Basic Latent Tree ModelS LTM) Bayesian network All variables are discrete Y1 Structure is a rooted tree Y2 Y3 Leaf nodes are observed(manifest X4 variables Internal nodes are not observed X1)(X2)(X3 X5)(X6)(X7 (latent variables) aso known as hierarchical Parameters latent class(HLc)models, HLC models(Zhang JMLR 2004) P(Y1),P(Y2Y1),P(X1Y2),P(2Y2), Semantics P(X1,…,Xn,Y1,…,Ym) I P(Z I parent(Z) parent z∈{x1+XnY1……,Ym}AAAI 2014 Tutorial Nevin L. Zhang HKUST 3 Basic Latent Tree Models (LTM)  Bayesian network  All variables are discrete  Structure is a rooted tree  Leaf nodes are observed (manifest variables)  Internal nodes are not observed (latent variables)  Parameters:  P(Y1), P(Y2|Y1),P(X1|Y2), P(X2|Y2), …  Semantics: Also known as Hierarchical latent class (HLC) models, HLC models (Zhang. JMLR 2004)