepted by MXNet (and the convention of R).</p> |
| |
| <p>In the label section, the number of each digit is fairly evenly distributed:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="n">table</span><span class="p">(</span><span class="n">train.y</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang=""> ## train.y |
| ## 0 1 2 3 4 5 6 7 8 9 |
| ## 4132 4684 4177 4351 4072 3795 4137 4401 4063 4188 |
| </code></pre></div> |
| <h2 id="configuring-the-network">Configuring the Network</h2> |
| |
| <p>Now that we have the data, let's configure the structure of our network:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><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="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">name</span><span class="o">=</span><span class="s2">"fc1"</span><span class="p">,</span><span class="w"> </span><span class="n">num_hidden</span><span class="o">=</span><span class="m">128</span><span class="p">)</span><span class="w"> |
| </span><span class="n">act1</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Activation</span><span class="p">(</span><span class="n">fc1</span><span class="p">,</span><span class="w"> </span><span class="n">name</span><span class="o">=</span><span class="s2">"relu1"</span><span class="p">,</span><span class="w"> </span><span class="n">act_type</span><span class="o">=</span><span class="s2">"relu"</span><span class="p">)</span><span class="w"> |
| </span><span class="n">fc2</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">act1</span><span class="p">,</span><span class="w"> </span><span class="n">name</span><span class="o">=</span><span class="s2">"fc2"</span><span class="p">,</span><span class="w"> </span><span class="n">num_hidden</span><span class="o">=</span><span class="m">64</span><span class="p">)</span><span class="w"> |
| </span><span class="n">act2</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Activation</span><span class="p">(</span><span class="n">fc2</span><span class="p">,</span><span class="w"> </span><span class="n">name</span><span class="o">=</span><span class="s2">"relu2"</span><span class="p">,</span><span class="w"> </span><span class="n">act_type</span><span class="o">=</span><span class="s2">"relu"</span><span class="p">)</span><span class="w"> |
| </span><span class="n">fc3</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">act2</span><span class="p">,</span><span class="w"> </span><span class="n">name</span><span class="o">=</span><span class="s2">"fc3"</span><span class="p">,</span><span class="w"> </span><span class="n">num_hidden</span><span class="o">=</span><span class="m">10</span><span class="p">)</span><span class="w"> |
| </span><span class="n">softmax</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.SoftmaxOutput</span><span class="p">(</span><span class="n">fc3</span><span class="p">,</span><span class="w"> </span><span class="n">name</span><span class="o">=</span><span class="s2">"sm"</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div> |
| <ol> |
| <li>In <code>mxnet</code>, we use the data type <code>symbol</code> to configure the network. <code>data <- mx.symbol.Variable("data")</code> uses <code>data</code> to represent the input data, i.e., the input layer.</li> |
| <li>We set the first hidden layer with <code>fc1 <- mx.symbol.FullyConnected(data, name="fc1", num_hidden=128)</code>. This layer has <code>data</code> as the input, its name, and the number of hidden neurons.</li> |
| <li>Activation is set with <code>act1 <- mx.symbol.Activation(fc1, name="relu1", act_type="relu")</code>. The activation function takes the output from the first hidden layer, <code>fc1</code>.</li> |
| <li>The second hidden layer takes the result from <code>act1</code> as input, with its name as "fc2" and the number of hidden neurons as 64.</li> |
| <li>The second activation is almost the same as <code>act1</code>, except we have a different input source and name.</li> |
| <li>This generates the output layer. Because there are only 10 digits, we set the number of neurons to 10.</li> |
| <li>Finally, we set the activation to softmax to get a probabilistic prediction.</li> |
| </ol> |
| |
| <h2 id="training">Training</h2> |
| |
| <p>We are almost ready for the training process. Before we start the computation, let's decide which device to use:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="n">devices</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.cpu</span><span class="p">()</span><span class="w"> |
| </span></code></pre></div> |
