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href="predict_image.html">Predict with pre-trained models</a></li> <li class="toctree-l4"><a class="reference internal" href="../vision/large_scale_classification.html">Large Scale Image Classification</a></li> </ul> </li> </ul> </li> <li class="toctree-l2"><a class="reference internal" href="../index.html#contributing-tutorials">Contributing Tutorials</a></li> </ul> </li> </ul> </div> </div> <div class="content"> <div class="page-tracker"></div> <div class="section" id="linear-regression"> <h1>Linear Regression<a class="headerlink" href="#linear-regression" title="Permalink to this headline">¶</a></h1> In this tutorial we’ll walk through how one can implement linear regression using MXNet APIs. The function we are trying to learn is: y = x1 + 2x2, where (x1,x2) are input features and y is the corresponding label. <div class="section" id="prerequisites"> <h2>Prerequisites<a class="headerlink" href="#prerequisites" title="Permalink to this headline">¶</a></h2> To complete this tutorial, we need: <ul class="simple"> <li>MXNet. See the instructions for your operating system in <a class="reference external" href="/versions/0.11.0/get_started/install.html">Setup and Installation</a>.</li> <li><a class="reference external" href="http://jupyter.org/index.html">Jupyter Notebook</a>.</li> </ul> <div class="highlight-default"><div class="highlight"><pre>$ pip install jupyter </pre></div> </div> To begin, the following code imports the necessary packages we’ll need for this exercise. <div class="highlight-python"><div class="highlight"><pre>import mxnet as mx import numpy as np import logging logging.getLogger().setLevel(logging.DEBUG) </pre></div> </div> </div> <div class="section" id="preparing-the-data"> <h2>Preparing the Data<a class="headerlink" href="#preparing-the-data" title="Permalink to this headline">¶</a></h2> In MXNet, data is input via Data Iterators. Here we will illustrate how to encode a dataset into an iterator that MXNet can use. The data used in the example is made up of 2D data points with corresponding integer labels. <div class="highlight-python"><div class="highlight"><pre>#Training data train_data = np.random.uniform(0, 1, [100, 2]) train_label = np.array([train_data[i][0] + 2 * train_data[i][1] for i in range(100)]) batch_size = 1 #Evaluation Data eval_data = np.array([[7,2],[6,10],[12,2]]) eval_label = np.array([11,26,16]) </pre></div> </div> Once we have the data ready, we need to put it into an iterator and specify parameters such as <code class="docutils literal">batch_size</code> and <code class="docutils literal">shuffle</code>. <code class="docutils literal">batch_size</code> specifies the number of examples shown to the model each time we update its parameters and <code class="docutils literal">shuffle</code> tells the iterator to randomize the order in which examples are shown to the model. <div class="highlight-python"><div class="highlight"><pre>train_iter = mx.io.NDArrayIter(train_data,train_label, batch_size, shuffle=True,label_name='lin_reg_label') eval_iter = mx.io.NDArrayIter(eval_data, eval_label, batch_size, shuffle=False) </pre></div> </div> In the above example, we have made use of <code class="docutils literal">NDArrayIter</code>, which is useful for iterating over both numpy ndarrays and MXNet NDArrays. In general, there are different types of iterators in MXNet and you can use one based on the type of data you are processing. Documentation for iterators can be found <a class="reference external" href="/versions/0.11.0/api/python/io.html">here</a>. </div> <div class="section" id="mxnet-classes"> <h2>MXNet Classes<a class="headerlink" href="#mxnet-classes" title="Permalink to this headline">¶</a></h2> <ol class="simple"> <li>IO: The IO class as we already saw works on the data and carries out operations such as feeding data in batches and shuffling.</li> <li>Symbol: The actual MXNet neural network is composed using symbols. MXNet has different types of symbols, including variable placeholders for input data, neural network layers, and operators that manipulate NDArrays.</li> <li>Module: The module class in MXNet is used to define the overall computation. It is initialized with the model we want to train, the training inputs (data and labels) and some additional parameters such as learning rate and the optimization algorithm to use.