$(25$ points$)$ Classifying images: Download the resource file "mnist.zip" and the Jupyter notebook

$"$hw$3\_$skeleton$1.$ipynb". Unzip the resource file into the same folder as the notebook $($this will create

a subfolder 'mnist' containing the training and test sets$).$ Extend the notebook by completing the

following tasks in Python. Ensure your written answers are provided directly in the notebook. In its

given form, the notebook trains a logistic regression model on the MNIST dataset to decide whether

a given data point $($a grayscale image of $28$ x $28$ pixels$)$ shows the digit $5$ or not. Note: This notebook

has been derived from the notebook $$Lecture$\_10\_$MNIST$\_$Basic$\_$Classifier.ipynb$$ discussed in class.

a$)(20$ points$)$ Extend the existing solution by conceiving and implementing an efficient single logistic

regression classifier capable of recognizing and distinguishing between all digits from $0$ to $9$ in the

MNIST dataset. Demonstrate the reduction of loss during training using the $60,000$ data points in

the training set. Report the classification accuracy on the test set of $10,000$ data points. Specify

the number of training iterations required for the classifier to achieve a classification accuracy of

$90\%$ or more.

b$)(5$ points$)$ For the solution achieved in $1$a$),$ which attains a classification accuracy of at least $90\%,$

determine the number of misclassifications for each digit from $0$ to $9.$ Identify and name the most

challenging and easiest digits to classify based on these counts.