Machine Learning(Logistic Regression)

CSE 5160 Machine Learning (Spring 2021) Assignment #3 (Due on April 16th, 2021)

All assignments are to be submitted to Blackboard. Please note that the due time of each assignment is at 11:55 pm (Blackboard time) on the due date. Please make sure to “submit” after uploading your files. Please do not attach unrelated files. You will not be able to change your files after deadline. 1. [40 marks] (Logistic Regression) Logistic regression aims to learn the parameters �⃑� from the

training set 𝐷 = {(�⃑�("),𝑦(")), 𝑖 = 1,2, . . . ,𝑚} so that the hypothesis ℎ$(�⃑�) = 𝑔(𝜃%�⃑�) (here

𝑔(𝑧) is the logistic or sigmod function 𝑔(𝑧) = & &' )!"

) can predict the output 𝑦 ∈ {0,1} given

an input vector �⃑�. Please derive the stochastic gradient ascent rule for logistic regression

learning problems.

2. [40 marks] (Logistic Regression) Manually train a hypothesis function based on the following

training instances using stochastic gradient ascent rule. The initial values of parameters are

𝜃* = 0.01 ,𝜃& = 0.01 ,𝜃+ = 0.01. The learning rate 𝛼 is 0.5. Please update each parameter at

least five times.

𝑥& 𝑥+ 𝑦

0 0 0 0 1 0 1 0 1 1 1 1