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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: Soft-margin for separable data ===== | + | ===== Part 3: Soft-margin SVM for separable data ===== |
Consider training a soft-margin SVM | Consider training a soft-margin SVM | ||
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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. | ||
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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> |