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</style></head><body><div class = "content"><div class = 'SectionBlock containment active'><h1 class = "S1"><span class = "S2"><span class="S0">Regularized logistic regression for quality assurance</span></span></h1><h2 class = "S3"><span class = "S2"><span class="S0">Problem statement</span></span></h2><div class = "S4"><span class = "S2"><span class="S0">During quality assurance (QA), each microchip from a fabrication plant goes through various tests to ensure it is functioning correctly. Suppose you are the product manager of the factory and you have the test results for some microchips on two different tests. From these two tests, you would like to determine whether the microchips should be accepted or rejected. To help you make the decision, you have a dataset of test results on past microchips, from which you can build a logistic regression model.</span></span></div><h2 class = "S3"><span class = "S2"><span class="S0">Load data</span></span></h2><div class = "S4"><span class = "S2"><span class="S0">The file QA_data.txt contains the dataset for our logistic regression problem. The first two columns contains the test scores and the third column contains a label which indicateds verdict. The dataset is loaded from the data file into the variables X and y:</span></span></div><div class = 'CodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">%% Load Data</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% The first two columns contains the X values and the third column</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% contains the label (y).</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">data = load(</span><span class="S9">'QA_data.txt'</span><span class="S0">);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">X = data(:, [1, 2]); y = data(:, 3);</span></span></div></div></div><h2 class = "S3"><span class = "S2"><span class="S0">Plot data</span></span></h2><div class = "S4"><span class = "S2"><span class="S0">Before starting to implement any learning algorithm, it is always good to visualize the data if possible. We start the exercise by first plotting the data to understand the problem we are working with.</span></span></div><div class = 'CodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">plotData(X, y);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">%Implementation of plotData is given at the last section of document</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% Put some labels </span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">hold </span><span class="S9">on</span><span class="S0">;</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% Labels and Legend</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">xlabel(</span><span class="S9">'Microchip Test 1'</span><span class="S0">);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">ylabel(</span><span class="S9">'Microchip Test 2'</span><span class="S0">);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% Specified in plot order</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">legend(</span><span class="S9">'y = 1'</span><span class="S0">, </span><span class="S9">'y = 0'</span><span class="S0">);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">title(</span><span class="S9">'Plot of training data'</span><span class="S0">);</span></span></div></div><div class = 'inlineWrapper outputs'><div class = "S6 lineNode"><span class = "S7"><span class="S0">hold </span><span class="S9">off</span><span class="S0">;</span></span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="D79ACE6F" data-scroll-top="null" data-scroll-left="null" data-testid="output_0" style="width: 937px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="figureElement" style="white-space: normal; 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" style="width: 100%; height: auto; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div></div></div></div></div></div></div><div class = "S11"><span class = "S2"><span class="S0">The axes are the two test scores, and the positive (</span></span><span class = "S2"><span class="S12">y </span></span><span class = "S2"><span class="S0">= 1, accepted) and negative (</span></span><span class = "S2"><span class="S12">y </span></span><span class = "S2"><span class="S0">= 0, rejected) examples are shown with different markers. Our dataset cannot be separated into positive and negative examples by a straight-line through the plot. Therefore, a straightforward application of logistic regression will not perform well on this dataset since logistic regression will only be able to find a linear decision boundary.</span></span><span class = "S2"><span class="S0"> </span></span></div><h2 class = "S3"><span class = "S2"><span class="S0">Feature mapping</span></span></h2><div class = "S4"><span class = "S2"><span class="S0">One way to fit the data better is to create more features from each data point. we will map the features into all polynomial terms of </span></span><span class = "S2"><span class="S12">x</span></span><span class = "S2"><span class="S0">1 </span></span><span class = "S2"><span class="S0">and </span></span><span class = "S2"><span class="S12">x</span></span><span class = "S2"><span class="S0">2 </span></span><span class = "S2"><span class="S0">up to the sixth power.</span></span></div><div class = "S4"><span style="vertical-align:-115px"><img 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" width="155.5" height="241" /></span></div><div class = "S4"><span class = "S2"><span class="S0">As a result of this mapping, our vector of two features (the scores on two QA tests) has been transformed into a 28-dimensional vector. A logistic regression classifier trained on this higher-dimension feature vector will have a more complex decision boundary and will appear nonlinear when drawn in our 2-dimensional plot.</span></span></div><div class = "S4"><span class = "S2"><span class="S0">While the feature mapping allows us to build a more expressive classifier, it also more susceptible to overfitting.