Latent Wishart Processes Loomning Maximum A Posteriori (MAP)Estimation Optimization via MAP estimation: argmax log [p(ZA)p(A) A o The theorem shows that finding the MAP estimate of A is equivalent to finding the MAP estimate of B.Hence,we maximize the following: L(B)=log{p(ZB)p(B)}=>logp(zb;,bx)+logp(B) [地-os1+ep(2】-K+0BB]+c i≠k FBab,P-bs+smo,pj-∑：b:+C whereandCisa constant independent of B. 4口，4辱+4之，至，三Q0 Li,Zhang and Yeung (CSE.HKUST) LWP A1 STATS200912/23Latent Wishart Processes Learning Maximum A Posteriori (MAP) Estimation Optimization via MAP estimation: argmax A log p(Z|A)p(A) The theorem shows that finding the MAP estimate of A is equivalent to finding the MAP estimate of B. Hence, we maximize the following: L(B) = log{p(Z|B)p(B)} = X i6=k log p(zik |bi , bk ) + log p(B) = X i6=k h zikb 0 ibk 2 − log(1 + exp(b 0 ibk 2 ))i − 1 2 tr (K + λI) −1 β BB0 + C = X i6=k h zikb 0 ibk /2 − log(1 + exp(b 0 ibk /2))i − 1 2 X i,k σikb 0 ibk + C, where [σik ] n i,k=1 = (K+λI)−1 β and C is a constant independent of B. Li, Zhang and Yeung (CSE, HKUST) LWP AISTATS 2009 12 / 23