Consider the following set of data points:

input

x$1$ x$2$

desired label

$11$

$1$

$10$

$1$

$01$

$0$

$-1-1$

$0$

$-10$

$0$

$-11$

$0$

As the above table shows, the data points are categorized $($labeled$)$ in two groups specified by the labels $1$ and $0.$

$($A$)$ Use the gradient descent learning algorithm to train a single neuron on the data samples given in the table above.

Repeat the gradient descent algorithm for only $3$ epochs.

Assume the learning rate is $0\mathrm{.}1$ with an initial weight vector of $(111).$

Note: Use four digits after the decimal point: x$.$xxxx $($e$.$g$.,0\mathrm{.}3410)$

Report the weights after one iteration w$0=$

w$1=$

w$2=$

Report the weights after two iterations w$0=$

w$1=$

w$2=$

Report the weights after three iterations w$0=$

w$1=$

w$2=$

$($B$)$ Calculate each epoch's loss function $($i$.$e$.,$ average square error$).$ Note: Use four digits after the decimal point: x$.$xxxx

Loss after one iteration $=$

Loss after two iterations $=$

Loss after three iterations $=$

$($C$)$ Based on the calculated loss values during iterations, which of the following conclusions can be drawn about the convergence of the optimization process?

Group of answer choices

The optimization process is not converging, as the loss values are increasing with each iteration.

The optimization process is converging, as the loss values are steadily decreasing with each iteration.

The optimization process is fluctuating, as the loss values are not showing a clear decreasing trend.

The optimization process has reached a plateau, as the loss values are remaining constant after the first iteration.

$($D$)$ Apply your trained model after the three iterations on the data given in Question $1$ and show the confusion matrix.

NOTE: Enter them in numbers. Use the default thresholding function if v $>=0,$ then it's classified as $1$; otherwise, it's $0.$

To evaluate your trained model on the training data, you would typically use your model's predictions against the actual labels from your dataset and present the performance as a confusion matrix, accuracy, etc. No updates are performed at this stage.

Predicted $1$

Predicted $0$

Actual $1$

Actual $0$

$($E$)$ Calculate the accuracy, sensitivity$,$ and specificity. NOTE: Report them in xx $($e$.$g$.,73)$ format.

Accuracy $=$

$\%$

Sensitivity $=$

$\%$

Specificity $=$

$\%$