Load data from mnist and reduce its size so the homework runs faster. Only use the first $15000$ images for training and $2000$ for test. The MNIST digits from keras datasets are already scaled to a value between $0$ and $1$ for the greyscale. You do not need to do any further scaling.

import matplotlib.pyplot as plt

import numpy as np

from tensorflow.keras.datasets import mnist

$($train$\_$images, train$\_$labels$),($test$\_$images, test$\_$labels$)=$ mnist.load$\_$data$()$

train$\_$images $=$ train$\_$images$[$:$15000,$:$,$:$]$

train$\_$labels $=$ train$\_$labels$[$:$15000]$

test$\_$images $=$ test$\_$images$[$:$2000,$:$,$:$]$

test$\_$labels $=$ test$\_$labels$[$:$2000]$

train$\_$images.shape

train$\_$images $=$ train$\_$images.reshape$((15000,28*28))$

train$\_$images $=$ train$\_$images.astype$("$float$32")/255$

test$\_$images $=$ test$\_$images.reshape$((2000,28*28))$

test$\_$images $=$ test$\_$images.astype$("$float$32")/255$

Problem $1$

a$)$ create a sequential model with two dense layers. The first layer should have $512$ neurons. Use ReLU for the first layers activation. Pick the best size and activation for the output layer

b$)$ Compile the model using the rmsprop optimizer. Use the appropriate loss and metrics for the MNIST classification problem.

c$)$ Fit the model using $25$ epochs, batch size $128$ and use $33\%$ of the data for validation $($validation$\_$split$=0\mathrm{.}33).$ Save the history into a variable called history.

d$)$e$)$ Plot out the model accuracy vs epoch for the training and validation data.

f$)$ Plot the model loss vs epoch for the training and validation data.

g$)$ Print the model summary

h$)$ Did the model overfit? Explain your reasoning. predict the digit for the first ten Part i$)$ Do four$-$fold cross validation on the model above and print out the validation accuracy for each fold. Also, plot the training and validation accuracy per fold

For problem $2,$ we are going to make a binary classifier using the same MNIST dataset. We are going to classify digits as zero or not zero.

a$)$ Make the train$\_$labels and test$\_$labels data be zero or one with one being everything that is not a zero.

b$)$ Create a model with one dense layer and one neuron. Choose the appropriate activation for binary classification.verything that is not a zero.old.test images, then compare to the actual values.

c$)$ compile the model using rmsprop for the optimizer. Choose the best loss and metrics for binary classification

d$)$ Fit the model and use the test$\_$images and test$\_$labels for the validation data instead of doing a validation split on the training data. Use $50$ epochs and the proper loss and metrics for a binary classification problem.

e$)$ Plot out the model accuracy vs epoch for the traning and validation data.

f$)$ Plot the model loss vs epoch for the training and validation data.

g$)$ print the model summary

h$)$ Did the model overfit? Explain your reasoning.