Q$24$ Part $2$: Classification $(14$ points$)$

$14$ Points

Instructions for Question $24$:

Subsections $24\mathrm{.}1$ and $24\mathrm{.}3$: The answer that you input for the values in the weight vector should be real with one digit after the decimal point $($e$.$g$.[1\mathrm{.}0,1\mathrm{.}1,0\mathrm{.}9,0\mathrm{.}9,-0\mathrm{.}9]).$ Note that there are no spaces between numbers. Use commas to separate numbers. You may include any relevant work for potential partial credit into the PDF you upload for subsection $24\mathrm{.}2.$

Subsection $24\mathrm{.}2$: You will upload a single PDF file here. In this PDF$,$ please include your answer to subsection $24\mathrm{.}2$ along with any supporting work for subsections $24\mathrm{.}1$ and $24\mathrm{.}3.$ Your work may be used to assign partial credit in case your answers to $24\mathrm{.}1$ and $24\mathrm{.}3$ are wrong, but showing work is not required.

Suppose we have a dataset of three sentences:

"good movie", $+$

"great film", $+$

"bad movie", $-$

Suppose our bag$-$of$-$words vocabulary is five tokens: $\backslash \{$good$,$ movie, great, film, bad$\backslash \}.$

Q$24\mathrm{.}1$

$5$ Points

Suppose we initialize the weight vector to $\backslash ([1\mathrm{.}0,1\mathrm{.}0,1\mathrm{.}0,1\mathrm{.}0,1\mathrm{.}0]\backslash )$ and execute perceptron with $\backslash (\backslash$alpha$=\backslash )0\mathrm{.}1.$ Give the new weight vector from executing one epoch of perceptron.

Q$24\mathrm{.}2$

$5$ Points

Now suppose we modify perceptron to use the following loss:

$\backslash (\backslash$mathcal$\{$L$\}($w$,\backslash$mathbf$\{$x$\},$ y$)=0\backslash )$ if correct

$\backslash (\backslash$mathcal$\{$L$\}($w$,\backslash$mathbf$\{$x$\},$ y$)=\backslash$left$($w$^\{\backslash$top$\}$ f$(\backslash$mathbf$\{$x$\})\backslash$right$)^\{2\}\backslash )$ else

Write the correct update for this loss.

Please upload your answer for subsection $24\mathrm{.}2$ along with any relevant supporting work for subsections $24\mathrm{.}1$ and $24\mathrm{.}3$ in a single pdf file here:

Please select file$($s$)$