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--- assignments:assignment3 [2013/10/06 15:23]
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+++ assignments:assignment3 [2015/10/02 09:42]
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 ========= Assignment 3: Support Vector Machines ============
+Due:  October 20th at 6pm
 ===== Part 1:  SVM with no bias term =====
-Formulate a soft-margin SVM without the bias term, i.e. $f(\mathbf{x}) = \mathbf{w}^{T} \mathbf{x}$.
+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.
 Compare it to the standard SVM formulation.
-What is the implication of the difference on the design of SMO-like algorithms?
+As we discussed in class, SMO-type algorithms for the dual optimize the smallest number of variables at a time, which is two variables.
-Recall that SMO algorithms work by iteratively optimizing two variables at a time.
+Is this still the case for the formulation you have derived?
 Hint:  consider the difference in the constraints.
-===== Part 2:  Closest Centroid Algorithm =====
+===== Part 2:  Soft-margin SVM for separable data =====
-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 SVM for separable data =====
 Consider training a soft-margin SVM
-with $C$ set to some positive constant. Suppose the training data is linearly separable.
+with the soft margin constant $C$ 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
@@ Line 23: / Line 21: @@
 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?
+a hard margin SVM over a soft-margin SVM?  Explain!
-===== Part 4:  Using SVMs =====
+===== Part 3:  Using SVMs =====
 The data for this question comes from a database called SCOP (structural
@@ Line 33: / Line 31: @@
 problem
 of distinguishing a particular class of proteins from a selection of
-examples sampled from the rest of the SCOP database.
+examples sampled from the rest of the SCOP database
+using features derived from their sequence (note that a protein is an arbitrary length sequence over the alphabet of the 20 amino acids).
 I chose to represent the proteins in
 terms of their motif composition.  A sequence motif is a
-pattern of nucleotides/amino acids that is conserved in evolution.
+pattern of amino acids that is conserved in evolution.
 Motifs are usually associated with regions of the protein that are
 important for its function, and are therefore useful in differentiating between classes of proteins.
@@ Line 48: / Line 47: @@
 In this part of the assignment we will explore the dependence of classifier accuracy on
-the kernel, kernel parameters, kernel normalization, and SVM parameter soft-margin parameter.
+the kernel, kernel parameters, kernel normalization, and the SVM soft-margin parameter.
-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.
+In your implementation you can use the scikit-learn [[http://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html | svm]] class.
-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:
-<code python>
->>> from PyML import ker
->>> data.attachKernel(ker.Gaussian(gamma = 0.1))
-</code>
-or
-<code python>
->>> from PyML import her
->>> data.attachKernel(ker.Polynomial(degree = 3))
-</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:
@@ Line 73: / Line 55: @@
 $$
 $$
-K_{poly}(\mathbf{x}, \mathbf{x'}) = (1 + \mathbf{x}^T \mathbf{x}') ^{p}
+K_{poly}(\mathbf{x}, \mathbf{x'}) = (\mathbf{x}^T \mathbf{x}' + 1) ^{p}
 $$
-Plot the accuracy of the SVM, measured using the balnced success rate
+Plot the accuracy of the SVM, measured using the area under the ROC curve
 as a function of both the soft-margin parameter of the SVM, and the free parameter
 of the kernel function.
+Accuracy should be measured in five-fold cross-validation.
 Show a couple of representative cross sections of this plot for a given value
-of the ridge parameter, and for a given value of the kernel parameter.
+of the soft margin parameter, and for a given value of the kernel parameter.
 Comment on the results.  When exploring the values of a continuous
 classifier/kernel parameter it is
@@ Line 86: / Line 70: @@
 polynomial kernel is not such a parameter).
-For this type of sparse dataset it is useful to normalize the input features.
+Next, we will compare the accuracy of an SVM with a Gaussian kernel on the raw data with accuracy obtained when the data is normalized to be unit vectors (the values of the features of each example are divided by its norm).
-One way to do so is to divide each input example by its norm.  This is
+This is different than standardization which operates at the level of individual features.  Normalizing to unit vectors is more appropriate for this dataset as it is sparse, i.e. most of the features are zero.
-accomplished in PyML by:
+Perform your comparison by comparing the accuracy measured by the area under the ROC curve in five-fold cross validation.
-<code python>
+The optimal values of kernel parameters should be measured by cross-validation, where the optimal SVM/kernel parameters are chosen using grid search on the training set of each fold.
->>> data.normalize()
+Use the scikit-learn [[http://scikit-learn.org/stable/tutorial/statistical_inference/model_selection.html
-</code>
+ | grid-search]] class for model selection.
-Compare the results under this normalization with what you obtain
-without normalization.
-You can visualize the whole kernel matrix associated with the data using the following commands:
-<code python>
+Finally, visualize the kernel matrix associated with the dataset.
->>> from PyML import ker
->>> ker.showKernel(data)
-</code>
 Explain the structure that you are seeing in the plot (it is more
 interesting when the data is normalized).
+===== Submission =====
+Submit your report via C.  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>

CS545 fall 2016

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