| <p>We assign CPU to <code>mxnet</code>. Now, you can run the following command to train the neural network! Note that <code>mx.set.seed</code> is the function that controls the random process in <code>mxnet</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">softmax</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">devices</span><span class="p">,</span><span class="w"> </span><span class="n">num.round</span><span class="o">=</span><span class="m">10</span><span class="p">,</span><span class="w"> </span><span class="n">array.batch.size</span><span class="o">=</span><span class="m">100</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><span class="n">initializer</span><span class="o">=</span><span class="n">mx.init.uniform</span><span class="p">(</span><span class="m">0.07</span><span class="p">),</span><span class="w"> |
| </span><span class="n">epoch.end.callback</span><span class="o">=</span><span class="n">mx.callback.log.train.metric</span><span class="p">(</span><span class="m">100</span><span class="p">))</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang=""> ## Start training with 1 devices |
| ## Batch [100] Train-accuracy=0.6563 |
| ## Batch [200] Train-accuracy=0.777999999999999 |
| ## Batch [300] Train-accuracy=0.827466666666665 |
| ## Batch [400] Train-accuracy=0.855499999999999 |
| ## [1] Train-accuracy=0.859832935560859 |
| ## Batch [100] Train-accuracy=0.9529 |
| ## Batch [200] Train-accuracy=0.953049999999999 |
| ## Batch [300] Train-accuracy=0.955866666666666 |
| ## Batch [400] Train-accuracy=0.957525000000001 |
| ## [2] Train-accuracy=0.958309523809525 |
| ## Batch [100] Train-accuracy=0.968 |
| ## Batch [200] Train-accuracy=0.9677 |
| ## Batch [300] Train-accuracy=0.9696 |
| ## Batch [400] Train-accuracy=0.970650000000002 |
| ## [3] Train-accuracy=0.970809523809526 |
| ## Batch [100] Train-accuracy=0.973 |
| ## Batch [200] Train-accuracy=0.974249999999999 |
| ## Batch [300] Train-accuracy=0.976 |
| ## Batch [400] Train-accuracy=0.977100000000003 |
| ## [4] Train-accuracy=0.977452380952384 |
| ## Batch [100] Train-accuracy=0.9834 |
| ## Batch [200] Train-accuracy=0.981949999999999 |
| ## Batch [300] Train-accuracy=0.981900000000001 |
| ## Batch [400] Train-accuracy=0.982600000000003 |
| ## [5] Train-accuracy=0.983000000000003 |
| ## Batch [100] Train-accuracy=0.983399999999999 |
| ## Batch [200] Train-accuracy=0.98405 |
| ## Batch [300] Train-accuracy=0.985000000000001 |
| ## Batch [400] Train-accuracy=0.985725000000003 |
| ## [6] Train-accuracy=0.985952380952384 |
| ## Batch [100] Train-accuracy=0.988999999999999 |
| ## Batch [200] Train-accuracy=0.9876 |
| ## Batch [300] Train-accuracy=0.988100000000001 |
| ## Batch [400] Train-accuracy=0.988750000000003 |
| ## [7] Train-accuracy=0.988880952380955 |
| ## Batch [100] Train-accuracy=0.991999999999999 |
| ## Batch [200] Train-accuracy=0.9912 |
| ## Batch [300] Train-accuracy=0.990066666666668 |
| ## Batch [400] Train-accuracy=0.990275000000003 |
| ## [8] Train-accuracy=0.990452380952384 |
| ## Batch [100] Train-accuracy=0.9937 |
| ## Batch [200] Train-accuracy=0.99235 |
| ## Batch [300] Train-accuracy=0.991966666666668 |
| ## Batch [400] Train-accuracy=0.991425000000003 |
| ## [9] Train-accuracy=0.991500000000003 |
| ## Batch [100] Train-accuracy=0.9942 |
| ## Batch [200] Train-accuracy=0.99245 |
| ## Batch [300] Train-accuracy=0.992433333333334 |
| ## Batch [400] Train-accuracy=0.992275000000002 |
| ## [10] Train-accuracy=0.992380952380955 |
| </code></pre></div> |
| <h2 id="making-a-prediction-and-submitting-to-the-competition">Making a Prediction and Submitting to the Competition</h2> |
| |
| <p>To make a prediction, type:</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</span><span class="p">)</span><span class="w"> |
| </span><span class="nf">dim</span><span class="p">(</span><span class="n">preds</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang=""> ## [1] 10 28000 |
| </code></pre></div> |
| <p>It is a matrix with 28000 rows and 10 cols, containing the desired classification probabilities from the output layer. To extract the maximum label for each row, use <code>max.col</code>:</p> |
| <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="w"> </span><span class="o">-</span><span class="w"> </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></code></pre></div><div class="highlight"><pre><code class="language-" data-lang=""> ## pred.label |
| ## 0 1 2 3 4 5 6 7 8 9 |
| ## 2818 3195 2744 2767 2683 2596 2798 2790 2784 2825 |
| </code></pre></div> |
| <p>With a little extra effort to modify the .csv format, our submission is ready for the competition!</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="n">submission</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">data.frame</span><span class="p">(</span><span class="n">ImageId</span><span class="o">=</span><span class="m">1</span><span class="o">:</span><span class="n">ncol</span><span class="p">(</span><span class="n">test</span><span class="p">),</span><span class="w"> </span><span class="n">Label</span><span class="o">=</span><span class="n">pred.label</span><span class="p">)</span><span class="w"> |
