Latent Wishart Processes Model Formulation LWP Model Prior: p(A)=Wn(q;B(K+Xl)), where K=[K(xi,xk)1with K(xi,Xk)being a kernel function defined on the input attributes,B>0,and A is a very small number to make∑>0. o Likelihood: p(ZIA)=Is(1-s张)1-with s张= exp(aik/2) i=1k=i+1 1+exp(aik/2） o Posterior: P(A Z)P(ZA)P(A) The input attributes and relational information are seamlessly integrated via the Bayesian approach. 三Q0 Li,Zhang and Yeung (CSE.HKUST) LWP A1 STATS200911/23Latent Wishart Processes Model Formulation LWP Model Prior: p(A) = Wn(q, β(K + λI)), where K = [K(xi , xk )]n i,k=1 with K(xi , xk ) being a kernel function defined on the input attributes, β > 0, and λ is a very small number to make Σ  0. Likelihood: p(Z|A) = Yn i=1 Yn k=i+1 s zik ik (1 − sik ) 1−zik with sik = exp(aik /2) 1 + exp(aik /2). Posterior: p(A|Z) ∝ p(Z|A)p(A) The input attributes and relational information are seamlessly integrated via the Bayesian approach. Li, Zhang and Yeung (CSE, HKUST) LWP AISTATS 2009 11 / 23