</span></span></div><div class = 'CodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% Add Polynomial Features</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% Note that mapFeature also adds a column of ones for us, so the intercept</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% term is handled</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">X = mapFeature(X(:,1), X(:,2));</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">%Implementation of mapFeature is at the end section</span></span></div></div></div><h2 class = "S3"><span class = "S2"><span class="S0">Sigmoid function</span></span></h2><div class = "S4"><span class = "S2"><span class="S0">The logistic regression hypothesis is defined as:</span></span></div><div class = "S13"><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="90" height="20" /></span></div><div class = "S4"><span class = "S2"><span class="S0">where function </span></span><span class = "S2"><span class="S12">g </span></span><span class = "S2"><span class="S0">is the sigmoid function. The sigmoid function is defined as:</span></span></div><div class = "S13"><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="88.5" height="36" /></span></div><div class = "S4"><span class = "S2"><span class="S0">For large positive values of </span></span><span class = "S2"><span class="S0">x</span></span><span class = "S2"><span class="S0">, the sigmoid should be close to 1, while for large negative values, the sigmoid should be close to 0. for 0 it should be exactly 0.5. Implementation of sigmoid function is given at the end of document.</span></span></div><h2 class = "S3"><span class = "S2"><span class="S0">Cost function and gradient</span></span></h2><div class = "S4"><span class = "S2"><span class="S0">The regularized cost function in logistic regression is </span></span></div><div class = "S13"><span style="vertical-align:-17px"><img src="data:image/png;base64,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" width="450.5" height="46" /></span></div><div class = "S4"><span class = "S2"><span class="S0">The gradient of the cost function is a vector where the </span></span><span class = "S2"><span class="S12">j</span></span><span class = "S2"><span class="S0">th </span></span><span class = "S2"><span class="S0">element is defined as follows:</span></span></div><div class = "S13"><span style="vertical-align:-17px"><img src="data:image/png;base64,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" 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" width="274.5" height="46" /></span></div><div class = "S4"><span class = "S2"><span class="S0">Let' compute initial cost using the initial value of </span></span><span class = "S2"><span class="S12">θ </span></span><span class = "S2"><span class="S0">(initialized to all zeros).</span></span></div><div class = 'CodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% Initialize fitting parameters</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">initial_theta = zeros(size(X, 2), 1);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% Set regularization parameter lambda to 1</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">lambda = 1;</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% Compute and display initial cost and gradient for regularized logistic</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% regression</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">[cost, grad] = costFunctionReg(initial_theta, X, y, lambda);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">%Implementation of costFunctionReg is at the end section</span></span></div></div><div class = 'inlineWrapper outputs'><div class = "S6 lineNode"><span class = "S7"><span class="S0">fprintf(</span><span class="S9">'Cost at initial theta (zeros): %f\n'</span><span class="S0">, cost);</span></span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement eoOutputWrapper embeddedOutputsTextElement" uid="85825E23" data-scroll-top="null" data-scroll-left="null" data-width="907" data-height="18" data-testid="output_1" style="max-height: 261px; width: 937px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="textElement" style="white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">Cost at initial theta (zeros): 0.693147</div></div></div></div></div><h2 class = "S3"><span class = "S2"><span class="S0">Learning parameters using builtin function</span></span></h2><div class = "S4"><span class = "S2"><span class="S0">Octave/MATLAB’s </span></span><span class = "S2"><span class="S0">fminunc </span></span><span class = "S2"><span class="S0">is an optimization solver that finds the minimum of an unconstrained</span></span><span class = "S2"><span class="S0"> </span></span><span class = "S2"><span class="S0">function. For logistic regression, we want to optimize the cost function </span></span><span class = "S2"><span class="S12">J</span></span><span class = "S2"><span class="S0">(</span></span><span class = "S2"><span class="S12">θ</span></span><span class = "S2"><span class="S0">) with parameters </span></span><span class = "S2"><span class="S12">θ</span></span><span class = "S2"><span class="S0">.</span></span></div><div class = "S4"><span class = "S2"><span class="S0">Concretely, we are going to use fminunc </span></span><span class = "S2"><span class="S0">to find the best parameters </span></span><span class = "S2"><span class="S12">θ </span></span><span class = "S2"><span class="S0">for the logistic regression cost function, given a fixed dataset (of </span></span><span class = "S2"><span class="S12">X </span></span><span class = "S2"><span class="S0">and </span></span><span class = "S2"><span class="S12">y </span></span><span class = "S2"><span class="S0">values) we will pass to </span></span><span class = "S2"><span class="S0">fminunc </span></span><span class = "S2"><span class="S0">the following inputs:</span></span><span class = "S2"><span class="S0"> </span></span></div><ul class = "S14"><li class = "S15"><span class = "S0"><span class="S0">The initial values of the parameters we are trying to optimize.</span></span></li><li class = "S15"><span class = "S0"><span class="S0">A function that, when given the training set and a particular </span></span><span class = "S0"><span class="S12">θ</span></span><span class = "S0"><span class="S0">, computes the logistic regression cost and gradient with respect to </span></span><span class = "S0"><span class="S12">θ </span></span><span class = "S0"><span class="S0">for the dataset (</span></span><span class = "S0"><span class="S12">X</span></span><span class = "S0"><span class="S0">, </span></span><span class = "S0"><span class="S12">y</span></span><span class = "S0"><span class="S0">).