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Unformatted text preview: tical bounds omitting a lot of speciﬁcs of the two problems).
(e) The plots are shown in Fig 1.
2. (a) The functions are on the course website. The distance must not be used, since it is
magnitudedependent. Measuring the angle between them is the most appropriate way.
The angle will vary, depending upon the ordering strategy used in Prob 1 and, conse
quently, the θ found in Prob 1. However, the answer corresponding to the strategy where
points are picked in their order in the input, the answer for data set ‘A’ was 0.0221 radi
ans or 1.2672◦ . We will accept answers < 0.0351 radians (or 2.011◦ ). Similarly, for data
set ‘B’, the most straigthforward strategy produced the diﬀerence as 0.0019 radians or
0.1114◦ . We will accept answers < 0.002 radians (or 0.1146◦ ). These latter limits are
based on the decision boundaries going through points at the margins of the maxmargin
classiﬁer.
a
b
(b) γgeom = 5.5731 and γgeom = 0.3267. These are the maximum margins achievable with
any linear classiﬁer through origin. 3. (a) The correct invocation of SVMlight in training is had by setting C to inﬁnity:
% svm_learn c +inf train01images.svm
Scanning examples...done
Reading examples into memory... <snip> ..OK. (12665 examples read)
Optimizing... <snip> .done. (687 iterations)
Optimization finished (0 misclassified, maxdiff=0.00100).
Runtime in cpuseconds: 1.30
Number of SV: 84 (including 0 at upper bound)
L1 loss: loss=0.00000
Norm of weight vector: w=0.00924
Norm of longest example vector: x=4380.65657
Estimated VCdim of classifier: VCdim<=890.06377
Computi...
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This document was uploaded on 03/20/2014 for the course EECS 6.867 at MIT.
 Fall '06
 TommiJaakkola
 Machine Learning

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