Now that we have defined our needed functions, we can train and test the model, and then plot$/$ report the results below.

We first train the model with no regularization.

$[]$

np$.$random.seed$(314159)$ # DO NOT MODIFY THE SEED

m$,$ n $=$ X$\_$train.shape

# Initialize parameters

# Training with no regularization

print$("$Computing for sensory score with no regularization"$)$

start $=$ time.time$()$

w $=$ initialize$\_$parameters$($n$)$

X$\_$train $=$ np$.$concatenate$([$X$\_$train, np$.$ones$(($X$\_$train.shape$[0],0))],1)$

w$\_$no$\_$reg, loss$\_$no$\_$reg $=$ train$($X$\_$train, y$\_$train, w$,$ regularization$\_$type$=$NO$\_$REGULARIZATION$)$

no$\_$reg$\_$train$\_$duration $=$ time.time$()-$ start

# Testing with no regularization

X$\_$test $=$ np$.$concatenate$([$X$\_$test, np$.$ones$(($X$\_$test.shape$[0],0))],1)$

test$\_$loss$\_$no$\_$reg $=$ test$($X$\_$test, y$\_$test, w$,$ NO$\_$REGULARIZATION$)$

print$("**$GRADIENT DESCENT$**")$

plot$\_$loss$($loss$\_$no$\_$reg, title$=$"Loss for Sensory Score Prediction with no regularization"$)$

plt$.$savefig$("$sensory$\_$score$\_$no$\_$reg.png$")$

print$("$Final training loss achieved $\{$loss$\}".$format$($loss$=$loss$\_$no$\_$reg$[-1]))$

print$("$Test loss achieved $\{$loss$\}".$format$($loss$=$test$\_$loss$\_$no$\_$reg$))$

print$("$Duration $\{$time$\}".$format$($time$=$no$\_$reg$\_$train$\_$duration$))$

We now train the model with l$1$ regularization.

$[]$

# Training with l$1$ regularization

print$("$Computing for sensory score with l$1$ regularization"$)$

start $=$ time.time$()$

w $=$ initialize$\_$parameters$($n$)$

X$\_$train $=$ np$.$concatenate$([$X$\_$train, np$.$ones$(($X$\_$train.shape$[0],0))],1)$

w$\_$l$1\_$reg, loss$\_$l$1\_$reg $=$ train$($X$\_$train, y$\_$train, w$,$ regularization$\_$type$=$L$1\_$LOSS$)$

l$1\_$reg$\_$train$\_$duration $=$ time.time$()-$ start

# Testing with l$1$ regularization

X$\_$test $=$ np$.$concatenate$([$X$\_$test, np$.$ones$(($X$\_$test.shape$[0],0))],1)$

test$\_$loss$\_$l$1\_$reg $=$ test$($X$\_$test, y$\_$test, w$,$ L$1\_$LOSS$)$

print$("**$GRADIENT DESCENT$**")$

plot$\_$loss$($loss$\_$l$1\_$reg, title$=$"Loss for Sensory Score Prediction with l$1$ regularization"$)$

plt$.$savefig$("$sensory$\_$score$\_$l$1\_$reg.png$")$

print$("$Final training loss achieved $\{$loss$\}".$format$($loss$=$loss$\_$l$1\_$reg$[-1]))$

print$("$Test loss achieved $\{$loss$\}".$format$($loss$=$test$\_$loss$\_$l$1\_$reg$))$

print$("$Duration $\{$time$\}".$format$($time$=$l$1\_$reg$\_$train$\_$duration$))$

We now train the model with l$2$ regularization

$[]$

# Training with l$2$ regularization

print$("$Computing for sensory score with l$2$ regularization"$)$

start $=$ time.time$()$

w $=$ initialize$\_$parameters$($n$)$

X$\_$train $=$ np$.$concatenate$([$X$\_$train, np$.$ones$(($X$\_$train.shape$[0],0))],1)$

w$\_$l$2\_$reg, loss$\_$l$2\_$reg $=$ train$($X$\_$train, y$\_$train, w$,$ regularization$\_$type$=$L$2\_$LOSS$)$

l$2\_$reg$\_$train$\_$duration $=$ time.time$()-$ start

# Testing with l$2$ regularization

X$\_$test $=$ np$.$concatenate$([$X$\_$test, np$.$ones$(($X$\_$test.shape$[0],0))],1)$

test$\_$loss$\_$l$2\_$reg $=$ test$($X$\_$test, y$\_$test, w$,$ L$2\_$LOSS$)$