</span></span></li><li class = "S15"><span class = "S0"><span class="S0">Regularization paramaeter lambda</span></span></li></ul><div class = "S4"><span class = "S2"><span class="S0">We already implemented everything needed to use the builtin function so let's use that</span></span></div><div class = 'CodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% Set Options</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">options = optimset(</span><span class="S9">'GradObj'</span><span class="S0">, </span><span class="S9">'on'</span><span class="S0">, </span><span class="S9">'MaxIter'</span><span class="S0">, 400);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% Optimize</span></span></div></div><div class = 'inlineWrapper outputs'><div class = "S6 lineNode"><span class = "S7"><span class="S0">[theta, </span><span class="S0">J</span><span class="S0">, </span><span class="S0">exit_flag</span><span class="S0">] = fminunc(@(t)(costFunctionReg(t, X, y, lambda)), initial_theta, options);</span></span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement eoOutputWrapper embeddedOutputsTextElement" uid="4CE181A6" data-scroll-top="null" data-scroll-left="null" data-width="907" data-height="87" data-testid="output_2" style="max-height: 261px; width: 937px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="textElement" style="white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">Local minimum found.<br><br>Optimization completed because the size of the gradient is less than<br>the default value of the optimality tolerance.<br><br><stopping criteria details></div></div></div></div></div><div class = "S11"><span class = "S2"><span class="S0">In this code snippet, we first defined the options to be used with fminunc. Specifically, we set the GradObj option to on, which tells fminunc that our function returns both the cost and the gradient. This allows fminunc to use the gradient when minimizing the function. Furthermore, we set the MaxIter option to 400, so that fminunc will run for at most 400 steps before it terminates. To specify the actual function we are minimizing, we use a "short-hand" for specifying functions with the </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="172.5" height="19" /></span><span class = "S2"><span class="S0">. This creates a function, with argument t, which calls your costFunction. This allows us to wrap the costFunction for use with fminunc.</span></span></div><h2 class = "S3"><span class = "S2"><span class="S0">Plot decision boundary</span></span></h2><div class = "S4"><span class = "S2"><span class="S0">We plot the non-linear decision boundary by computing the classifier’s predictions on an evenly spaced grid and then and drew a contour plot of where the predictions change from </span></span><span class = "S2"><span class="S12">y </span></span><span class = "S2"><span class="S0">= 0 to </span></span><span class = "S2"><span class="S12">y </span></span><span class = "S2"><span class="S0">= 1.</span></span></div><div class = 'CodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% Plot Boundary</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">plotDecisionBoundary(theta, X, y);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">hold </span><span class="S9">on</span><span class="S0">;</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">title(sprintf(</span><span class="S9">'lambda = %g'</span><span class="S0">, lambda))</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% Labels and Legend</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">xlabel(</span><span class="S9">'Microchip Test 1'</span><span class="S0">)</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">ylabel(</span><span class="S9">'Microchip Test 2'</span><span class="S0">)</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">legend(</span><span class="S9">'y = 1'</span><span class="S0">, </span><span class="S9">'y = 0'</span><span class="S0">, </span><span class="S9">'Decision boundary'</span><span class="S0">)</span></span></div></div><div class = 'inlineWrapper outputs'><div class = "S6 lineNode"><span class = "S7"><span class="S0">hold </span><span class="S9">off</span><span class="S0">;</span></span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="6917B521" data-scroll-top="null" data-scroll-left="null" data-testid="output_3" style="width: 937px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="figureElement" 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" style="width: 100%; height: auto; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div></div></div></div></div></div></div><h2 class = "S3"><span class = "S2"><span class="S0">Performance on training data</span></span></h2><div class = "S4"><span class = "S2"><span class="S0">Let's check how our model is performing on the training data</span></span></div><div class = 'CodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% Compute accuracy on our training set</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">p = predict(theta, X);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">%Implementation of predict is given in the last section</span></span></div></div><div class = 'inlineWrapper outputs'><div class = "S6 lineNode"><span class = "S7"><span class="S0">fprintf(</span><span class="S9">'Train Accuracy: %f\n'</span><span class="S0">, mean(double(p == y)) * 100);</span></span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement eoOutputWrapper embeddedOutputsTextElement" uid="2B42D487" data-scroll-top="null" data-scroll-left="null" data-width="907" data-height="18" data-testid="output_4" style="max-height: 261px; width: 937px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="textElement" style="white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">Train Accuracy: 83.050847</div></div></div></div></div><h2 class = "S3"><span class = "S2"><span class="S0">Effect of regularization parameter</span></span></h2><div class = "S4"><span class = "S2"><span class="S0">Let's see how changing value of regularization parameter effects decision boundary by plotting graphs</span></span></div><div class = 'CodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span><span class="S0">lambda = 0;</span></span></div></div><div class = 'inlineWrapper outputs'><div class = "S6 lineNode"><span class = "S7"><span class="S0">[theta, </span><span class="S0">J</span><span class="S0">, </span><span class="S0">exit_flag</span><span class="S0">] = fminunc(@(t)(costFunctionReg(t, X, y, lambda)), initial_theta, options);</span></span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement eoOutputWrapper embeddedOutputsTextElement" uid="80CA64C5" data-scroll-top="null" data-scroll-left="null" data-width="907" data-height="59" data-testid="output_5" style="max-height: 261px; width: 937px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="textElement" style="white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">Solver stopped prematurely.