Implement the LASSO algorithr.

The algorithm loops itercnt times. During each iteration, the algorithm updates each coordinate $w_d$ in the

weight vector $w($see the slides to the update formula$).$ The coordinates should be updated in order. The

first coordinate should not be regularized, that is$,$ the update for the first feature is $w_d=\frac{c_d}{a_d}($see the

slides$),$ as this feature corresponds to the bias term.

The algorithm should return the updated weights $w.$ There are $2$ codes. One to fill the blank as the answer. But for the easyness I will give the answer checking python code since it automatically corrects the answer. Write the answer accordingly. Answer: "import sys

import numpy as np

def lasso$($X$,$ y$,$ s$,$ reg, itercnt$)$:

$"""$

Subgradient optimization for Lasso

Parameters

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

X : an array of size $($n$,$ k$)$

training input data for the regressor

y : an array of size n

training output for the regressor

s : an array of size k

initial weights

reg : real

weight for the regularization term

itercnt : int

number of iterations

Returns

$-------$

w : an array of size k

weights after itercnt iterations

$"""$

cnt$,$ k $=$ X$.$shape

# make a copy of the initial vector

# we can now change single elements of w without changing s

w $=$ s$.$copy$()$

# place your code here

return w

def main$($argv$)$:

D $=$ np$.$loadtxt$($argv$[1])$

y $=$ D$[$:$,0].$copy$()$ # copy is needed, otherwise next line will mess up the splice

D$[$:$,0]=1$ # replace the output column of D with constant, now the first feature gives us the bias term

reg $=$ float$($argv$[2])$

itercnt $=$ int$($argv$[3])$

w $=$ np$.$zeros$($D$.$shape$[1])$ # starting point for weights

print$($lasso$($D$,$ y$,$ w$,$ reg, itercnt$))$

# This allows the script to be used as a module and as a standalone program

if $\_\_$name$\_\_=="\_\_$main$\_\_"$:

if len$($sys$.$argv$)!=4$:

print$(\text{'}$usage: python $\%$s filename' $\%$ sys$.$argv$[0])$

else:

main$($sys$.$argv$)"$ Answer correcting python code: $"$#$!/$usr$/$bin$/$env python$3$

import sys

import unittest

from tmc import points

from tmc$.$utils import load, get$\_$out

import numpy as np

from $.$utils import errormsg, ApproxTest

@points$(\text{'}2\mathrm{.}3\mathrm{.}1\text{'},\text{'}2\mathrm{.}3\mathrm{.}2\text{'},\text{'}2\mathrm{.}3\mathrm{.}3\text{'},\text{'}2\mathrm{.}3\mathrm{.}4\text{'},\text{'}2\mathrm{.}3\mathrm{.}5\text{'})$

class LassoTester$($ApproxTest$)$:

def test$\_$lasso$($self$)$:

lasso $=$ load$(\text{'}$src$.$lasso', 'lasso'$)$

D $=$ np$.$loadtxt$(\text{'}$test$/$toy$.$txt$\text{'})$

y $=$ D$[$:$,0].$copy$()$ # copy is needed, otherwise next line will mess up the splice

D$[$:$,0]=1$ # replace the label column of D with constant, now the first feature gives us the bias term

w $=$ np$.$zeros$($D$.$shape$[1])$

w $=$ lasso$($D$,$ y$,$ w$,10,100)$

w$1=$ np$.$zeros$(11)$

w$1[0]=3\mathrm{.}01421845$

w$1[3]=0\mathrm{.}97828604$

w$1[5]=0\mathrm{.}9834849$

self.assertApprox$($w$1,$ w$,$ errormsg$("$Incorrect weights $($input toy.txt$,$ lam $=10,$ itercnt $=100)",$ w$1,$ w$))"$