Before we start
You may choose to go to the PC classrooms or finish this HW elsewhere.
It won’t affect a thing. For fairness’ sake, we’ll use discord as the Q&A system.
Tiny changes: we WILL answer questions asked verbally in class this time.
You can still use discord for Q&A.
Join the discord server for TA support
This is the same one as the program assignment #1 and #2 used.
Ask questions on it, and we shall reply. (We won’t respond to raised hands.)
Try not to ask for obvious answers or bug fixes.
Memes and chit chat welcome
Objective
Linear Regression - 55% + (10%)
Data Generation - 15%Randomly generate 1000 (xi,yi) pairs which follow the equation (1)
yi=3x3i+2x2i−3xi+1+ϵi(1)
where −1.5<xi<1.0, ϵi∼N(0,0.5) and N represents Normal distribution
Data Preprocessing - 10%Generate degree-K polynomial features x^ from x
x^i=⎡⎣⎢⎢⎢⎢⎢⎢1xix2i…xKi⎤⎦⎥⎥⎥⎥⎥⎥
You must experiments 4 different K settings, K=1,2,3,4
hint
Model Construction - 20%Linear RegressionWhich makes predictions y^=wx^, s.t.
w=argminw′||y−w′x^||2
You must construct Linear Regression models to fit and predict data generated by (1)
Validation - 0%Due to the simplicity of Linear Regression, you are not required to implement validation methods.
Results - 10% + (10%)Show the fitted weights and the equations
Show the predicted y^ for −1.5<x<1.0
Bonus - show the results in a single figure - (10%)
Legend equations must be written in LaTeX
Use × instead of ∗ to represent multiplication operations
Use xi instead of x
Limit the floating-point numeric weights to be 2 decimal placesi.e. no 1.54323423456 but 1.54
There should be no redundant signs before weights, i.e no 1+−3.36×xi
Logistic Regression - 45% + (10%)
Data Generation - 15%Randomly generate 1000 (xi0,xi1,yi) triplets which follows (2)
[xi0xi1]∼N([yiyi],[0.1000.1])(2)
where yi is randomly assigned as 0 or 1.
Model Construction - 20%Logistic RegressionWhose divider Mw uses Logistic function L to perform classification
Mw(xi)=L(w⋅x)=11+e−w⋅x
Takes L2-norm as the objective function to optimize weight w
w=argminw′||y−Mw′(x)||2
Construct a Logistic Regression model to predict yi from [xi0xi1]T generated from equation (2)
Validation - 0%Validation methods are not required in this assignment either.
Results - 10% + (10%)Show the model accuracy - 5%
Show the model weights and the corresponded terms - 5%e.g.
yi=L(4.2+7.7×xi0+6.9×xi1)
Bonus - show the decision boundary with a figure - (10%)
