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 C.4, Problem 4E
Program Plan Intro
To show that value of the maximum of the binomial distribution b(k; n, p) is approximately for the given statement.
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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()) = 00 + 01x(e). The parameters 6o and 0, are scalars and are learned
by minimizing mean-squared-error loss with L2-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), y@), n, 0, 01, A.
2. Compute L
3. Compute
4. Write update rules for 6, and O1
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
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3. Compute 20₁
4. Write update rules for 0o and 0₁
Hint:
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w>0
w=0
w <0
Chapter C Solutions
Introduction to Algorithms
Ch. C.1 - Prob. 1ECh. C.1 - Prob. 2ECh. C.1 - Prob. 3ECh. C.1 - Prob. 4ECh. C.1 - Prob. 5ECh. C.1 - Prob. 6ECh. C.1 - Prob. 7ECh. C.1 - Prob. 8ECh. C.1 - Prob. 9ECh. C.1 - Prob. 10E
Ch. C.1 - Prob. 11ECh. C.1 - Prob. 12ECh. C.1 - Prob. 13ECh. C.1 - Prob. 14ECh. C.1 - Prob. 15ECh. C.2 - Prob. 1ECh. C.2 - Prob. 2ECh. C.2 - Prob. 3ECh. C.2 - Prob. 4ECh. C.2 - Prob. 5ECh. C.2 - Prob. 6ECh. C.2 - Prob. 7ECh. C.2 - Prob. 8ECh. C.2 - Prob. 9ECh. C.2 - Prob. 10ECh. C.3 - Prob. 1ECh. C.3 - Prob. 2ECh. C.3 - Prob. 3ECh. C.3 - Prob. 4ECh. C.3 - Prob. 5ECh. C.3 - Prob. 6ECh. C.3 - Prob. 7ECh. C.3 - Prob. 8ECh. C.3 - Prob. 9ECh. C.3 - Prob. 10ECh. C.4 - Prob. 1ECh. C.4 - Prob. 2ECh. C.4 - Prob. 3ECh. C.4 - Prob. 4ECh. C.4 - Prob. 5ECh. C.4 - Prob. 6ECh. C.4 - Prob. 7ECh. C.4 - Prob. 8ECh. C.4 - Prob. 9ECh. C.5 - Prob. 1ECh. C.5 - Prob. 2ECh. C.5 - Prob. 3ECh. C.5 - Prob. 4ECh. C.5 - Prob. 5ECh. C.5 - Prob. 6ECh. C.5 - Prob. 7ECh. C - Prob. 1P
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