Page - 304 - in Differential Geometrical Theory of Statistics

Entropy2016,18, 442 0 10 20 30 0.00 0.05 0.10 0.15 0.20 0.25 0.30 GMM1 −15 −10 −5 0 5 10 150.00 0.05 0.10 0.15 0.20 GMM2 102 103 104 105 20 40 60 80 100 120 KL(GMM1 :GMM2) CELB CEUB CEALB CEAUB CGQLB 102 103 104 105 6 8 10 12 14 16 18 20 KL(GMM2 :GMM1) CELB CEUB CEALB CEAUB CGQLB (c)KLdivergencebetweentwoGaussianmixturemodels 0 2 4 6 8 10 12 14 16 0.00 0.05 0.10 0.15 0.20 0.25 GaMM1 0 5 10 15 20 25 30 35 40 0.000 0.005 0.010 0.015 0.020 0.025 GaMM2 102 103 104 105 −3 −2 −1 0 1 2 KL(GaMM1 :GaMM2) CELB CEUB CEALB CEAUB CGQLB 102 103 104 105 −3 −2 −1 0 1 KL(GaMM2 :GaMM1) CELB CEUB CEALB CEAUB CGQLB (d)KLdivergencebetweentwoGammamixturemodels Figure 2. Lower and upper bounds on the KL divergence betweenmixturemodels. The y-axis meansKLdivergence. Solid/dashedlinesrepresent thecombinatorial/adaptivebounds, respectively. Theerror-barsshowthe0.95confidence intervalbyMonteCarloestimationusingthecorresponding samplesize (x-axis). ThenarrowdottedbarsshowtheCGQLBestimationw.r.t. thesamplesize. 304