Solution to exercise (D_KL violates triangle inequality)
[All logs are natural logs.]
A = B = C =
0.001 0.5 0.999
0.999 0.5 0.001
D(A,C) = 6.892;
D(A,B) = 0.685;
D(B,C) = 2.761
D(A,C) is greater than
D(A,B)+D(B,C) = 3.446
Solution to exercise (D_SRE(a,b) = 0.5(D_KL(b,a) + D_KL(a,b)), is it a distance?)
The answer is no, it's not.
The probability vectors above A, B, C, provide a counterexample.
D(A,C) = 6.892
is greater than
D(A,B)+D(B,C) = 3.446.
David MacKay
Last modified: Mon Jul 2 21:55:23 2007