</li> </ol> </div> <div class="section" id="defining-the-model"> <h2>Defining the Model<a class="headerlink" href="#defining-the-model" title="Permalink to this headline">¶</a></h2> MXNet uses Symbols for defining a model. Symbols are the building blocks and make up various components of the model. Symbols are used to define: <ol class="simple"> <li>Variables: A variable is a placeholder for future data. This symbol is used to define a spot which will be filled with training data/labels in the future when we commence training.</li> <li>Neural Network Layers: The layers of a network or any other type of model are also defined by Symbols. Such a symbol takes one or more previous symbols as inputs, performs some transformations on them, and creates one or more outputs. One such example is the <code class="docutils literal">FullyConnected</code> symbol which specifies a fully connected layer of a neural network.</li> <li>Outputs: Output symbols are MXNet’s way of defining a loss. They are suffixed with the word “Output” (eg. the <code class="docutils literal">SoftmaxOutput</code> layer). You can also <a class="reference external" href="https://github.com/dmlc/mxnet/blob/master/docs/tutorials/r/CustomLossFunction.md#how-to-use-your-own-loss-function">create your own loss function</a>. Some examples of existing losses are: <code class="docutils literal">LinearRegressionOutput</code>, which computes the l2-loss between it’s input symbol and the labels provided to it; <code class="docutils literal">SoftmaxOutput</code>, which computes the categorical cross-entropy.</li> </ol> The ones described above and other symbols are chained together with the output of one symbol serving as input to the next to build the network topology. More information about the different types of symbols can be found <a class="reference external" href="/versions/0.11.0/api/python/symbol.html">here</a>. <div class="highlight-python"><div class="highlight"><pre>X = mx.sym.Variable('data') Y = mx.symbol.Variable('lin_reg_label') fully_connected_layer = mx.sym.FullyConnected(data=X, name='fc1', num_hidden = 1) lro = mx.sym.LinearRegressionOutput(data=fully_connected_layer, label=Y, name="lro") </pre></div> </div> The above network uses the following layers: <ol class="simple"> <li><code class="docutils literal">FullyConnected</code>: The fully connected symbol represents a fully connected layer of a neural network (without any activation being applied), which in essence, is just a linear regression on the input attributes. It takes the following parameters:<ul> <li><code class="docutils literal">data</code>: Input to the layer (specifies the symbol whose output should be fed here)</li> <li><code class="docutils literal">num_hidden</code>: Number of hidden neurons in the layer, which is same as the dimensionality of the layer’s output</li> </ul> </li> <li><code class="docutils literal">LinearRegressionOutput</code>: Output layers in MXNet compute training loss, which is the measure of inaccuracy in the model’s predictions. The goal of training is to minimize the training loss. In our example, the <code class="docutils literal">LinearRegressionOutput</code> layer computes the l2 loss against its input and the labels provided to it. The parameters to this layer are:<ul> <li><code class="docutils literal">data</code>: Input to this layer (specifies the symbol whose output should be fed here)</li> <li><code class="docutils literal">label</code>: The training labels against which we will compare the input to the layer for calculation of l2 loss</li> </ul> </li> </ol> Note on naming convention: the label variable’s name should be the same as the <code class="docutils literal">label_name</code> parameter passed to your training data iterator. The default value of this is <code class="docutils literal">softmax_label</code>, but we have updated it to <code class="docutils literal">lin_reg_label</code> in this tutorial as you can see in <code class="docutils literal">Y = mx.symbol.Variable('lin_reg_label')</code> and <code class="docutils literal">train_iter = mx.io.NDArrayIter(..., label_name='lin_reg_label')</code>. Finally, the network is input to a Module, where we specify the symbol whose output needs to be minimized (in our case, <code class="docutils literal">lro</code> or the <code class="docutils literal">lin_reg_output</code>), the learning rate to be used while optimization and the