Preliminaries Wishart Processes Wishart Processes oWishart distribution: An n x n random symmetric positive definite matrix A is said to have a Wishart distribution with parameters n,q,and n x n scale matrix Σ>O,written as A~Wn(q,Σ)，if its p.d.f.is given by |A(q-n-1)/2 2m2T9/21znep(-2(z-1A)）,9≥n Here 0 means that is positive definite(p.d.). ●Wishart processes: Given an input space={x1,x2,...},the kernel function A(xi,xj)xi,xj e}is said to be a Wishart process (WP)if for any n E N and {x1,...,xn,the nxn random matrix A=[A(xi,xj)=1 follows a Wishart distribution. 4日4日+4言4至，至)及0 Li,Zhang and Yeung (CSE,HKUST) LWP AISTATS 2009 6/23Preliminaries Wishart Processes Wishart Processes Wishart distribution: An n × n random symmetric positive definite matrix A is said to have a Wishart distribution with parameters n, q, and n × n scale matrix Σ  0, written as A ∼ Wn(q, Σ), if its p.d.f. is given by |A| (q−n−1)/2 2 qn/2 Γn(q/2)|Σ| q/2 exp  − 1 2 tr(Σ −1A)  , q ≥ n. Here Σ  0 means that Σ is positive definite (p.d.). Wishart processes: Given an input space X = {x1, x2, . . .}, the kernel function {A(xi , xj) | xi , xj ∈ X } is said to be a Wishart process (WP) if for any n ∈ N and {x1, . . . , xn} ⊆ X , the n×n random matrix A = [A(xi , xj)]n i,j=1 follows a Wishart distribution. Li, Zhang and Yeung (CSE, HKUST) LWP AISTATS 2009 6 / 23