$2.($b$)$

$1$ point possible $($graded$)$

Using the same relationship between and as defined above, suppose is a linear classifier for the feature vectors, and is a linear classifier for the original data vectors. Given a that produces good classifications of the feature vectors, determine a that will identically classify the associated $\text{'}$s$.$

Note: Use trans$(...)$ for transpose operations, theta$\_$z as and assume is a fixed matrix $($enter this as A$).$

Note: Expects $($an vector$),$ not $.$

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$2.($c$)$

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Given the same classifiers as in $($b$),$ if there is a that produces good classifications of the data vectors, will there always be a that will identically classify the associated $\text{'}$s$?$

Note: is a fixed matrix.

Yes

No

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$2.($d$)$

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Given the same classifiers as in $($b$),$ if there is a that produces good classifications of the data vectors, will there always be a that will identically classify the associated $\text{'}$s$?$

Note: Now assume that you can change the matrix $.$

Yes

No

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$2.($e$)$

$2$ points possible $($graded$)$

If $,$ can we find a more accurate classifier by training in $-$space, as measured on the training data?

Yes

No

Depends

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How about on unseen data?

Yes

No

Depends