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| <li class="toctree-l1 current"><a class="current reference internal" href="#">Built-in Algorithms</a><ul> |
| <li class="toctree-l2"><a class="reference internal" href="#step-1-get-dataset">Step 1: Get Dataset</a></li> |
| <li class="toctree-l2"><a class="reference internal" href="#step-2-reshape-format">Step 2: Reshape & Format</a></li> |
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| <div class="section" id="built-in-algorithms"> |
| <h1>Built-in Algorithms<a class="headerlink" href="#built-in-algorithms" title="Permalink to this headline">ΒΆ</a></h1> |
| <p>Prerequisite:</p> |
| <ul class="simple"> |
| <li><p><a class="reference internal" href="../getting_started/install.html"><span class="doc">Install SystemDS</span></a></p></li> |
| </ul> |
| <p>This example goes through an algorithm from the list of builtin algorithms that can be applied to a dataset. |
| For simplicity the dataset used for this is <a class="reference external" href="http://yann.lecun.com/exdb/mnist/">MNIST</a>, |
| since it is commonly known and explored.</p> |
| <p>If one wants to skip the explanation then the full script is available at the bottom of this page.</p> |
| <div class="section" id="step-1-get-dataset"> |
| <h2>Step 1: Get Dataset<a class="headerlink" href="#step-1-get-dataset" title="Permalink to this headline">ΒΆ</a></h2> |
| <p>SystemDS provides builtin for downloading and setup of the MNIST dataset. |
| To setup this simply use:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">systemds.examples.tutorials.mnist</span> <span class="kn">import</span> <span class="n">DataManager</span> |
| <span class="n">d</span> <span class="o">=</span> <span class="n">DataManager</span><span class="p">()</span> |
| <span class="n">X</span> <span class="o">=</span> <span class="n">d</span><span class="o">.</span><span class="n">get_train_data</span><span class="p">()</span> |
| <span class="n">Y</span> <span class="o">=</span> <span class="n">d</span><span class="o">.</span><span class="n">get_train_labels</span><span class="p">()</span> |
| </pre></div> |
| </div> |
| <p>Here the DataManager contains the code for downloading and setting up numpy arrays containing the data.</p> |
| </div> |
| <div class="section" id="step-2-reshape-format"> |
| <h2>Step 2: Reshape & Format<a class="headerlink" href="#step-2-reshape-format" title="Permalink to this headline">ΒΆ</a></h2> |
| <p>Usually data does not come in formats that perfectly fits the algorithms, to make this tutorial more |
| realistic some data preprocessing is required to change the input to fit.</p> |
| <p>First the training data, X, has multiple dimensions resulting in a shape (60000, 28, 28). |
| The dimensions correspond to first the number of images 60000, then the number of row pixels, 28, |
| and finally the column pixels, 28.</p> |
| <p>To use this data for logistic regression we have to reduce the dimensions. |
| The input X is the training data. |
| It require the data to have two dimensions, the first resemble the |
| number of inputs, and the other the number of features.</p> |
| <p>Therefore to make the data fit the algorithm we reshape the X dataset, like so:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">X</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="mi">60000</span><span class="p">,</span> <span class="mi">28</span><span class="o">*</span><span class="mi">28</span><span class="p">))</span> |
| </pre></div> |
| </div> |
| <p>This takes each row of pixels and append to each other making a single feature vector per image.</p> |
| <p>The Y dataset also does not perfectly fit the logistic regression algorithm, this is because the labels |
| for this dataset is values ranging from 0, to 9, each label correspond to the integer shown in the image. |
| unfortunately the algorithm require the labels to be distinct integers from 1 and upwards.</p> |
| <p>Therefore we add 1 to each label such that the labels go from 1 to 10, like this:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Y</span> <span class="o">=</span> <span class="n">Y</span> <span class="o">+</span> <span class="mi">1</span> |
| </pre></div> |
| </div> |
| <p>With these steps we are now ready to train a simple model.</p> |
| </div> |
| <div class="section" id="step-3-training"> |
| <h2>Step 3: Training<a class="headerlink" href="#step-3-training" title="Permalink to this headline">ΒΆ</a></h2> |
