1 Rademacher Complexity iid DIz, denote Rs(F) the empirical Rademacher Given a space Z and a sample S = {z1,..., zm} with z; complexity of the function class F of functions f: Z R. Let G,G1, G2 denote arbitrary classes of functions Z - [a, b), and let c,d be arbitrary real numbers. Show (a) Rs(cG+ d) = |c{Rs(G), where cG + d:= {cg+dg € G}. (b) Rs(conv(G)) = Rs(G), where conv(G) := {C"-1 9;9;|n € N, a; 2 0, E,a; = 1, gi e G}. (c) Řs(G1 + G2) = Rs(G1) + Rs(G2), where Rs(G1) + Rs(G2) := {g(2) = g1(2) + g2(2)|g1 € G1G2}.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 54E
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Rademacher Complexity
iid
Dz, denote Rs(F) the empirical Rademacher
Given a space Z and a sample S = {21, ..., zm} with z
complexity of the function class F of functions f : Z → R. Let G, G1, G2 denote arbitrary classes of functions
Z - [a, b), and let c, d be arbitrary real numbers. Show
(a) Rs(cG+d) = |c{Rs(G), where cG + d:= {cg+d\g E G}.
(b) Rs(conv(G)) = Řs(G), where conv(G) := {C"-1 9:9;|n € N, a; > 0, E; a; = 1, gi E G}.
(c) Rs(G1 + G2) = Ñs(G1) + Rs(G2), where Rs(G1) + Rs(G2) := {g(2) = g1(2) + g2(z)|g1 € G1G2}.
%3D
%3D
Transcribed Image Text:1 Rademacher Complexity iid Dz, denote Rs(F) the empirical Rademacher Given a space Z and a sample S = {21, ..., zm} with z complexity of the function class F of functions f : Z → R. Let G, G1, G2 denote arbitrary classes of functions Z - [a, b), and let c, d be arbitrary real numbers. Show (a) Rs(cG+d) = |c{Rs(G), where cG + d:= {cg+d\g E G}. (b) Rs(conv(G)) = Řs(G), where conv(G) := {C"-1 9:9;|n € N, a; > 0, E; a; = 1, gi E G}. (c) Rs(G1 + G2) = Ñs(G1) + Rs(G2), where Rs(G1) + Rs(G2) := {g(2) = g1(2) + g2(z)|g1 € G1G2}. %3D %3D
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