<br><br>fminunc stopped because it exceeded the iteration limit,<br>options.MaxIterations = 400 (the selected value).</div></div></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">plotDecisionBoundary(theta, X, y);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper outputs'><div class = "S6 lineNode"><span class = "S7"><span class="S0">title(sprintf(</span><span class="S9">'lambda = %g'</span><span class="S0">, lambda));</span></span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="DEF36D82" data-scroll-top="null" data-scroll-left="null" data-testid="output_6" style="width: 937px; 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" style="width: 100%; height: auto; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div></div></div></div></div></div></div><div class = "S11"><span class = "S2"><span class="S0">Without any regularization our model overfits which is bad for generalization</span></span></div><div class = 'CodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">lambda = 100;</span></span></div></div><div class = 'inlineWrapper outputs'><div class = "S6 lineNode"><span class = "S7"><span class="S0">[theta, J, exit_flag] = fminunc(@(t)(costFunctionReg(t, X, y, lambda)), initial_theta, options);</span></span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement eoOutputWrapper embeddedOutputsTextElement" uid="C0592A6B" data-scroll-top="null" data-scroll-left="null" data-width="907" data-height="87" data-testid="output_7" style="max-height: 261px; width: 937px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="textElement" style="white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">Local minimum found.<br><br>Optimization completed because the size of the gradient is less than<br>the default value of the optimality tolerance.<br><br><stopping criteria details></div></div></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">plotDecisionBoundary(theta, X, y);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper outputs'><div class = "S6 lineNode"><span class = "S7"><span class="S0">title(sprintf(</span><span class="S9">'lambda = %g'</span><span 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" style="width: 100%; height: auto; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div></div></div></div></div></div></div><div class = "S11"><span class = "S2"><span class="S0">Too much regularization causes underfiting which is also bad for generalization</span></span></div></div><div class = "S0"></div><div class = 'SectionBlock containment'><h2 class = "S16"><span class = "S2"><span class="S0">Implementation of functions</span></span></h2><div class = "S4"><span class = "S2"><span class="S0">Implementation of plotData</span></span></div><div class = 'CodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">function </span><span class="S0">plotData(X, y)</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">%PLOTDATA Plots the data points X and y into a new figure </span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% PLOTDATA(x,y) plots the data points with + for the positive examples</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% and o for the negative examples. X is assumed to be a Mx2 matrix.</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% Create New Figure</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">figure; hold </span><span class="S9">on</span><span class="S0">;</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">pos = find(y==1); neg = find(y == 0);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% Plot Examples</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">plot(X(pos, 1), X(pos, 2), </span><span class="S9">'k+'</span><span class="S0">,</span><span class="S9">'LineWidth'</span><span class="S0">, 2,</span><span class="S9">'MarkerSize'</span><span class="S0">, 7);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">plot(X(neg, 1), X(neg, 2), </span><span class="S9">'ko'</span><span class="S0">, </span><span class="S9">'MarkerFaceColor'</span><span class="S0">, </span><span class="S9">'y'</span><span class="S0">,</span><span class="S9">'MarkerSize'</span><span class="S0">, 7);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% =========================================================================</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">hold </span><span class="S9">off</span><span class="S0">;</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">end</span></span></div></div></div><div class = "S11"><span class = "S2"><span class="S0">Implementation of mapFeature</span></span></div><div class = 'CodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">function </span><span class="S0">out = mapFeature(X1, X2)</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% MAPFEATURE Feature mapping function to polynomial features</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">%</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% MAPFEATURE(X1, X2) maps the two input features</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% to quadratic features used in the regularization exercise.</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">%</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% Returns a new feature array with more features, comprising of </span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% X1, X2, X1.^2, X2.^2, X1*X2, X1*X2.^2, etc..</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">%</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% Inputs X1, X2 must be the same size</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">%</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">degree = 6;</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">out = ones(size(X1(:,1)));</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">for </span><span class="S0">i = 1:degree</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S17">for </span><span class="S0">j = 0:i</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S0">out</span><span class="S0">(:, end+1) = (X1.