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