$3$ Points

Given the following weight vector for a logistic regression model:

features $=("$happy$",$ "sad", "fortunate", "bad"$)$

$\backslash [$

w$=(2,1,-1,0)$

$\backslash ]$

and given the following test example:

"I can't stand this bad piece of technology"

What will the probability of this test instance being negative according to the logistic regression model? Enter your answer as a decimal with two digits after the decimal point $($e$.$g$.,0\mathrm{.}13).$

Q$6$

$4$ Points

Which of the following is true about the basic feedforward neural network $\backslash ($ P$($y $\backslash$mid x$)=\backslash )\backslash (\backslash$operatorname$\{$softmax$\}($W g$($V f$($x$)))\backslash )$ with $\backslash ($ g$=\backslash$tanh $\backslash )?$ Select all that apply.

I. This is a nonconvex optimization problem

II$.$ This is a convex optimization problem

III. If all layers are initialized with zeros, the network will not learn

IV$.$ If all layers are initialized with zeros, the network will learn too slowly

V$.$ If all layers are initialized with Uniform$(-1,1),$ the network will not learn

VI$.$ If all layers are initialized with Uniform$(-0\mathrm{.}01,0\mathrm{.}01),$ the network will not learn

Q$7$

$3$ Points

Which of the following neural network components could help increase the training accuracy of a neural network?

I. Batch normalization

II$.$ Dropout

III. Large batch sizes and longer training

IV$.$ Negating the input feature vectors