^(i-j)).*(X2.^j);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S17">end</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">end</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">end</span></span></div></div></div><div class = "S11"><span class = "S2"><span class="S0">Implementation of sigmoid function</span></span></div><div class = "S4"><span class = "S2"><span class="S0">The code works with vectors and matrices. For a matrix, function performs the sigmoid function on every element</span></span></div><div class = 'CodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">function </span><span class="S0">g = sigmoid(z)</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">%SIGMOID Compute sigmoid function</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% g = SIGMOID(z) computes the sigmoid of z.</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">g = zeros(size(z));</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">for </span><span class="S0">row_index = 1:size(z,1)</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S17">for </span><span class="S0">col_index = 1: size(z,2)</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> val = z(row_index, col_index);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> g(row_index, col_index) = 1/(1 + exp(-val));</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S17">end</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">end</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">end</span></span></div></div></div><div class = "S11"><span class = "S2"><span class="S0">Implementation of costFunctionReg</span></span></div><div class = 'CodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">function </span><span class="S0">[J, grad] = costFunctionReg(theta, X, y, lambda)</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% theta as the parameter for regularized logistic regression and the</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% gradient of the cost w.r.t. to the parameters. </span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% Initialize some useful values</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">m = length(y); </span><span class="S8">% number of training examples</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% We need to return the following variables correctly </span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">J = 0;</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">grad = zeros(size(theta));</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">for </span><span class="S0">index = 1:m</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> y_i = y(index);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> x_i = X(index,:);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> h_theta_i = sigmoid(x_i * theta);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> J = J + ( -y_i * log(h_theta_i) - (1-y_i) * log(1-h_theta_i ) );</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">end</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">J = J/m;</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">total = sum(theta.^2);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">total = total - theta(1)^2; </span><span class="S8">%We do not regularize theta_zero</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">J = J + (lambda/(2*m)) * total;</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">total = 0;</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">for </span><span class="S0">index = 1:m</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> y_i = y(index);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> x_i = X(index,:);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> h_theta_i = sigmoid(x_i * theta);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> total = total + (h_theta_i - y_i) * X(index,1);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">end</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">grad(1) = total / m;</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">for </span><span class="S0">theta_index = 2:size(theta)</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> total = 0;</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S17">for </span><span class="S0">index = 1:m</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> y_i = y(index);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> x_i = X(index,:);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> h_theta_i = sigmoid(x_i * theta);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> total = total + (h_theta_i - y_i) * X(index,theta_index);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S17">end</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> total = total/m;</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> grad(theta_index) = total + (lambda/m) * theta(theta_index);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">end</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% =============================================================</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">end</span></span></div></div></div><div class = "S11"><span class = "S2"><span class="S0">Implementation of plotDecisionBoundary</span></span></div><div class = 'CodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">function </span><span class="S0">plotDecisionBoundary(theta, X, y)</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">%PLOTDECISIONBOUNDARY Plots the data points X and y into a new figure with</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">%the decision boundary defined by theta</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% PLOTDECISIONBOUNDARY(theta, X,y) plots the data points with + for the </span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% positive examples and o for the negative examples. X is assumed to be </span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% a either </span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% 1) Mx3 matrix, where the first column is an all-ones column for the </span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% intercept.