assignments:assignment3
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assignments:assignment3 [2015/10/02 12:12] asa |
assignments:assignment3 [2015/10/07 12:04] asa |
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| Formulate a soft-margin SVM without the bias term, i.e. one where the discriminant function is equal to $\mathbf{w}^{T} \mathbf{x}$. | Formulate a soft-margin SVM without the bias term, i.e. one where the discriminant function is equal to $\mathbf{w}^{T} \mathbf{x}$. | ||
| Derive the saddle point conditions, KKT conditions and the dual. | Derive the saddle point conditions, KKT conditions and the dual. | ||
| - | Compare it to the standard SVM formulation. | + | Compare it to the standard SVM formulation that was derived in class. |
| - | As we discussed in class, SMO-type algorithms for the dual optimize the smallest number of variables at a time, which is two variables. | + | In class we discussed SMO-type algorithms for optimizing the dual SVM. At each step SMO optimizes two variables at a time, which is the smallest number possible. |
| - | Is this still the case for the formulation you have derived? | + | Is this still the case for the formulation you have derived? In other words, is two the smallest number of variables that can be optimized at a time? |
| Hint: consider the difference in the constraints. | Hint: consider the difference in the constraints. | ||
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| K_{gauss}(\mathbf{x}, \mathbf{x'}) = \exp(-\gamma || \mathbf{x} - \mathbf{x}' ||^2) | K_{gauss}(\mathbf{x}, \mathbf{x'}) = \exp(-\gamma || \mathbf{x} - \mathbf{x}' ||^2) | ||
| $$ | $$ | ||
| + | and | ||
| $$ | $$ | ||
| - | K_{poly}(\mathbf{x}, \mathbf{x'}) = (\mathbf{x}^T \mathbf{x}' + 1) ^{p} | + | K_{poly}(\mathbf{x}, \mathbf{x'}) = (\mathbf{x}^T \mathbf{x}' + 1) ^{p}. |
| $$ | $$ | ||
| Line 110: | Line 111: | ||
| Part 1: 40 points. | Part 1: 40 points. | ||
| (10 points): Primal SVM formulation is correct | (10 points): Primal SVM formulation is correct | ||
| - | (10 points): Lagrangian found correctly | + | ( 7 points): Lagrangian found correctly |
| - | (10 points): Derivation of saddle point equations | + | ( 8 points): Derivation of saddle point equations |
| (10 points): Derivation of the dual | (10 points): Derivation of the dual | ||
| ( 5 points): Discussion of the implication of the form of the dual for SMO-like algorithms | ( 5 points): Discussion of the implication of the form of the dual for SMO-like algorithms | ||
assignments/assignment3.txt · Last modified: 2016/09/20 09:34 by asa
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