$9.($coding$)$ baseline Multi$-$Layer Perceptron model for the MNIST dataset

$1)$

import numpy

from keras.datasets import mnist

from keras.models import Sequential

from keras.layers import Dense

from keras.layers import Dropout

from keras.utils import np$\_$utils

from keras.datasets import mnist

import matplotlib.pyplot as plt

# load $($downloaded if needed$)$ the MNIST dataset

$3$

$($X$\_$train, Y$\_$train$),($X$\_$test, Y$\_$test$)=$ mnist.load$\_$data$()$

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describe $($X$\_$train, Y$\_$train$),($X$\_$test, Y$\_$test$)$

YOUR WORK HERE $(2$ pts$)$

$$

# flatten $28*28$ images to a $784$ vector for each image

num$\_$pixels $=$ X$\_$train.shape$[1]*$ X$\_$train.shape$[2]$

X$\_$train $=$ X$\_$train.reshape$($X$\_$train.shape$[0],$ num$\_$pixels$).$astype$(\text{'}$float$32\text{'})$

X$\_$test $=$ X$\_$test.reshape$($X$\_$test.shape$[0],$ num$\_$pixels$).$astype$(\text{'}$float$32\text{'})$

# normalize inputs from $0-255$ to $0-1$

X$\_$train $=$ X$\_$train $/255.$

X$\_$test $=$ X$\_$test $/255.$

# one hot encode outputs

Y$\_$train $=$ np$\_$utils.to$\_$categorical$($Y$\_$train$)$

Y$\_$test $=$ np$\_$utils.to$\_$categorical$($Y$\_$test$)$

num$\_$classes $=$ Y$\_$test.shape$[1]$

# define baseline model

# create model

model $=$ Sequential$()$

model.add$($Dense$($num$\_$pixels, input$\_$dim$=$num$\_$pixels, activation$=$'relu'$))$

model.add$($Dense$($num$\_$classes, activation$=$'softmax'$))$

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show model$\_$summary

YOUR WORK HERE $(2$ pts$)$

$$

# Compile model

model.compile$($loss$=$'categorical$\_$crossentropy', optimizer$=$'adam', metrics$=[\text{'}$accuracy$\text{'}])$

# Fit the model

# change epochs and batch$\_$size later

model.fit$($X$\_$train, Y$\_$train, validation$\_$data$=($X$\_$test, Y$\_$test$),$ epochs$=10,$ batch$\_$size$=200,$ verbose$=2)$

# Final evaluation of the model

scores $=$ model.evaluate$($X$\_$test, y$\_$test, verbose$=0)$

print$("$Baseline Error: $\%\mathrm{.}2$f$\%\%"\%(100-$scores$[1]*100))$

$2)[4$ pts$]$ Explain the change in performance by changing these parameters: epochs and batch$\_$size $($five

times$)$

$3)[4$ pts$]$ Add a few additional hidden layers in the network and explain the changes in performance.