</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% 2) MxN, N>3 matrix, where the first column is all-ones</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% Plot Data</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">plotData(X(:,2:3), y);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">hold </span><span class="S9">on</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">if </span><span class="S0">size(X, 2) <= 3</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S8">% Only need 2 points to define a line, so choose two endpoints</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> plot_x = [min(X(:,2))-2, max(X(:,2))+2];</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S8">% Calculate the decision boundary line</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> plot_y = (-1./theta(3)).*(theta(2).*plot_x + theta(1));</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S8">% Plot, and adjust axes for better viewing</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> plot(plot_x, plot_y);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S8">% Legend, specific for the exercise</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> legend(</span><span class="S9">'Admitted'</span><span class="S0">, </span><span class="S9">'Not admitted'</span><span class="S0">, </span><span class="S9">'Decision Boundary'</span><span class="S0">);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> axis([30, 100, 30, 100]);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">else</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S8">% Here is the grid range</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> u = linspace(-1, 1.5, 50);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> v = linspace(-1, 1.5, 50);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> z = zeros(length(u), length(v));</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S8">% Evaluate z = theta*x over the grid</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S17">for </span><span class="S0">i = 1:length(u)</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S17">for </span><span class="S0">j = 1:length(v)</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> z(i,j) = mapFeature(u(i), v(j))*theta;</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S17">end</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S17">end</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> z = z'; </span><span class="S8">% important to transpose z before calling contour</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S8">% Plot z = 0</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S8">% Notice you need to specify the range [0, 0]</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> contour(u, v, z, [0, 0], </span><span class="S9">'LineWidth'</span><span class="S0">, 2);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">end</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">hold </span><span class="S9">off</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">end</span></span></div></div></div><div class = "S11"><span class = "S2"><span class="S0">Implementation of predict</span></span></div><div class = 'CodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">function </span><span class="S0">p = predict(theta, X)</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">%PREDICT Predict whether the label is 0 or 1 using learned logistic </span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">%regression parameters theta</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% p = PREDICT(theta, X) computes the predictions for X using a </span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% threshold at 0.5 (i.e., if sigmoid(theta'*x) >= 0.5, predict 1)</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">m = size(X, 1); </span><span class="S8">% Number of training examples</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0">p = zeros(m, 1);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">for </span><span class="S0">index = 1:m</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> x_i = X(index,:);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> h_theta_i = sigmoid(x_i * theta);</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S17">if</span><span class="S0">(h_theta_i<.5)</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> p(index) = 0;</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S17">else</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> p(index) = 1;</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"> </span><span class="S17">end</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">end</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S8">% =========================================================================</span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S0"></span></span></div></div><div class = 'inlineWrapper'><div class = "S6 lineNode"><span class = "S7"><span class="S17">end</span></span></div></div></div></div></div><br><!-- <br>##### SOURCE BEGIN #####<br>%% Regularized logistic regression for quality assurance<br>%% Problem statement<br>% During quality assurance (QA), each microchip from a fabrication plant goes <br>% through various tests to ensure it is functioning correctly. Suppose you are <br>% the product manager of the factory and you have the test results for some microchips <br>% on two different tests. From these two tests, you would like to determine whether <br>% the microchips should be accepted or rejected. To help you make the decision, <br>% you have a dataset of test results on past microchips, from which you can build <br>% a logistic regression model.<br>%% Load data<br>% The file QA_data.txt contains the dataset for our logistic regression problem. <br>% The first two columns contains the test scores and the third column contains <br>% a label which indicateds verdict. The dataset is loaded from the data file into <br>% the variables X and y:<br><br>%% Load Data<br>% The first two columns contains the X values and the third column<br>% contains the label (y).<br><br>data = load('QA_data.txt');<br>X = data(:, [1, 2]); y = data(:, 3);<br>%% Plot data<br>% Before starting to implement any learning algorithm, it is always good to <br>% visualize the data if possible. We start the exercise by first plotting the <br>% data to understand the problem we are working with.