Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 9.3, Problem 5E
Program Plan Intro
To describe a linear-time
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implement Bresenham line drawing algorithm:For Slope |m|<1:Either value of x is increasedOR both x and y is increased using decision parameter.
Consider the same house rent prediction problem where you are supposed to predict price
of a house based on just its area. Suppose you have n samples with their respective areas,
x(¹), x(²),...,x(n), their true house rents y(¹), y(2),..., y(n). Let's say, you train a linear regres-
sor that predicts f(x)) = 0 + 0₁x). The parameters, and 0₁ are scalars and are learned
by minimizing mean-squared-error loss with L1-regularization through gradient descent with
a learning rate a and the regularization strength constant A. Answer the following questions.
1. Express the loss function(L) in terms of x(i),y(i), n, 00, 01, X.
2. Compute L
200
ƏL
3. Compute 20₁
4. Write update rules for 0o and 0₁
Hint:
d|w|
dw
undefined
-1
w>0
w=0
w <0
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Introduction to Algorithms
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