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We are given the following training examples (1.2, 3.2), (2.8, 8.5), (2,4.7), (0.9, 2.9), (5.1,11) Suppose the weights are wo = wi = 1 initially. We want to minimize the cumulative loss Ls(h, c) that corresponds to the half of the residual sum of squares; i.e., we have that m 1 Ls(h, c) = RSSs(h, c) E(yi – h(x;))? i=1 0.01, perform three iterations of full gradient descent, listing wo and wi (a) at each itgration. , Using 7 = (b). What is the value that we predict at the following points r1 = 1.5 and r2 = 4.5?

We are given the following training examples (1.2, 3.2), (2.8, 8.5), (2,4.7), (0.9, 2.9), (5.1,11) Suppose the weights are wo = wi = 1 initially. We want to minimize the cumulative loss Ls(h, c) that corresponds to the half of the residual sum of squares; i.e., we have that m 1 Ls(h, c) = RSSs(h, c) E(yi – h(x;))? i=1 0.01, perform three iterations of full gradient descent, listing wo and wi (a) at each itgration. , Using 7 = (b). What is the value that we predict at the following points r1 = 1.5 and r2 = 4.5?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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We are given the following training examples (1.2, 3.2), (2.8, 8.5), (2,4.7), (0.9, 2.9), (5.1, 11) Suppose the weights are wo = wi that corresponds to the half of the residual sum of squares; i.e., we have that = 1 initially. We want to minimize the cumulative loss Ls(h, c) m 1 RSSS(h, c) 1 Ls(h, c) = E(yi – h(x;))? i=1 , Using n = 0.01, perform three iterations of full gradient descent, listing wo and wi (a) at each iteration. (b). What is the value that we predict at the following points x1 = 1.5 and x2 4.5?
Transcribed Image Text:We are given the following training examples (1.2, 3.2), (2.8, 8.5), (2,4.7), (0.9, 2.9), (5.1, 11) Suppose the weights are wo = wi that corresponds to the half of the residual sum of squares; i.e., we have that = 1 initially. We want to minimize the cumulative loss Ls(h, c) m 1 RSSS(h, c) 1 Ls(h, c) = E(yi – h(x;))? i=1 , Using n = 0.01, perform three iterations of full gradient descent, listing wo and wi (a) at each iteration. (b). What is the value that we predict at the following points x1 = 1.5 and x2 4.5?
Another Method: Gradient Descent Unthresholded perceptron: Xo = 1 a Wo W1 X1 W2 n h(x) = o(x) = wT.x= ) w; · x; X2 Σ i=0 Wn Define the cumulative loss Ls (h, c) to be 1 Ls (h, c) = Yd (X4.Ya)ES We want to minimize this cumulative loss. • Note that Ls (h, c) = "Rs (h, c), using the square loss lsq. • This is very typical in machine learning. We usually minimize an objective function that is a modification of the empirical risk. • Here the modification is for mathematical convenience; we try to make our update rule simpler. In other cases we will be introducing more terms trying to satisfy additional goals/constraints.
Transcribed Image Text:Another Method: Gradient Descent Unthresholded perceptron: Xo = 1 a Wo W1 X1 W2 n h(x) = o(x) = wT.x= ) w; · x; X2 Σ i=0 Wn Define the cumulative loss Ls (h, c) to be 1 Ls (h, c) = Yd (X4.Ya)ES We want to minimize this cumulative loss. • Note that Ls (h, c) = "Rs (h, c), using the square loss lsq. • This is very typical in machine learning. We usually minimize an objective function that is a modification of the empirical risk. • Here the modification is for mathematical convenience; we try to make our update rule simpler. In other cases we will be introducing more terms trying to satisfy additional goals/constraints.
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