<br><br>plotData(X, y);<br>%Implementation of plotData is given at the last section of document<br><br>% Put some labels <br>hold on;<br><br>% Labels and Legend<br>xlabel('Microchip Test 1');<br>ylabel('Microchip Test 2');<br><br>% Specified in plot order<br>legend('y = 1', 'y = 0');<br><br>title('Plot of training data');<br>hold off;<br>%% <br>% The axes are the two test scores, and the positive (_y _= 1, accepted) <br>% and negative (_y _= 0, rejected) examples are shown with different markers. <br>% Our dataset cannot be separated into positive and negative examples by a straight-line <br>% through the plot. Therefore, a straightforward application of logistic regression <br>% will not perform well on this dataset since logistic regression will only be <br>% able to find a linear decision boundary. <br>%% *Feature mapping*<br>% One way to fit the data better is to create more features from each data point. <br>% we will map the features into all polynomial terms of _x_1 and _x_2 up to the <br>% sixth power.<br>% <br>% $$\mathrm{mapFeature}\left(x\right)=\left\lbrack \begin{array}{c}1\\x_1 <br>% \\x_2 \\x_1^2 \\x_1 x_2 \\x_2^2 \\x_1^3 \\\ldotp \ldotp \ldotp \\x_1 x_2^5 \\x_2^6 <br>% \end{array}\right\rbrack$$<br>% <br>% As a result of this mapping, our vector of two features (the scores on <br>% two QA tests) has been transformed into a 28-dimensional vector. A logistic <br>% regression classifier trained on this higher-dimension feature vector will have <br>% a more complex decision boundary and will appear nonlinear when drawn in our <br>% 2-dimensional plot.<br>% <br>% While the feature mapping allows us to build a more expressive classifier, <br>% it also more susceptible to overfitting.<br><br>% Add Polynomial Features<br><br>% Note that mapFeature also adds a column of ones for us, so the intercept<br>% term is handled<br>X = mapFeature(X(:,1), X(:,2));<br>%Implementation of mapFeature is at the end section<br>%% Sigmoid function<br>% The logistic regression hypothesis is defined as:<br>% <br>% $$h\left(\theta \right)=g\left(\theta^T x\right)$$<br>% <br>% where function _g _is the sigmoid function. The sigmoid function is defined <br>% as:<br>% <br>% $$g\left(z\right)=\frac{1}{1+e^{-z} }$$<br>% <br>% For large positive values of x, the sigmoid should be close to 1, while <br>% for large negative values, the sigmoid should be close to 0. for 0 it should <br>% be exactly 0.5. Implementation of sigmoid function is given at the end of document.<br>%% *Cost function and gradient*<br>% The regularized cost function in logistic regression is <br>% <br>% $$J\left(\theta \right)=\frac{1}{m}\sum_{i=1}^m \left\lbrack -y^{\left(i\right)} <br>% \log \left(h_{\theta } \left(x^{\left(i\right)} \right)\right)-\left(1-y^{\left(i\right)} <br>% \right)\log \left(1-h_{\theta } \left(x^{\left(i\right)} \right)\right)\right\rbrack <br>% +\frac{\lambda }{2m}\sum_{j=1}^n \theta_j^2$$<br>% <br>% The gradient of the cost function is a vector where the _j_th element is <br>% defined as follows:<br>% <br>% $$\frac{\partial }{\partial \theta_j }J\left(\theta \right)=\frac{1}{m}\sum_{i=1}^m <br>% \left(h_{\theta } \left(x^{\left(i\right)} \right)-y^{\left(i\right)} \right)x_j^{\left(i\right)} <br>% \;\mathrm{for}\;j=0$$<br>% <br>% $$\left(\frac{1}{m}\sum_{i=1}^m \left(h_{\theta } \left(x^{\left(i\right)} <br>% \right)-y^{\left(i\right)} \right)x_j^{\left(i\right)} \;\right)+\frac{\lambda <br>% }{m}\theta_j \;\mathrm{for}\;j\ge 1$$<br>% <br>% Let' compute initial cost using the initial value of _θ _(initialized to <br>% all zeros).<br><br>% Initialize fitting parameters<br>initial_theta = zeros(size(X, 2), 1);<br><br>% Set regularization parameter lambda to 1<br>lambda = 1;<br><br>% Compute and display initial cost and gradient for regularized logistic<br>% regression<br>[cost, grad] = costFunctionReg(initial_theta, X, y, lambda);<br>%Implementation of costFunctionReg is at the end section<br>fprintf('Cost at initial theta (zeros): %f\n', cost);<br>%% *Learning parameters using builtin function*<br>% Octave/MATLAB’s fminunc is an optimization solver that finds the minimum of <br>% an unconstrained function. For logistic regression, we want to optimize the <br>% cost function _J_(_θ_) with parameters _θ_.<br>% <br>% Concretely, we are going to use fminunc to find the best parameters _θ <br>% _for the logistic regression cost function, given a fixed dataset (of _X _and <br>% _y _values) we will pass to fminunc the following inputs: <br>% <br>% * The initial values of the parameters we are trying to optimize.<br>% * A function that, when given the training set and a particular _θ_, computes <br>% the logistic regression cost and gradient with respect to _θ _for the dataset <br>% (_X_, _y_).<br>% * Regularization paramaeter lambda<br>% <br>% We already implemented everything needed to use the builtin function so <br>% let's use that<br><br>% Set Options<br>options = optimset('GradObj', 'on', 'MaxIter', 400);<br><br>% Optimize<br>[theta, J, exit_flag] = fminunc(@(t)(costFunctionReg(t, X, y, lambda)), initial_theta, options);<br>%% <br>% In this code snippet, we first defined the options to be used with fminunc. <br>% Specifically, we set the GradObj option to on, which tells fminunc that our <br>% function returns both the cost and the gradient. This allows fminunc to use <br>% the gradient when minimizing the function. Furthermore, we set the MaxIter option <br>% to 400, so that fminunc will run for at most 400 steps before it terminates. <br>% To specify the actual function we are minimizing, we use a "short-hand" for <br>% specifying functions with the $@\left(t\right)\;\left(\mathrm{costFunction}\left(t,X,y\right)\right)$. <br>% This creates a function, with argument t, which calls your costFunction. This <br>% allows us to wrap the costFunction for use with fminunc.<br>%% Plot decision boundary<br>% We plot the non-linear decision boundary by computing the classifier’s predictions <br>% on an evenly spaced grid and then and drew a contour plot of where the predictions <br>% change from _y _= 0 to _y _= 1.