| </span><span class="n">write.csv</span><span class="p">(</span><span class="n">submission</span><span class="p">,</span><span class="w"> </span><span class="n">file</span><span class="o">=</span><span class="s1">'submission.csv'</span><span class="p">,</span><span class="w"> </span><span class="n">row.names</span><span class="o">=</span><span class="kc">FALSE</span><span class="p">,</span><span class="w"> </span><span class="n">quote</span><span class="o">=</span><span class="kc">FALSE</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div> |
| <h2 id="lenet">LeNet</h2> |
| |
| <p>Now let's use a new network structure: <a href="http://yann.lecun.com/exdb/lenet/">LeNet</a>. It has been proposed by Yann LeCun for recognizing handwritten digits. We'll demonstrate how to construct and train a LeNet in <code>mxnet</code>.</p> |
| |
| <p>First, we construct the network:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="c1"># input</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="s1">'data'</span><span class="p">)</span><span class="w"> |
| </span><span class="c1"># first conv</span><span class="w"> |
| </span><span class="n">conv1</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Convolution</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">data</span><span class="p">,</span><span class="w"> </span><span class="n">kernel</span><span class="o">=</span><span class="nf">c</span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="m">5</span><span class="p">),</span><span class="w"> </span><span class="n">num_filter</span><span class="o">=</span><span class="m">20</span><span class="p">)</span><span class="w"> |
| </span><span class="n">tanh1</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Activation</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">conv1</span><span class="p">,</span><span class="w"> </span><span class="n">act_type</span><span class="o">=</span><span class="s2">"tanh"</span><span class="p">)</span><span class="w"> |
| </span><span class="n">pool1</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Pooling</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">tanh1</span><span class="p">,</span><span class="w"> </span><span class="n">pool_type</span><span class="o">=</span><span class="s2">"max"</span><span class="p">,</span><span class="w"> |
| </span><span class="n">kernel</span><span class="o">=</span><span class="nf">c</span><span class="p">(</span><span class="m">2</span><span class="p">,</span><span class="m">2</span><span class="p">),</span><span class="w"> </span><span class="n">stride</span><span class="o">=</span><span class="nf">c</span><span class="p">(</span><span class="m">2</span><span class="p">,</span><span class="m">2</span><span class="p">))</span><span class="w"> |
| </span><span class="c1"># second conv</span><span class="w"> |
| </span><span class="n">conv2</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Convolution</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">pool1</span><span class="p">,</span><span class="w"> </span><span class="n">kernel</span><span class="o">=</span><span class="nf">c</span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="m">5</span><span class="p">),</span><span class="w"> </span><span class="n">num_filter</span><span class="o">=</span><span class="m">50</span><span class="p">)</span><span class="w"> |
| </span><span class="n">tanh2</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Activation</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">conv2</span><span class="p">,</span><span class="w"> </span><span class="n">act_type</span><span class="o">=</span><span class="s2">"tanh"</span><span class="p">)</span><span class="w"> |
| </span><span class="n">pool2</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Pooling</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">tanh2</span><span class="p">,</span><span class="w"> </span><span class="n">pool_type</span><span class="o">=</span><span class="s2">"max"</span><span class="p">,</span><span class="w"> |
| </span><span class="n">kernel</span><span class="o">=</span><span class="nf">c</span><span class="p">(</span><span class="m">2</span><span class="p">,</span><span class="m">2</span><span class="p">),</span><span class="w"> </span><span class="n">stride</span><span class="o">=</span><span class="nf">c</span><span class="p">(</span><span class="m">2</span><span class="p">,</span><span class="m">2</span><span class="p">))</span><span class="w"> |
| </span><span class="c1"># first fullc</span><span class="w"> |
| </span><span class="n">flatten</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Flatten</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">pool2</span><span class="p">)</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="o">=</span><span class="n">flatten</span><span class="p">,</span><span class="w"> </span><span class="n">num_hidden</span><span class="o">=</span><span class="m">500</span><span class="p">)</span><span class="w"> |
