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Theorem 3.6 Lower bound, realizable case Let H be a hypothesis set with VC-dimension d> 1. Then, for any learning algorithm A, there erist a distribution D over X and a target function f e H such that d- 1 Rp(hs. f) > 32m > 1/100. Pr (3.33)

Theorem 3.6 Lower bound, realizable case Let H be a hypothesis set with VC-dimension d> 1. Then, for any learning algorithm A, there erist a distribution D over X and a target function f e H such that d- 1 Rp(hs. f) > 32m > 1/100. Pr (3.33)

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Theorem 3.6 Lower bound, realizable case Let H be a hypothesis set with VC-dimension d > 1. Then, for any learning algorithm A, there exist a distribution D over X and a target function f e H such that d - 1 Pr S-Dm Rp(hs, f) > 2 1/100. (3.33) 32m Proof Let X = {r0, 21,...,T4-1} CX be a set that is fully shattered by H. For any e > 0, we choose D such that its support is reduced to X and so that one point (ro) has very high probability (1 - e), with the rest of the probability mass distributed uniformly among the other points: 8e Prfro] = 1-8e and Vie [1, d- 1], Pra = (3.34) %3D
Transcribed Image Text:Theorem 3.6 Lower bound, realizable case Let H be a hypothesis set with VC-dimension d > 1. Then, for any learning algorithm A, there exist a distribution D over X and a target function f e H such that d - 1 Pr S-Dm Rp(hs, f) > 2 1/100. (3.33) 32m Proof Let X = {r0, 21,...,T4-1} CX be a set that is fully shattered by H. For any e > 0, we choose D such that its support is reduced to X and so that one point (ro) has very high probability (1 - e), with the rest of the probability mass distributed uniformly among the other points: 8e Prfro] = 1-8e and Vie [1, d- 1], Pra = (3.34) %3D
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