Problem #1
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10/11:
The goal of this problem is to help you appreciate the importance
of the feature space in which active learning is performed. We've
provided you two feature mappings: phi_1 and phi_2. The first one
maps X_in to a space that is essentially the same as the original space
(except for an added offset). The second one, on the other hand,
maps X_in to a space that is quite different. Thus, if the regression
is linear in phi_2's space, the problem discusses what happens when
active learning is performed in phi_1's space (which is almost like
the original space) vs. phi_2's space.
To clarify this, we're updating the problem set so that the last sentence
of Prob 1(c) should instead be:
"For each set of points, use the feature mapping $\phi_2$ to perform
regression and compute the resulting mean squared prediction errors (MSE)
over the entire data set (again, using $\phi_2$)."
Note that this change also effects how regression (and evaluation) is
performed in 1(d).
Also, we emphasize that IF YOU HAVE ALREADY SUBMITTED THE SOLUTIONS,
YOU NEED NOT RESUBMIT! Solutions adhering to the original problem statement
will not be penalized.
10/10: Some students had trouble loading the file 'al.mat'.
This was usually because they were using an older version of MATLAB.
We've updated the data file 'al.mat'. The updated file contains exactly
the same data, but is saved so as to be compatible with both
MATLAB v6 and MATLAB v7. The original data file is still
available-- as "al_orig.mat"
10/10: When choosing points according to the active learning strategy, at
each iteration you may (1) restrict your choices to only those points that
have not been previously selected or (2) choose from all points, even
those points that have been chosen earlier (i.e., idx will then contain
repeated entries). Either strategy is acceptable. When
following (2), you must use y_noisy for each of the instances of the
repeated data point. We recognize that in a more realistic active
learning setting, you'd have the opportunity to make multiple distinct
observations at a single point; that is not the case here.
10/10: When computing MSPE, you must compare the predicted values of y
to the true value (y_true), not y_noisy.
10/10: The values of k1 and k2 specified in part (c) are also the ones
to be used in part (d).
Problem #2
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Problem #3
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10/9: The discriminant function we expect you to write should be of the form:
f = discriminant function(alpha, X, kernel type, X test)
X was missing as an argument.
10/10: The perceptron update rules should be written with '<=' rather than strict inequality '<' tests for mistakes.