This question covers the Support Vector Machine and requires you to refer to the following two-dimensional...

  

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This question covers the Support Vector Machine and requires you to refer to the following two-dimensional training data: arg max x1 -3 (a) [1 mark] Plot the data (no need to provide any code if you do this in Python). Is the data linearly separable? n i=1 -2 -1 0 1 2 3 (b) [11 marks] In this section, we will build an SVM classifier by hand. Recall that the dual formulation of the SVM classifier for a dataset of size n is n - 04-19 i=1 j=1 I2 Y 9 -1 4 -1 1 -1 -3 1 1 1 4 -1 9 -1 subject to a, 20, for all i, ai = 0. Solve for (a,...,07) for the provided dataset. (Hint: Using the plot in the previous section and your knowledge of SVMs, try to simplify the (dual) objective before doing any calculus.) (c) [3 marks] For your SVM, compute the corresponding weight vector (w R) and bias t. Superimpose a plot of the SVM onto the scatter in (a). What is the margin for this model? (d) [2 marks] Discuss briefly the following claim: Linear classifiers are unable to represent non-linear functions. (e) [3 marks] In your own words, explain what is meant by the 'kernel trick'. Why is this such an important technique for machine learning? This question covers the Support Vector Machine and requires you to refer to the following two-dimensional training data: arg max x1 -3 (a) [1 mark] Plot the data (no need to provide any code if you do this in Python). Is the data linearly separable? n i=1 -2 -1 0 1 2 3 (b) [11 marks] In this section, we will build an SVM classifier by hand. Recall that the dual formulation of the SVM classifier for a dataset of size n is n - 04-19 i=1 j=1 I2 Y 9 -1 4 -1 1 -1 -3 1 1 1 4 -1 9 -1 subject to a, 20, for all i, ai = 0. Solve for (a,...,07) for the provided dataset. (Hint: Using the plot in the previous section and your knowledge of SVMs, try to simplify the (dual) objective before doing any calculus.) (c) [3 marks] For your SVM, compute the corresponding weight vector (w R) and bias t. Superimpose a plot of the SVM onto the scatter in (a). What is the margin for this model? (d) [2 marks] Discuss briefly the following claim: Linear classifiers are unable to represent non-linear functions. (e) [3 marks] In your own words, explain what is meant by the 'kernel trick'. Why is this such an important technique for machine learning?