| <p>To start with, we setup a SystemDS context:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">systemds.context</span> <span class="kn">import</span> <span class="n">SystemDSContext</span> |
| <span class="n">sds</span> <span class="o">=</span> <span class="n">SystemDSContext</span><span class="p">()</span> |
| </pre></div> |
| </div> |
| <p>Then setup the data:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">systemds.matrix</span> <span class="kn">import</span> <span class="n">Matrix</span> |
| <span class="n">X_ds</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">(</span><span class="n">sds</span><span class="p">,</span> <span class="n">X</span><span class="p">)</span> |
| <span class="n">Y_ds</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">(</span><span class="n">sds</span><span class="p">,</span> <span class="n">Y</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| <p>to reduce the training time and verify everything works, it is usually good to reduce the amount of data, |
| to train on a smaller sample to start with:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">sample_size</span> <span class="o">=</span> <span class="mi">1000</span> |
| <span class="n">X_ds</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">(</span><span class="n">sds</span><span class="p">,</span> <span class="n">X</span><span class="p">[:</span><span class="n">sample_size</span><span class="p">])</span> |
| <span class="n">Y_ds</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">(</span><span class="n">sds</span><span class="p">,</span> <span class="n">Y</span><span class="p">[:</span><span class="n">sample_size</span><span class="p">])</span> |
| </pre></div> |
| </div> |
| <p>And now everything is ready for our algorithm:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">systemds.operator.algorithm</span> <span class="kn">import</span> <span class="n">multiLogReg</span> |
| |
| <span class="n">bias</span> <span class="o">=</span> <span class="n">multiLogReg</span><span class="p">(</span><span class="n">X_ds</span><span class="p">,</span> <span class="n">Y_ds</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| <p>Note that nothing has been calculated yet, in SystemDS, since it only happens when you call compute:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">bias_r</span> <span class="o">=</span> <span class="n">bias</span><span class="o">.</span><span class="n">compute</span><span class="p">()</span> |
| </pre></div> |
| </div> |
| <p>bias is a matrix, that if matrix multiplied with an instance returns a value distribution where, the highest value is the predicted type. |
| This is the matrix that could be saved and used for predicting labels later.</p> |
| </div> |
| <div class="section" id="step-3-validate"> |
| <h2>Step 3: Validate<a class="headerlink" href="#step-3-validate" title="Permalink to this headline">ΒΆ</a></h2> |
| <p>To see what accuracy the model achieves, we have to load in the test dataset as well.</p> |
| <p>this can also be extracted from our builtin MNIST loader, to keep the tutorial short the operations are combined:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Xt</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">(</span><span class="n">sds</span><span class="p">,</span> <span class="n">d</span><span class="o">.</span><span class="n">get_test_data</span><span class="p">()</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="mi">10000</span><span class="p">,</span> <span class="mi">28</span><span class="o">*</span><span class="mi">28</span><span class="p">)))</span> |
| <span class="n">Yt</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">(</span><span class="n">sds</span><span class="p">,</span> <span class="n">d</span><span class="o">.</span><span class="n">get_test_labels</span><span class="p">())</span> <span class="o">+</span> <span class="mi">1</span> |
| </pre></div> |
| </div> |
| <p>The above loads the test data, and reshapes the X data the same way the training data was reshaped.</p> |
| <p>Finally we verify the accuracy by calling:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">systemds.operator.algorithm</span> <span class="kn">import</span> <span class="n">multiLogRegPredict</span> |
