assignments:assignment5
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assignments:assignment5 [2015/10/31 09:07] asa |
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| - | ==== Data ==== | + | ===== Data ===== |
| In this assignment you will compare several feature selection methods on several datasets. | In this assignment you will compare several feature selection methods on several datasets. | ||
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| where $\mu_i^{(+)}$ is the average of feature $i$ in the positive examples, | where $\mu_i^{(+)}$ is the average of feature $i$ in the positive examples, | ||
| where $\sigma_i^{(+)}$ is the standard deviation of feature $i$ in the positive examples, and $\mu_i^{(-)}, \sigma_i^{(-)}$ are defined analogously for the negative examples. | where $\sigma_i^{(+)}$ is the standard deviation of feature $i$ in the positive examples, and $\mu_i^{(-)}, \sigma_i^{(-)}$ are defined analogously for the negative examples. | ||
| - | In order for your function to work with the scikit-learn filter framework it needs to have two parameters: ''golub(X, y)'', where X is the feature matrix, and y is a vector of labels. All scikit-learn filter methods return two values - a vector of scores, and a vector of p-values. For our purposes, we won't use p-values associated with the Golub scores, so just return the computed vector of scores twice: if your vector of scores is stored in an array called scores, have the return statement be: | + | In order for your function to work with the scikit-learn filter framework it needs to have two parameters: ''golub(X, y)'', where X is the feature matrix, and y is a vector of labels. All scikit-learn filter methods return two values - a vector of scores, and a vector of p-values. For our purposes, we won't use p-values associated with the Golub scores, so just return the computed vector of scores twice (''return scores,scores'' if your vector of scores is stored in an array called scores) |
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| - | ''return scores,scores'' | + | |
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| ===== Part 2: Embedded methods: L1 SVM ===== | ===== Part 2: Embedded methods: L1 SVM ===== | ||
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| Compare the accuracy of an L1 SVM to an SVM that uses RFE to select relevant features. | Compare the accuracy of an L1 SVM to an SVM that uses RFE to select relevant features. | ||
| - | Compare the accuracy of a regular L2 SVM trained on those features with an L2 SVM trained on all the features computed using 5-fold cross-validation. | + | Compare the accuracy of a regular L2 SVM trained on the features selected by the L1 SVM with the accuracy of an L2 SVM trained on all the features (compute accuracy using 5-fold cross-validation). |
| It has been argued in the literature that L1-SVMs often leads to solutions that are too sparse. As a workaround, implement the following strategy: | It has been argued in the literature that L1-SVMs often leads to solutions that are too sparse. As a workaround, implement the following strategy: | ||
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| * Create $k$ sub-samples of the data in which you randomly choose 80% of the examples. | * Create $k$ sub-samples of the data in which you randomly choose 80% of the examples. | ||
| * For each sub-sample train an L1-SVM. | * For each sub-sample train an L1-SVM. | ||
| - | * For each feature compute a score that is the average weight vector | + | * For each feature compute a score that is the number of sub-samples for which that feature yielded a non-zero score. |
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| + | ===== Part 3: Method comparison ===== | ||
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| + | Compute the accuracy of a Linear L2 SVM as a function of the number of selected features on the leukemia and Arcene datasets for the following feature selection methods: | ||
| + | |||
| + | * The Golub score | ||
| + | * L1-SVM feature selection using subsamples | ||
| + | * RFE-SVM | ||
| + | |||
| + | Make sure that your evaluation provides an un-biased estimate of classifier performance. | ||
| + | Comment on the results. | ||
| + | For the above experiment you do not need to select the optimal value for the SVM soft-margin constant. | ||
| + | Compare these results to results obtained using internal cross-validation for selecting | ||
| + | the soft margin constant $C$ over a grid of values. | ||
| + | In writing your code, use scikit-learn's ability to combine analysis steps using the [[http://scikit-learn.org/stable/modules/pipeline.html |Pipeline class]]. This will be particularly useful for performing model selection. | ||
| - | Do your results change if you do model selection for the resulting classifier over a grid of values for the soft margin constant $C$? | ||
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| Grading sheet for assignment 3 | Grading sheet for assignment 3 | ||
| - | Part 1: 40 points. | + | Part 1: 15 points. |
| - | (10 points): Primal SVM formulation is correct | + | (15 points): Correct implementation of the Golub score |
| - | ( 7 points): Lagrangian found correctly | + | |
| - | ( 8 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: 10 points. | + | Part 2: 35 points. |
| + | (15 points): Comparison of L1 chosen features with use of all features. | ||
| + | (20 points): Correct implementation of L1-SVM feature selection using sub-samples. | ||
| Part 3: 40 points. | Part 3: 40 points. | ||
| - | (20 points): Accuracy as a function of parameters and discussion of the results | + | (25 points): Accuracy as a function of number of features and discussion of the results |
| - | (15 points): Comparison of normalized and non-normalized kernels and correct model selection | + | (15 points): Same, with model selection |
| - | ( 5 points): Visualization of the kernel matrix and observations made about it | + | |
| Report structure, grammar and spelling: 10 points | Report structure, grammar and spelling: 10 points | ||
assignments/assignment5.txt · Last modified: 2016/10/18 09:18 by asa
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