USE JUPYTER LAB, below is the provided code and at the end are the questions:

import numpy as np

import pandas as pd

import seaborn as sns

import math

from sklearn import preprocessing

from sklearn import datasets

from sklearn.tree import plot$\_$tree

from sklearn.tree import export$\_$text

from sklearn.tree import DecisionTreeClassifier

from sklearn import metrics #Import scikit$-$learn metrics module for accuracy calculation

from sklearn.metrics import confusion$\_$matrix, ConfusionMatrixDisplay

from sklearn.model$\_$selection import train$\_$test$\_$split

from sklearn.datasets import make$\_$moons

from sklearn.ensemble import RandomForestClassifier

import sklearn

from scipy import stats

import matplotlib

import matplotlib.pyplot as plt

$\%$matplotlib inline

matplotlib.style.use$(\text{'}$ggplot$\text{'})$

np$.$random.seed$(1)$

$----------$

Loading the digits dataset $($classification$).$

The digists dataset has $1797$ records

Each record is a $8$x$8$ image $(64$ dimensions$)$ and there are $10$ class labels for this dataset

Each image $($record$)$ is labeled by the number it represents

The intensities of the original pixels are binned to values ranging from $0$ to $16$

$-----------$

from sklearn.datasets import load$\_$digits

digits $=$ load$\_$digits$()$

X $=$ digits.data

y $=$ digits.target

$----$

#Learning about how the data is stored

print$("$X$\_$shape", X$.$shape, $"$

y$\_$shape",y$.$shape$)$

print$($X$[0$:$2,])$ #Check the values for the first two images

print$($y$[0$:$2])$ #Print the class labels for the first two images

$-----$

#Show the first image

plt$.$gray$()$

plt$.$matshow$($X$[0,$:$].$reshape$(8,8))$ #show the first image, first reshape the $64$ values vector into an $8$x$8$ matrix

plt$.$show$()$

$------$

#plotting the first $8$ images

fig $,$ axes $=$ plt$.$subplots$($nrows$=2,$ ncols$=4,$ figsize$=(6,3))$

for id$,$ ax in enumerate$($axes$.$flatten$())$:

image $=$ X$[$id$,$:$].$reshape$(8,8)$

ax$.$set$\_$axis$\_$off$()$

#ax$.$imshow$($image$,$ cmap$=$plt$.$cm$.$gray$\_$r$)$ #You can try this and comment the line below

ax$.$imshow$($image$,$ cmap$=$'gray'$)$

ax$.$set$\_$title$("$Label: $\%$i$"\%$ y$[$id$],$ fontsize $=9)$

plt$.$tight$\_$layout$()$

plt$.$show$()$

$--------$

# Split data into $70\%$ train and $30\%$ test subsets

#X$\_$train, X$\_$test, y$\_$train, y$\_$test $=$ train$\_$test$\_$split$($X$,$ y$,$ test$\_$size$=0\mathrm{.}3,$ shuffle$=$True, random$\_$state$=42)$

X$\_$train, X$\_$test, y$\_$train, y$\_$test $=$ train$\_$test$\_$split$($X$,$ y$,$ test$\_$size$=0\mathrm{.}3,$ shuffle$=$False$)$

print$("$Training Data",X$\_$train.shape$)$

print$("$Testing Data",X$\_$test.shape$)$

counts, bins $=$ np$.$histogram$($y$\_$test$)$

print$("$Number of records in each class", counts$)$

plt$.$stairs$($counts$,$ bins$)$

$-------$

Q$1-$A Train a decision tree on the training data and report the training and testing accuracy of the decision tree.$$

Q$1-$B Plot the first $8$ images in the testing datasets.

The title of each subfigure should be True: label Predicted: label

Q$1-$C Plot the first $8$ images in the testing datasets that were misclassified.

The title of each subfigure should be True: label Predicted: label

Q$1-$D Print the classification report using classification$\_$report from metrics in sklearn

Q$1-$E Plot the confusion matrix using ConfusionMatrixDisplay

Q$1-$F $(5$ points$)$ Plot the decision tree using plot$\_$tree

Q$1-$G Cross Validation

Report the accuracies for the $5-$fold cross validation $($use cv$=5).$

The cross validation method takes the decision tree model, the entire dataset, and the class labels.

For this line:$$

print$("\%0\mathrm{.}2$f accuracy with a standard deviation of $\%0\mathrm{.}2$f$"\%($scores$.$mean$(),$ scores.std$()))$

this is a sample output

$[0\mathrm{.}808333330\mathrm{.}719444440\mathrm{.}796657380\mathrm{.}827298050\mathrm{.}79108635]$

$0\mathrm{.}79$ accuracy with a standard deviation of $0\mathrm{.}04$

Q$1-$H Random Forest Classifier

Train a random forest on X$\_$train and report the accuracy on X$\_$test

Use $100$ trees in the random forest classifier. Recall that number of records in X$\_$train $(1257)$

Fine$-$tune the max$\_$samples $($try different numbers$)$ for RandomForestClassifier

to achieve an accuracy higher than $91\%($a big improvement from the $78\%)$

$---------------------$

Q$2$ Finding the best split using gini index

data $=$ np$.$array$([[1,2,3,1],[2,3,3,0],[3,2,2,1],[2,2,6,1],[1,2,5,1],[1,3,2,0],[2,3,6,0],[3,3,4,1]])$

print$("$Values

$",$data$[$:$,$:$-1])$

print$("$Class Label",data$[$:$,-1])$

n $=$ data.shape$[0]$

d $=$ data.shape$[1]-1$ #number of columns, ignore the last column $($class label$)$

$---------$

Q$2-$A $(10$ points$)$ Write a function that computes the gini$\_$index of a dataset D

Use math.power$($P$\_$positive$/$n $,2)$ to calculate $($P$\_$positive$/$n$)^2$

If the data has zero records, the gini$\_$index is zero The last column of the dataset is the class label

#Write a function that computes the gini$\_$index for a dataset

#$1-(($P$\_$positive$/$n$)^2+($P$\_$negative$/$n$)^2)$

#use math.power$($P$\_$positive$/$n$,2)$ to calculate $($P$\_$positive$/$n$)^2$

#If the data has zero records, the gini$\_$index is zero

#The last column of the dataset is the class label

def get$\_$gini$\_$index$($D$)$:

n $=$ D$.$shape$[0]$

gini$\_$index $=$ "calculate it$"$

#Write your code here

return$($gini$\_$index$)$

print$($get$\_$gini$\_$index$($data$))$ #You should get $0\mathrm{.}46875$

$-----$