| <span class="p">[</span><span class="n">m</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">,</span> <span class="n">acc</span><span class="p">]</span> <span class="o">=</span> <span class="n">multiLogRegPredict</span><span class="p">(</span><span class="n">Xt</span><span class="p">,</span> <span class="n">bias</span><span class="p">,</span> <span class="n">Yt</span><span class="p">)</span><span class="o">.</span><span class="n">compute</span><span class="p">()</span> |
| <span class="nb">print</span><span class="p">(</span><span class="n">acc</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| <p>There are three outputs from the multiLogRegPredict call.</p> |
| <ul class="simple"> |
| <li><p>m, is the mean probability of correctly classifying each label.</p></li> |
| <li><p>y_pred, is the predictions made using the model, bias, trained.</p></li> |
| <li><p>acc, is the accuracy achieved by the model.</p></li> |
| </ul> |
| <p>If the subset of the training data is used then you could expect an accuracy of 85% in this example |
| using 1000 pictures of the training data.</p> |
| </div> |
| <div class="section" id="step-4-tuning"> |
| <h2>Step 4: Tuning<a class="headerlink" href="#step-4-tuning" title="Permalink to this headline">ΒΆ</a></h2> |
| <p>Now that we have a working baseline we can start tuning parameters.</p> |
| <p>But first it is valuable to know how much of a difference in performance there is on the training data, vs the test data. |
| This gives an indication of if we have exhausted the learning potential of the training data.</p> |
| <p>To see how our accuracy is on the training data we use the Predict function again, but with our training data:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">m</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">,</span> <span class="n">acc</span><span class="p">]</span> <span class="o">=</span> <span class="n">multiLogRegPredict</span><span class="p">(</span><span class="n">X_ds</span><span class="p">,</span> <span class="n">bias</span><span class="p">,</span> <span class="n">Y_ds</span><span class="p">)</span><span class="o">.</span><span class="n">compute</span><span class="p">()</span> |
| <span class="nb">print</span><span class="p">(</span><span class="n">acc</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| <p>In this specific case we achieve 100% accuracy on the training data, indicating that we have fit the training data, |
| and have nothing more to learn from the data as it is now.</p> |
| <p>To improve further we have to increase the training data, here for example we increase it |
| from our sample of 1k to the full training dataset of 60k, in this example the maxi is set to reduce the number of iterations the algorithm takes, |
| to again reduce training time:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">X_ds</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">(</span><span class="n">sds</span><span class="p">,</span> <span class="n">X</span><span class="p">)</span> |
| <span class="n">Y_ds</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">(</span><span class="n">sds</span><span class="p">,</span> <span class="n">Y</span><span class="p">)</span> |
| |
| <span class="n">bias</span> <span class="o">=</span> <span class="n">multiLogReg</span><span class="p">(</span><span class="n">X_ds</span><span class="p">,</span> <span class="n">Y_ds</span><span class="p">,</span> <span class="n">maxi</span><span class="o">=</span><span class="mi">30</span><span class="p">)</span> |
| |
| <span class="p">[</span><span class="n">_</span><span class="p">,</span> <span class="n">_</span><span class="p">,</span> <span class="n">train_acc</span><span class="p">]</span> <span class="o">=</span> <span class="n">multiLogRegPredict</span><span class="p">(</span><span class="n">X_ds</span><span class="p">,</span> <span class="n">bias</span><span class="p">,</span> <span class="n">Y_ds</span><span class="p">)</span><span class="o">.</span><span class="n">compute</span><span class="p">()</span> |
| <span class="p">[</span><span class="n">_</span><span class="p">,</span> <span class="n">_</span><span class="p">,</span> <span class="n">test_acc</span><span class="p">]</span> <span class="o">=</span> <span class="n">multiLogRegPredict</span><span class="p">(</span><span class="n">Xt</span><span class="p">,</span> <span class="n">bias</span><span class="p">,</span> <span class="n">Yt</span><span class="p">)</span><span class="o">.</span><span class="n">compute</span><span class="p">()</span> |