| </span><span class="n">tanh3</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Activation</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">fc1</span><span class="p">,</span><span class="w"> </span><span class="n">act_type</span><span class="o">=</span><span class="s2">"tanh"</span><span class="p">)</span><span class="w"> |
| </span><span class="c1"># second fullc</span><span class="w"> |
| </span><span class="n">fc2</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="o">=</span><span class="n">tanh3</span><span class="p">,</span><span class="w"> </span><span class="n">num_hidden</span><span class="o">=</span><span class="m">10</span><span class="p">)</span><span class="w"> |
| </span><span class="c1"># loss</span><span class="w"> |
| </span><span class="n">lenet</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.SoftmaxOutput</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">fc2</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div> |
| <p>Then let's reshape the matrices into arrays:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">train.array</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">train.x</span><span class="w"> |
| </span><span class="nf">dim</span><span class="p">(</span><span class="n">train.array</span><span class="p">)</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">28</span><span class="p">,</span><span class="w"> </span><span class="m">28</span><span class="p">,</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">ncol</span><span class="p">(</span><span class="n">train.x</span><span class="p">))</span><span class="w"> |
| </span><span class="n">test.array</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">test</span><span class="w"> |
| </span><span class="nf">dim</span><span class="p">(</span><span class="n">test.array</span><span class="p">)</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">28</span><span class="p">,</span><span class="w"> </span><span class="m">28</span><span class="p">,</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">ncol</span><span class="p">(</span><span class="n">test</span><span class="p">))</span><span class="w"> |
| </span></code></pre></div> |
| <p>We want to compare training speed on different devices, so define the devices:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">n.gpu</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="m">1</span><span class="w"> |
| </span><span class="n">device.cpu</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.cpu</span><span class="p">()</span><span class="w"> |
| </span><span class="n">device.gpu</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">lapply</span><span class="p">(</span><span class="m">0</span><span class="o">:</span><span class="p">(</span><span class="n">n.gpu</span><span class="m">-1</span><span class="p">),</span><span class="w"> </span><span class="k">function</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> |
| </span><span class="n">mx.gpu</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> |
| </span><span class="p">})</span><span class="w"> |
| </span></code></pre></div> |
| <p>We can pass a list of devices to ask MXNet to train on multiple GPUs (you can do this for CPUs, |
| but because internal computation of CPUs is already multi-threaded, there is less gain than with using GPUs).</p> |
| |
| <p>Start by training on the CPU first. Because this takes a bit time, we run it for just one iteration.</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">tic</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="nf">proc.time</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">lenet</span><span class="p">,</span><span class="w"> </span><span class="n">X</span><span class="o">=</span><span class="n">train.array</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">device.cpu</span><span class="p">,</span><span class="w"> </span><span class="n">num.round</span><span class="o">=</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">array.batch.size</span><span class="o">=</span><span class="m">100</span><span class="p">,</span><span class="w"> |
| </span><span class="n">learning.rate</span><span class="o">=</span><span class="m">0.05</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">wd</span><span class="o">=</span><span class="m">0.00001</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><span class="n">epoch.end.callback</span><span class="o">=</span><span class="n">mx.callback.log.train.metric</span><span class="p">(</span><span class="m">100</span><span class="p">))</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang=""> ## Start training with 1 devices |
| ## Batch [100] Train-accuracy=0.1066 |
| ## Batch [200] Train-accuracy=0.16495 |
| ## Batch [300] Train-accuracy=0.401766666666667 |
| ## Batch [400] Train-accuracy=0.537675 |
