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, 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 0, and 61 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 ƏL 4. Write update rules for 0, and 01

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter11: Nonlinear Programming
Section11.1: Review Of Differential Calculus
Problem 7P
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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
Transcribed Image Text: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
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