A convex function f(x) satisfies f(xa+ (1-A)b) Af(a) + (1-A)f(b).Jensen's inequality states that, for any convex...

 

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A convex function f(x) satisfies f(xa+ (1-A)b) Af(a) + (1-A)f(b).Jensen's inequality states that, for any convex function f(x), any function g(x) and any probability density p(x) [ f(g(x))p(x)dx ([ 9(x)p(x)da). f Use this to show that the KL divergence satisfies KL(p,q) > 0, p(x) 6= q (x), KL(p,p) = 0 A convex function f(x) satisfies f(xa+ (1-A)b) Af(a) + (1-A)f(b).Jensen's inequality states that, for any convex function f(x), any function g(x) and any probability density p(x) [ f(g(x))p(x)dx ([ 9(x)p(x)da). f Use this to show that the KL divergence satisfies KL(p,q) > 0, p(x) 6= q (x), KL(p,p) = 0