Latent Wishart Processes Out-of-Sample Extension Embedding for Test Data Let Z=211 andΣ= ∑11 ∑12 Z21Z22 工21工22 where Z11,Σ11are nm×n1 matrices and Z22,Σ22are2×2 matrices. The n instances corresponding to Z11,11 are training data and the n2 instances corresponding to Z22,E22 are new test data. [A11 B1Bi B1B2 B2B B2B2 B2 。Because B~Nn.g(0,Σ&lg),we have B1~Wn1,g(0,Σi18lg)and B2|B1~N2,g(E21ΣB1,工221⑧lg), whereΣ221=Σ22-Σ21ΣiΣ12 Li,Zhang and Yeung (CSE,HKUST) LWP A1 STATS200914/23Latent Wishart Processes Out-of-Sample Extension Embedding for Test Data Let Z =  Z11 Z12 Z21 Z22  and Σ =  Σ11 Σ12 Σ21 Σ22  , where Z11, Σ11 are n1×n1 matrices and Z22, Σ22 are n2×n2 matrices. The n1 instances corresponding to Z11, Σ11 are training data and the n2 instances corresponding to Z22, Σ22 are new test data. Similarly, we partition A =  A11 A12 A21 A22  =  B1B0 1 B1B0 2 B2B0 1 B2B0 2  , B =  B1 B2  . Because B ∼ Nn,q(0, Σ⊗Iq), we have B1 ∼ Nn1,q(0, Σ11⊗Iq) and B2 | B1 ∼ Nn2,q ￾ Σ21Σ −1 11 B1, Σ22·1 ⊗ Iq
, where Σ22·1 = Σ22 − Σ21Σ −1 11 Σ12. Li, Zhang and Yeung (CSE, HKUST) LWP AISTATS 2009 14 / 23