Show work for all questions.

Consider the following set of data points. As the above table shows, the data points are categorized $($labeled$)$ in two groups specified by the labels $"1^{}$ and

$"0".$ Use the gradient descent learning algorithm to train a single neuron on the data samples given in the table above. Repeat the gradient descent

$($e$.$g$.,0\mathrm{.}3410]$

Report the weights after one iteration:

w$0=$

$w1=$

$w2=$

Report the weights after two iterations:

wo $=$

$w1=$

$w2=$

Report the weights after three iterations:

wo $=$

$w1=$

$w2=$

Calculate each epoch's loss function $($i$.$e$.,$ average square error$).$ Note: Use four digits after the decimal point: $xxr{x}_{{?}_{?}}$

Loss after one iteration $=$

Loss after two iterations $=$

Loss after three iterations $=$

Based on the calculated loss values during iterations, which of the following conclusions can be drawn about the convergence of the optimization

process?

A$.$ The optimization process is not converging, as the lo$5$s values are increasing with each iteration.

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

C$.$ The optimization process is fluctuating, as the lo$5$s values are not showing a clear decreasing trend.

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

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 $v0,$ 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.

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

Accuracy $=$

Sensitivity $=$

Specificity $=$