| ## [1] Train-accuracy=0.557136038186157 |
| </code></pre></div><div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="nf">proc.time</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">tic</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang=""> ## user system elapsed |
| ## 130.030 204.976 83.821 |
| </code></pre></div> |
| <p>Train on a GPU:</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">tic</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="nf">proc.time</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">lenet</span><span class="p">,</span><span class="w"> </span><span class="n">X</span><span class="o">=</span><span class="n">train.array</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">device.gpu</span><span class="p">,</span><span class="w"> </span><span class="n">num.round</span><span class="o">=</span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="n">array.batch.size</span><span class="o">=</span><span class="m">100</span><span class="p">,</span><span class="w"> |
| </span><span class="n">learning.rate</span><span class="o">=</span><span class="m">0.05</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">wd</span><span class="o">=</span><span class="m">0.00001</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><span class="n">epoch.end.callback</span><span class="o">=</span><span class="n">mx.callback.log.train.metric</span><span class="p">(</span><span class="m">100</span><span class="p">))</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang=""> ## Start training with 1 devices |
| ## Batch [100] Train-accuracy=0.1066 |
| ## Batch [200] Train-accuracy=0.1596 |
| ## Batch [300] Train-accuracy=0.3983 |
| ## Batch [400] Train-accuracy=0.533975 |
| ## [1] Train-accuracy=0.553532219570405 |
| ## Batch [100] Train-accuracy=0.958 |
| ## Batch [200] Train-accuracy=0.96155 |
| ## Batch [300] Train-accuracy=0.966100000000001 |
| ## Batch [400] Train-accuracy=0.968550000000003 |
| ## [2] Train-accuracy=0.969071428571432 |
| ## Batch [100] Train-accuracy=0.977 |
| ## Batch [200] Train-accuracy=0.97715 |
| ## Batch [300] Train-accuracy=0.979566666666668 |
| ## Batch [400] Train-accuracy=0.980900000000003 |
| ## [3] Train-accuracy=0.981309523809527 |
| ## Batch [100] Train-accuracy=0.9853 |
| ## Batch [200] Train-accuracy=0.985899999999999 |
| ## Batch [300] Train-accuracy=0.986966666666668 |
| ## Batch [400] Train-accuracy=0.988150000000002 |
| ## [4] Train-accuracy=0.988452380952384 |
| ## Batch [100] Train-accuracy=0.990199999999999 |
| ## Batch [200] Train-accuracy=0.98995 |
| ## Batch [300] Train-accuracy=0.990600000000001 |
| ## Batch [400] Train-accuracy=0.991325000000002 |
| ## [5] Train-accuracy=0.991523809523812 |
| </code></pre></div><div class="highlight"><pre><code class="language-r" data-lang="r"><span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="nf">proc.time</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">tic</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang=""> ## user system elapsed |
| ## 9.288 1.680 6.889 |
| </code></pre></div> |
| <p>By using a GPU processor, we significantly speed up training! |
| Now, we can submit the result to Kaggle to see the improvement of our ranking!</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.array</span><span class="p">)</span><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="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="w"> |
| </span><span class="n">submission</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">data.frame</span><span class="p">(</span><span class="n">ImageId</span><span class="o">=</span><span class="m">1</span><span class="o">:</span><span class="n">ncol</span><span class="p">(</span><span class="n">test</span><span class="p">),</span><span class="w"> </span><span class="n">Label</span><span class="o">=</span><span class="n">pred.label</span><span class="p">)</span><span class="w"> |
| </span><span class="n">write.csv</span><span class="p">(</span><span class="n">submission</span><span class="p">,</span><span class="w"> </span><span class="n">file</span><span class="o">=</span><span class="s1">'submission.csv'</span><span class="p">,</span><span class="w"> </span><span class="n">row.names</span><span class="o">=</span><span class="kc">FALSE</span><span class="p">,</span><span class="w"> </span><span class="n">quote</span><span class="o">=</span><span class="kc">FALSE</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div> |
| <p><img src="https://raw.githubusercontent.com/dmlc/web-data/master/mxnet/knitr/mnistCompetition-kaggle-submission.png" alt=""></p> |
| |
| <h2 id="next-steps">Next Steps</h2> |
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| <li><a href="https://mxnet.io/tutorials/r/charRnnModel.html">Character Language Model using RNN</a></li> |
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