Use Python to solve. Below are the data and python code to fill:

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import numpy as np

import pandas as pd

from matplotlib import pyplot as plt

from sklearn.svm import SVC

from cvxopt import matrix as cvxopt$\_$matrix

from cvxopt import solvers as cvxopt$\_$solvers

#Data set

# blanks $($data$)$

#Data for the next section

X $=$ # blanks $($predictors$)$ #

y $=$ # blanks $($target$)$ #

#Initializing values and computing H$.$ Note the $1.$ to force to float type

m$,$n $=$ X$.$shape

y $=$ y$.$reshape$(-1,1)*1.$

X$\_$dash $=$ y $*$ X

H $=$ np$.$dot$($X$\_$dash $,$ X$\_$dash.T$)*1.$

#Converting into cvxopt format

P $=$ # blank$(1)$ #

q $=$ # blank$(2)$ #

G $=$ # blank$(3)$ #

h $=$ # blank$(4)$ #

A $=$ cvxopt$\_$matrix$($y$.$reshape$(1,-1))$

b $=$ # blank$(5)$ #

#Setting solver parameters $($change default to decrease tolerance$)$

cvxopt$\_$solvers.options$[\text{'}$show$\_$progress'$]=$ False

cvxopt$\_$solvers.options$[\text{'}$abstol$\text{'}]=1$e$-10$

cvxopt$\_$solvers.options$[\text{'}$reltol$\text{'}]=1$e$-10$

cvxopt$\_$solvers.options$[\text{'}$feastol$\text{'}]=1$e$-10$

#Run solver

sol $=$ cvxopt$\_$solvers.qp$($P$,$ q$,$ G$,$ h$,$ A$,$ b$)$

alphas $=$ np$.$array$($sol$[\text{'}$x$\text{'}])$

#w parameter in vectorized form

w $=$ # blank$(6)$ #

#Selecting the set of indices S corresponding to non zero parameters

S $=($alphas $>1$e$-4).$flatten$()$

#Computing b

b $=$ # blanks$(7)$ #

#Display results

print$(\text{'}$Alphas $=\text{'},$alphas$[$alphas $>1$e$-4])$

print$(\text{'}$w $=\text{'},$ w$.$flatten$())$

print$(\text{'}$b $=\text{'},$ b$)$ Problem $2$

In this problem, we will implement the SVM dual problem code in Python using 'CVXOPT' library. 'CVXOPT' is a library to solve convex optimization problems as well as quadratic optimization problems. We will be using the dataset $\text{'}$T$11-2.$DAT' available on webcourse. The first column represents our binary response variable and the last two columns our predictors.

a$.$ The file $\text{'}$svm$\_$sep$\_$p$.$py$\text{'}$ is posted on webcourse. This code assumes that the data set is linear separable. Consequently, we will use the SVM dual problem for this question. Fill in the blanks and execute the procedure. Report the values of $\text{'}\backslash (\backslash$boldsymbol$\{\backslash$alpha$\}\backslash )\text{'},$ number of support vectors,