| <span class="nb">print</span><span class="p">(</span><span class="n">train_acc</span><span class="p">,</span> <span class="s2">" "</span><span class="p">,</span> <span class="n">test_acc</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| <p>With this change the accuracy achieved changes from the previous value to 92%. This is still low on this dataset as can be seen on <a class="reference external" href="http://yann.lecun.com/exdb/mnist/">MNIST</a>. |
| But this is a basic implementation that can be replaced by a variety of algorithms and techniques.</p> |
| </div> |
| <div class="section" id="full-script"> |
| <h2>Full Script<a class="headerlink" href="#full-script" title="Permalink to this headline">ΒΆ</a></h2> |
| <p>The full script, some steps are combined to reduce the overall script. |
| One noteworthy change is the + 1 is done on the matrix ready for SystemDS, |
| this makes SystemDS responsible for adding the 1 to each value.:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">systemds.context</span> <span class="kn">import</span> <span class="n">SystemDSContext</span> |
| <span class="kn">from</span> <span class="nn">systemds.matrix</span> <span class="kn">import</span> <span class="n">Matrix</span> |
| <span class="kn">from</span> <span class="nn">systemds.operator.algorithm</span> <span class="kn">import</span> <span class="n">multiLogReg</span><span class="p">,</span> <span class="n">multiLogRegPredict</span> |
| <span class="kn">from</span> <span class="nn">systemds.examples.tutorials.mnist</span> <span class="kn">import</span> <span class="n">DataManager</span> |
| |
| <span class="n">d</span> <span class="o">=</span> <span class="n">DataManager</span><span class="p">()</span> |
| |
| <span class="k">with</span> <span class="n">SystemDSContext</span><span class="p">()</span> <span class="k">as</span> <span class="n">sds</span><span class="p">:</span> |
| <span class="c1"># Train Data</span> |
| <span class="n">X</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">(</span><span class="n">sds</span><span class="p">,</span> <span class="n">d</span><span class="o">.</span><span class="n">get_train_data</span><span class="p">()</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="mi">60000</span><span class="p">,</span> <span class="mi">28</span><span class="o">*</span><span class="mi">28</span><span class="p">)))</span> |
| <span class="n">Y</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">(</span><span class="n">sds</span><span class="p">,</span> <span class="n">d</span><span class="o">.</span><span class="n">get_train_labels</span><span class="p">())</span> <span class="o">+</span> <span class="mf">1.0</span> |
| <span class="n">bias</span> <span class="o">=</span> <span class="n">multiLogReg</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">maxi</span><span class="o">=</span><span class="mi">30</span><span class="p">)</span> |
| <span class="c1"># Test data</span> |
| <span class="n">Xt</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">(</span><span class="n">sds</span><span class="p">,</span> <span class="n">d</span><span class="o">.</span><span class="n">get_test_data</span><span class="p">()</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="mi">10000</span><span class="p">,</span> <span class="mi">28</span><span class="o">*</span><span class="mi">28</span><span class="p">)))</span> |
| <span class="n">Yt</span> <span class="o">=</span> <span class="n">Matrix</span><span class="p">(</span><span class="n">sds</span><span class="p">,</span> <span class="n">d</span><span class="o">.</span><span class="n">get_test_labels</span><span class="p">())</span> <span class="o">+</span> <span class="mf">1.0</span> |
| <span class="p">[</span><span class="n">m</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">,</span> <span class="n">acc</span><span class="p">]</span> <span class="o">=</span> <span class="n">multiLogRegPredict</span><span class="p">(</span><span class="n">Xt</span><span class="p">,</span> <span class="n">bias</span><span class="p">,</span> <span class="n">Yt</span><span class="p">)</span><span class="o">.</span><span class="n">compute</span><span class="p">()</span> |
| |
| <span class="nb">print</span><span class="p">(</span><span class="n">acc</span><span class="p">)</span> |
| </pre></div> |
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