<br><br>% Plot Boundary<br>plotDecisionBoundary(theta, X, y);<br>hold on;<br>title(sprintf('lambda = %g', lambda))<br><br>% Labels and Legend<br>xlabel('Microchip Test 1')<br>ylabel('Microchip Test 2')<br><br>legend('y = 1', 'y = 0', 'Decision boundary')<br>hold off;<br>%% Performance on training data<br>% Let's check how our model is performing on the training data<br><br>% Compute accuracy on our training set<br>p = predict(theta, X);<br>%Implementation of predict is given in the last section<br>fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);<br>%% Effect of regularization parameter<br>% Let's see how changing value of regularization parameter effects decision <br>% boundary by plotting graphs<br><br>lambda = 0;<br>[theta, J, exit_flag] = fminunc(@(t)(costFunctionReg(t, X, y, lambda)), initial_theta, options);<br>plotDecisionBoundary(theta, X, y);<br><br>title(sprintf('lambda = %g', lambda));<br>%% <br>% Without any regularization our model overfits which is bad for generalization<br><br><br>lambda = 100;<br>[theta, J, exit_flag] = fminunc(@(t)(costFunctionReg(t, X, y, lambda)), initial_theta, options);<br>plotDecisionBoundary(theta, X, y);<br><br>title(sprintf('lambda = %g', lambda));<br>%% <br>% Too much regularization causes underfiting which is also bad for generalization<br>%% Implementation of functions<br>% Implementation of plotData<br>%%<br>function plotData(X, y)<br>%PLOTDATA Plots the data points X and y into a new figure <br>% PLOTDATA(x,y) plots the data points with + for the positive examples<br>% and o for the negative examples. X is assumed to be a Mx2 matrix.<br><br>% Create New Figure<br>figure; hold on;<br><br>pos = find(y==1); neg = find(y == 0);<br>% Plot Examples<br>plot(X(pos, 1), X(pos, 2), 'k+','LineWidth', 2,'MarkerSize', 7);<br>plot(X(neg, 1), X(neg, 2), 'ko', 'MarkerFaceColor', 'y','MarkerSize', 7);<br>% =========================================================================<br>hold off;<br><br>end<br>%% <br>% Implementation of mapFeature<br><br>function out = mapFeature(X1, X2)<br>% MAPFEATURE Feature mapping function to polynomial features<br>%<br>% MAPFEATURE(X1, X2) maps the two input features<br>% to quadratic features used in the regularization exercise.<br>%<br>% Returns a new feature array with more features, comprising of <br>% X1, X2, X1.^2, X2.^2, X1*X2, X1*X2.^2, etc..<br>%<br>% Inputs X1, X2 must be the same size<br>%<br><br>degree = 6;<br>out = ones(size(X1(:,1)));<br>for i = 1:degree<br> for j = 0:i<br> out(:, end+1) = (X1.^(i-j)).*(X2.^j);<br> end<br>end<br><br>end<br>%% <br>% Implementation of sigmoid function<br>% <br>% The code works with vectors and matrices. For a matrix, function performs <br>% the sigmoid function on every element<br><br>function g = sigmoid(z)<br>%SIGMOID Compute sigmoid function<br>% g = SIGMOID(z) computes the sigmoid of z.<br><br>g = zeros(size(z));<br>for row_index = 1:size(z,1)<br> for col_index = 1: size(z,2)<br> val = z(row_index, col_index);<br> g(row_index, col_index) = 1/(1 + exp(-val));<br> end<br>end<br>end<br>%% <br>% Implementation of costFunctionReg<br><br>function [J, grad] = costFunctionReg(theta, X, y, lambda)<br>%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization<br>% J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using<br>% theta as the parameter for regularized logistic regression and the<br>% gradient of the cost w.r.t. to the parameters. <br><br>% Initialize some useful values<br>m = length(y); % number of training examples<br><br>% We need to return the following variables correctly <br>J = 0;<br>grad = zeros(size(theta));<br><br>for index = 1:m<br> y_i = y(index);<br> x_i = X(index,:);<br> h_theta_i = sigmoid(x_i * theta);<br> J = J + ( -y_i * log(h_theta_i) - (1-y_i) * log(1-h_theta_i ) );<br>end<br><br>J = J/m;<br><br>total = sum(theta.^2);<br><br>total = total - theta(1)^2; %We do not regularize theta_zero<br><br>J = J + (lambda/(2*m)) * total;<br><br><br>total = 0;<br>for index = 1:m<br> y_i = y(index);<br> x_i = X(index,:);<br> h_theta_i = sigmoid(x_i * theta);<br> total = total + (h_theta_i - y_i) * X(index,1);<br>end<br>grad(1) = total / m;<br><br>for theta_index = 2:size(theta)<br> total = 0;<br> for index = 1:m<br> y_i = y(index);<br> x_i = X(index,:);<br> h_theta_i = sigmoid(x_i * theta);<br> total = total + (h_theta_i - y_i) * X(index,theta_index);<br> end<br> total = total/m;<br> grad(theta_index) = total + (lambda/m) * theta(theta_index);<br>end<br><br>% =============================================================<br>end<br>%% <br>% Implementation of plotDecisionBoundary<br><br>function plotDecisionBoundary(theta, X, y)<br>%PLOTDECISIONBOUNDARY Plots the data points X and y into a new figure with<br>%the decision boundary defined by theta<br>% PLOTDECISIONBOUNDARY(theta, X,y) plots the data points with + for the <br>% positive examples and o for the negative examples. X is assumed to be <br>% a either <br>% 1) Mx3 matrix, where the first column is an all-ones column for the <br>% intercept.<br>% 2) MxN, N>3 matrix, where the first column is all-ones<br><br>% Plot Data<br>plotData(X(:,2:3), y);<br>hold on<br><br>if size(X, 2) <= 3<br> % Only need 2 points to define a line, so choose two endpoints<br> plot_x = [min(X(:,2))-2, max(X(:,2))+2];<br><br> % Calculate the decision boundary line<br> plot_y = (-1./theta(3)).*(theta(2).*plot_x + theta(1));<br><br> % Plot, and adjust axes for better viewing<br> plot(plot_x, plot_y);<br> <br> % Legend, specific for the exercise<br> legend('Admitted', 'Not admitted', 'Decision Boundary');<br> axis([30, 100, 30, 100]);<br>else<br> % Here is the grid range<br> u = linspace(-1, 1.5, 50);<br> v = linspace(-1, 1.5, 50);<br><br> z = zeros(length(u), length(v));<br> % Evaluate z = theta*x over the grid<br> for i = 1:length(u)<br> for j = 1:length(v)<br> z(i,j) = mapFeature(u(i), v(j))*theta;<br> end<br> end<br> z = z'; % important to transpose z before calling contour<br><br> % Plot z = 0<br> % Notice you need to specify the range [0, 0]<br> contour(u, v, z, [0, 0], 'LineWidth', 2);<br>end<br>hold off<br><br>end<br>%% <br>% Implementation of predict<br><br>function p = predict(theta, X)<br>%PREDICT Predict whether the label is 0 or 1 using learned logistic <br>%regression parameters theta<br>% p = PREDICT(theta, X) computes the predictions for X using a <br>% threshold at 0.5 (i.e., if sigmoid(theta'*x) >= 0.5, predict 1)<br><br>m = size(X, 1); % Number of training examples<br><br>p = zeros(m, 1);<br><br>for index = 1:m<br> x_i = X(index,:);<br> h_theta_i = sigmoid(x_i * theta);<br> if(h_theta_i<.5)<br> p(index) = 0;<br> else<br> p(index) = 1;<br> end<br>end<br>% =========================================================================<br><br>end<br>##### SOURCE END #####<br>--></body></html>