Show the following property of KL-divergence (i.e. convexity of KL-divergence). Let M1, M2, V1, V2 be distributions. Then for any λ = [0, 1] - - D(λµ₁ + (1 − λ)µ2||Av₁ + (1 − X)12) ≤ XD(µ1||11) + (1 − X)D(µ2||12) Hint Use Log-Sum Inequality.
Show the following property of KL-divergence (i.e. convexity of KL-divergence). Let M1, M2, V1, V2 be distributions. Then for any λ = [0, 1] - - D(λµ₁ + (1 − λ)µ2||Av₁ + (1 − X)12) ≤ XD(µ1||11) + (1 − X)D(µ2||12) Hint Use Log-Sum Inequality.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![Show the following property of KL-divergence (i.e. convexity of KL-divergence).
Let M1, M2, V1, V2 be distributions. Then for any λ = [0, 1]
-
-
D(λµ₁ + (1 − λ)µ2||Av₁ + (1 − X)12) ≤ XD(µ1||11) + (1 − X)D(µ2||12)
Hint Use Log-Sum Inequality.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1822b493-2c18-4a65-99e5-18fca75fe15d%2F78b70890-ea6b-433f-89c5-3c9f6f0a2e23%2Fmvir48ro_processed.png&w=3840&q=75)
Transcribed Image Text:Show the following property of KL-divergence (i.e. convexity of KL-divergence).
Let M1, M2, V1, V2 be distributions. Then for any λ = [0, 1]
-
-
D(λµ₁ + (1 − λ)µ2||Av₁ + (1 − X)12) ≤ XD(µ1||11) + (1 − X)D(µ2||12)
Hint Use Log-Sum Inequality.
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