a$.$

b$.$ c$.$

d$.$ e$.$

CS $559$: Machine Learning: Fundamentals and Applications

Assignment $1$ Due: $6/4/2024$ Tuesday $11$:$59$ p$.$m$.$

The assignment must be individual work and must not be copied or shared. Any tendency to cheat$/$copy evidence will lead to a $0$ mark for the assignment.

Students must only use Pandas, NumPy, Matplotlib, and Scipy if the problem does not specify libraries$/$packages$.$

All codes will be tested in grading. Any codes with an error will be marked $0.$ Make sure to restart the kernel and run it all before the submission. Delete any codes that do not want to be graded. Results must be displayed.

All problems must be submitted in a single notebook file. Do not use a text editor to write codes.

Bayesian Theorem $[40$ pts$]$

Load the provided data set as follows.

import pandas as pd

df $=$ pd$.$read csv$(./$data$.$csv$)$

$[10$ pts$]$ Calculate a prior probability of x and y$,$ p$($x $=0),$ p$($x $=1),$ p$($y $=0),$ and p$($y $=1).$

$[10$ pts$]$ Calculate the likelihood of x$,$ p$($x $=0|$y $=0),$ p$($x $=1|$y $=0),$ p$($x $=0|$y $=1),$ and

p$($x $=1|$y $=1).$

$[10$ pts$]$ Calculate the probability of y$,$ p$($y$).$

$[10$ pts$]$ Calculate the posterior probabilities, p$($y $=1|$x $=0),$ p$($y $=0|$x $=0),$ p$($y $=1|$x $=1),$ and p$($y $=0|$x $=1).$