assignments:assignment3
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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 ===== | ||
| Line 12: | Line 14: | ||
| ===== 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 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 | ||
| Line 36: | Line 49: | ||
| * 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 64: | ||
| >>> 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 balanced 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 84: | ||
| 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: | ||
| Line 89: | Line 104: | ||
| Explain the structure that you are seeing in the plot (it is more | Explain the structure that you are seeing in the plot (it is more | ||
| interesting when the data is normalized). | interesting when the data is normalized). | ||
| + | |||
| + | ===== Submission ===== | ||
| + | |||
| + | Submit your report via RamCT. Python code can be displayed in your report if it is succinct (not more than a page or two at the most) or submitted separately. The latex sample document shows how to display Python code in a latex document. | ||
| + | Also, please check-in a text file named README that describes what you found most difficult in completing this assignment (or provide that as a comment on ramct). | ||
| + | |||
| + | ===== Grading ===== | ||
| + | |||
| + | Here is what the grade sheet will look like for this assignment. A few general guidelines for this and future assignments in the course: | ||
| + | |||
| + | * Always provide a description of the method you used to produce a given result in sufficient detail such that the reader can reproduce your results on the basis of the description. You can use a few lines of python code or pseudo-code. If your code is more than a few lines, you can include it as an appendix to your report. For example, for the first part of the assignment, provide the protocol you use to evaluate classifier accuracy. | ||
| + | * You can provide results in the form of tables, figures or text - whatever form is most appropriate for a given problem. There are no rules about how much space each answer should take. BUT we will take off points if we have to wade through a lot of redundant data. | ||
| + | * In any machine learning paper there is a discussion of the results. There is a similar expectation from your assignments that you reason about your results. For example, for the learning curve problem, what can you say on the basis of the observed learning curve? | ||
| + | |||
| + | <code> | ||
| + | Grading sheet for assignment 2 | ||
| + | |||
| + | Part 1: 30 points. | ||
| + | (10 points): Lagrangian found correctly | ||
| + | ( 5 points): Derivation of saddle point equations | ||
| + | (10 points): Derivation of the dual | ||
| + | ( 5 points): Discussion of the implication of the form of the dual for SMO-like algorithms | ||
| + | |||
| + | Part 2: 15 points. | ||
| + | |||
| + | Part 3: 15 points. | ||
| + | |||
| + | Part 1: 40 points. | ||
| + | (25 points): Accuracy as a function of parameters and discussion of the results | ||
| + | (10 points): Comparison of normalized and non-normalized results | ||
| + | ( 5 points): Visualization of the kernel matrix and observations made about it | ||
| + | |||
| + | Report structure, grammar and spelling: 15 points | ||
| + | ( 5 points): Heading and subheading structure easy to follow and | ||
| + | clearly divides report into logical sections. | ||
| + | ( 5 points): Code, math, figure captions, and all other aspects of | ||
| + | report are well-written and formatted. | ||
| + | ( 5 points): Grammar, spelling, and punctuation. | ||
| + | </code> | ||
assignments/assignment3.txt · Last modified: 2016/09/20 09:34 by asa
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