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(ii) Write out each of the two expressions that make up the loss function (lly - B||2 and X||WB||2) explicitly using summations. Explain the role played by each of the two terms (explain what W is doing). Be as specific as possible. What to submit: your answer, and any working either typed or handwritten. (iii) Recall from Homework 1 the coordinate-level iterative scheme. Derive closed-form expres- sions for B₁, B2,..., , where for j = 1, 2, ...,p: B₁ = arg min L(B1,..., Bj-1, Bj, Bj+1,..., Bp). B; What to submit: a closed form expression along with your working.

(ii) Write out each of the two expressions that make up the loss function (lly - B||2 and X||WB||2) explicitly using summations. Explain the role played by each of the two terms (explain what W is doing). Be as specific as possible. What to submit: your answer, and any working either typed or handwritten. (iii) Recall from Homework 1 the coordinate-level iterative scheme. Derive closed-form expres- sions for B₁, B2,..., , where for j = 1, 2, ...,p: B₁ = arg min L(B1,..., Bj-1, Bj, Bj+1,..., Bp). B; What to submit: a closed form expression along with your working.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(i) Consider the loss function: 1 L(B) = ||ly - B|| + A||W B|| 2.
Transcribed Image Text:(i) Consider the loss function: 1 L(B) = ||ly - B|| + A||W B|| 2.
(ii) Write out each of the two expressions that make up the loss function (||y-B||2 and X||WB||2) explicitly using summations. Explain the role played by each of the two terms (explain what W is doing). Be as specific as possible. What to submit: your answer, and any working either typed or handwritten. (iii) Recall from Homework 1 the coordinate-level iterative scheme.8 Derive closed-form expres- sions for B₁, B2, ..., p where for j = 1,2, ..., p: B₁ = arg min L(B₁,..., Bj-1, Bj, Bj+1,... , Bp). B; What to submit: a closed form expression along with your working.
Transcribed Image Text:(ii) Write out each of the two expressions that make up the loss function (||y-B||2 and X||WB||2) explicitly using summations. Explain the role played by each of the two terms (explain what W is doing). Be as specific as possible. What to submit: your answer, and any working either typed or handwritten. (iii) Recall from Homework 1 the coordinate-level iterative scheme.8 Derive closed-form expres- sions for B₁, B2, ..., p where for j = 1,2, ..., p: B₁ = arg min L(B₁,..., Bj-1, Bj, Bj+1,... , Bp). B; What to submit: a closed form expression along with your working.
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