• New York University

• CS-GY 6143

ECE-GY 6143: Introduction to Machine Learning
Midterm , Spring 2019
Prof. Sundeep Rangan
1. (13 points) Least squares with a transformation. Consider the following model for a scalar
target ^ y from features x = (x1; x2),
y^ = f(x; θ) = (θ θ0 0 + + θ θ1 1( (1 + x1 +θ2θ)2xx12) if if x x1 1 < x ≥ x2 2
where θ = (θ0; θ1; θ2) are parameters.
(a) (9 points) Write this as a linear model. That is, find basis functions φi(x) and parameters
βi such that
y^ =
p X i
=1
βiφi(x):
Use a minimum number p of basis functions. Write the linear model parameters βi in
terms of θj.
(b) (4 points) Given a linear parameter estimate β, how do you find θ in the original model?