assignments:assignment3
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| ===== Part 2: Closest Centroid Algorithm ===== | ===== Part 2: Closest Centroid Algorithm ===== | ||
| - | Express the closest centroid algorithm in terms of kernels, i.e. determine how the coefficients $\alpha_i$ will be determined 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 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 | ||
| Line 36: | Line 47: | ||
| * A. Ben-Hur and D. Brutlag. [[http://bioinformatics.oxfordjournals.org/content/19/suppl_1/i26.abstract | Remote homology detection: a motif based approach]]. In: Proceedings, eleventh international conference on intelligent systems for molecular biology. Bioinformatics 19(Suppl. 1): i26-i33, 2003. | * A. Ben-Hur and D. Brutlag. [[http://bioinformatics.oxfordjournals.org/content/19/suppl_1/i26.abstract | Remote homology detection: a motif based approach]]. In: Proceedings, eleventh international conference on intelligent systems for molecular biology. Bioinformatics 19(Suppl. 1): i26-i33, 2003. | ||
| - | Download the dataset associated with this assignment from the homework | + | In this part of the assignment we will explore the dependence of classifier accuracy on |
| - | page of the course. | + | the kernel, kernel parameters, kernel normalization, and SVM parameter soft-margin parameter. |
| - | In this assignment we will explore the dependence of classifier accuracy on | + | The use of the SVM class is discussed in the PyML [[http://pyml.sourceforge.net/tutorial.html#svms|tutorial]], and by using help(SVM) in the python interpreter. |
| - | the kernel, kernel parameters, kernel normalization, and SVM parameter. | + | |
| - | The use of the SVM class is discussed in the PyML [[http://pyml.sourceforge.net/tutorial.html#svms|tutorial]]. | + | |
| - | By default a dataset is instantiated with a linear kernel attached to it. | + | By default, a dataset is instantiated with a linear kernel attached to it. |
| To use a different kernel you need to attach a new kernel to the dataset: | To use a different kernel you need to attach a new kernel to the dataset: | ||
| <code python> | <code python> | ||
| Line 53: | Line 62: | ||
| >>> data.attachKernel(ker.Polynomial(degree = 3)) | >>> data.attachKernel(ker.Polynomial(degree = 3)) | ||
| </code> | </code> | ||
| + | Alternatively, you can instantiate an SVM with a given kernel: | ||
| + | <code python> | ||
| + | >>> classifier = SVM(ker.Gaussian(gamma = 0.1)) | ||
| + | </code> | ||
| + | This will override the kernel the data is associated with. | ||
| + | |||
| In this question we will consider both the Gaussian and polynomial kernels: | In this question we will consider both the Gaussian and polynomial kernels: | ||
| $$ | $$ | ||
| - | K_{gaus}(\mathbf{x}, \mathbf{x'}) = \exp(-\gamma || \mathbf{x} - \mathbf{x}' ||^2) | + | K_{gauss}(\mathbf{x}, \mathbf{x'}) = \exp(-\gamma || \mathbf{x} - \mathbf{x}' ||^2) |
| $$ | $$ | ||
| $$ | $$ | ||
| 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 classifier, measured using the success rate and the area under the ROC curve | + | Plot the accuracy of the SVM, measured using the balnced success rate |
| - | as a function of both the ridge parameter of the classifier, 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. | ||
| Show a couple of representative cross sections of this plot for a given value | Show a couple of representative cross sections of this plot for a given value | ||
| Line 67: | Line 82: | ||
| Comment on the results. When exploring the values of a continuous | Comment on the results. When exploring the values of a continuous | ||
| classifier/kernel parameter it is | classifier/kernel parameter it is | ||
| - | useful use values that are distributed on an exponential grid, | + | useful to use values that are distributed on an exponential grid, |
| i.e. something like 0.01, 0.1, 1, 10, 100 (note that the degree of the | i.e. something like 0.01, 0.1, 1, 10, 100 (note that the degree of the | ||
| polynomial kernel is not such a parameter). | polynomial kernel is not such a parameter). | ||
| - | + | For this type of sparse dataset it is useful to normalize the input features. | |
| - | For this type of sparse dataset it is useful to normalize the input features before | + | |
| - | training and testing your classifier. | + | |
| One way to do so is to divide each input example by its norm. This is | One way to do so is to divide each input example by its norm. This is | ||
| accomplished in PyML by: | accomplished in PyML by: | ||
assignments/assignment3.txt · Last modified: 2016/09/20 09:34 by asa
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