number of epochs we want to train our model for. <div class="highlight-python"><div class="highlight"><pre>model = mx.mod.Module( symbol = lro , data_names=['data'], label_names = ['lin_reg_label']# network structure ) </pre></div> </div> We can visualize the network we created by plotting it: <div class="highlight-python"><div class="highlight"><pre>mx.viz.plot_network(symbol=lro) </pre></div> </div> </div> <div class="section" id="training-the-model"> <h2>Training the model<a class="headerlink" href="#training-the-model" title="Permalink to this headline">¶</a></h2> Once we have defined the model structure, the next step is to train the parameters of the model to fit the training data. This is accomplished using the <code class="docutils literal">fit()</code> function of the <code class="docutils literal">Module</code> class. <div class="highlight-python"><div class="highlight"><pre>model.fit(train_iter, eval_iter, optimizer_params={'learning_rate':0.005, 'momentum': 0.9}, num_epoch=50, eval_metric='mse', batch_end_callback = mx.callback.Speedometer(batch_size, 2)) </pre></div> </div> </div> <div class="section" id="using-a-trained-model-testing-and-inference"> <h2>Using a trained model: (Testing and Inference)<a class="headerlink" href="#using-a-trained-model-testing-and-inference" title="Permalink to this headline">¶</a></h2> Once we have a trained model, we can do a couple of things with it - we can either use it for inference or we can evaluate the trained model on test data. The latter is shown below: <div class="highlight-python"><div class="highlight"><pre>model.predict(eval_iter).asnumpy() </pre></div> </div> We can also evaluate our model according to some metric. In this example, we are evaluating our model’s mean squared error (MSE) on the evaluation data. <div class="highlight-python"><div class="highlight"><pre>metric = mx.metric.MSE() model.score(eval_iter, metric) </pre></div> </div> Let us try and add some noise to the evaluation data and see how the MSE changes: <div class="highlight-python"><div class="highlight"><pre>eval_data = np.array([[7,2],[6,10],[12,2]]) eval_label = np.array([11.1,26.1,16.1]) #Adding 0.1 to each of the values eval_iter = mx.io.NDArrayIter(eval_data, eval_label, batch_size, shuffle=False) model.score(eval_iter, metric) </pre></div> </div> We can also create a custom metric and use it to evaluate a model. More information on metrics can be found in the <a class="reference external" href="/versions/0.11.0/api/python/model.html#evaluation-metric-api-reference">API documentation</a>. <div class="btn-group" role="group"> <div class="download-btn"><a download="linear-regression.ipynb" href="linear-regression.ipynb"> linear-regression.ipynb</a></div></div></div> </div> </div> </div> <div aria-label="main navigation" class="sphinxsidebar rightsidebar" role="navigation"> <div class="sphinxsidebarwrapper"> <h3><a href="../../index.html">Table Of Contents</a></h3> <ul> <li><a class="reference internal" href="#">Linear Regression</a><ul> <li><a class="reference internal" href="#prerequisites">Prerequisites</a></li> <li><a class="reference internal" href="#preparing-the-data">Preparing the Data</a></li> <li><a class="reference internal" href="#mxnet-classes">MXNet Classes</a></li> <li><a class="reference internal" href="#defining-the-model">Defining the Model</a></li> <li><a class="reference internal" href="#training-the-model">Training the model</a></li> <li><a class="reference internal" href="#using-a-trained-model-testing-and-inference">Using a trained model: (Testing and Inference)</a></li> </ul> </li> </ul> </div> </div> </div><div class="footer"> <div class="section-disclaimer"> <div class="container"> <div> <img height="60" src="https://raw.githubusercontent.com/dmlc/web-data/master/mxnet/image/apache_incubator_logo.png"/> Apache MXNet is an effort undergoing incubation at The Apache Software Foundation (ASF), sponsored by the Apache Incubator. Incubation is required of all newly accepted projects until a further review indicates that the infrastructure, communications, and decision making process have stabilized in a manner consistent with other successful ASF projects. While incubation status is not necessarily a reflection of the completeness or stability of the code, it does indicate that the project has yet to be fully endorsed by the ASF. 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