assignments:assignment3
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assignments:assignment3 [2013/10/06 13:33] asa |
assignments:assignment3 [2013/10/06 20:54] asa |
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| ========= Assignment 3: Support Vector Machines ============ | ========= Assignment 3: Support Vector Machines ============ | ||
| + | |||
| + | Due: October 20th at 6pm | ||
| ===== Part 1: SVM with no bias term ===== | ===== Part 1: SVM with no bias term ===== | ||
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| Express the closest centroid algorithm in terms of kernels, i.e. determine how the coefficients $\alpha_i$ will be computed using a given labeled dataset. | Express the closest centroid algorithm in terms of kernels, i.e. determine how the coefficients $\alpha_i$ will be computed using a given labeled dataset. | ||
| - | ===== Part 3: Using SVMs ===== | + | ===== Part 3: Soft-margin SVM for separable data ===== |
| + | |||
| + | Consider training a soft-margin SVM | ||
| + | with $C$ set to some positive constant. Suppose the training data is linearly separable. | ||
| + | Since increasing the $\xi_i$ can only increase the objective of the primal problem (which | ||
| + | we are trying to minimize), at the optimal solution to the primal problem, all the | ||
| + | training examples will have $\xi_i$ equal | ||
| + | to zero. True or false? Explain! | ||
| + | Given a linearly separable dataset, is it necessarily better to use a | ||
| + | a hard margin SVM over a soft-margin SVM? | ||
| + | |||
| + | ===== Part 4: Using SVMs ===== | ||
| The data for this question comes from a database called SCOP (structural | The data for this question comes from a database called SCOP (structural | ||
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| K_{poly}(\mathbf{x}, \mathbf{x'}) = (1 + \mathbf{x}^T \mathbf{x}') ^{p} | K_{poly}(\mathbf{x}, \mathbf{x'}) = (1 + \mathbf{x}^T \mathbf{x}') ^{p} | ||
| $$ | $$ | ||
| - | Plot the accuracy of the SVM, measured using the balnced success rate | + | Plot the accuracy of the SVM, measured using the balanced success rate |
| as a function of both the soft-margin parameter of the SVM, and the free parameter | as a function of both the soft-margin parameter of the SVM, and the free parameter | ||
| of the kernel function. | of the kernel function. | ||
assignments/assignment3.txt · Last modified: 2016/09/20 09:34 by asa
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