Questions

25S-STATS-102B-LEC-3 S25 Midterm Exam- Requires Respondus LockDown Browser

Multiple choice

Please select all the statements about Newton's method and gradient descent that are correct.

Options

A.Newton’s method typically reaches an optimal solution faster than gradient descent and doesn’t suffer from the issue of slow crawling.

B.There are no ways to simplify the computation of the Hessian matrix when using Newton’s method.

C.Both Newton’s method and gradient descent face similar issues when the algorithm encounters a flat region in the objective function.

D.Newton’s method typically reaches an optimal solution faster than gradient descent, but it suffers from scaling limitations.

E.Unlike gradient descent, Newton’s method doesn’t need to address numerical stability issues.

F.Newton’s method typically reaches an optimal solution faster than gradient descent and doesn’t suffer from the zig-zagging behavior commonly observed in gradient descent.

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Step-by-Step Analysis

Let's break down each answer option and evaluate its truthfulness in the context of Newton’s method versus gradient descent. Option A: "Newton’s method typically reaches an optimal solution faster than gradient descent and doesn’t suffer from the issue of slow crawling." This statement is asserting that Newton’s method consistently outpaces gradient descent and avoids slow progress. In many well-behaved, smoothly curved problems, Newton’s method indeed converges quickly near the optimum due to its use of second-order information (the Hessian). However, this speed is not universal: far from the optimum or on ill-conditioned problems, Newton’s method can be slow to start or may even fail without line searches or regularization. The phrase "doesn......Login to view full explanation

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