Computational Information Geometry Wonderland

I wrote a small program to illustrate the information monotonicity property of f-divergences (including Kullback-Leibler). Here is a numerical example for histograms of 8 bins that we reduce to histograms in 4 and 2 bins. The KL measure is less at coarser resolution than higher resolution.

Check the information monotonicity of Kullback-Leibler divergence:
by merging bins into a coarser histogram, the Kullback-Leibler divergence is less than the higher resolution:
0.08522624581487719 0.1320022228947157 0.13591019441965485 0.06674528382980667 0.05029196864402132 0.19946790829780184 0.20516964900877682 0.1251865270903457
0.02648151081895093 0.17500830227728026 0.2779122146863664 0.06203415984687348 0.2535969883830692 0.04424529112439828 0.1320533102395284 0.028668222623533027
                KL(p,q)=0.46400208957858724     KL(q,p)=0.4558758820302893
4 bins  KL(p,q)=0.10555546240269079     KL(q,p)=0.09733318810652078
2 bins  KL(p,q)=0.029647768170771346    KL(q,p)=0.029836929625659273
Information monotonicity holds only for Csiszar's f-divergences