More general latent variable tree models Some internal nodes can be observed Internal nodes can be continuous Choi et al. JMLR 20I D) Forest @E回 2。 @e@@ @ BsisO G @@ Primary focus of this tutorial the basic ltm AAAl2014 Tutorial Nevin L Zhang HKUST
AAAI 2014 Tutorial Nevin L. Zhang HKUST 6 More General Latent Variable Tree Models Some internal nodes can be observed Internal nodes can be continuous Forest Primary focus of this tutorial: the basic LTM (Choi et al. JMLR 2011)
Part l: Concept and Properties Latent tree Models Definition Relationship with finite mixture models Relationship with phylogenetictrees Basic Properties AAAl2014 Tutorial Nevin L Zhang HKUST
AAAI 2014 Tutorial Nevin L. Zhang HKUST 7 Part II: Concept and Properties Latent Tree Models Definition Relationship with finite mixture models Relationship with phylogenetic trees Basic Properties
Finite Mixture Models( FMM) Gaussian Mixture Models(GMM) Continuous attributes p(x)=∑P(z=k)xz=k)=∑xp(x2=k) p(x2z=k)=N(xuk,∑k) Graphical model z X1,xX2,Xx3,X4,x5,X6,X7,X8×9 AAAl2014 Tutorial Nevin L Zhang HKUST
AAAI 2014 Tutorial Nevin L. Zhang HKUST 8 Finite Mixture Models (FMM) Gaussian Mixture Models (GMM): Continuous attributes Graphical model
Finite Mixture Models FMM) GMM with independence assumption Block diagonal co-variable matrix X1 2 X3 X1 X2 0 Y2(3) Graphical Model XI X3 X2 AAAl2014 Tutorial Nevin L Zhang HKUST
AAAI 2014 Tutorial Nevin L. Zhang HKUST 9 Finite Mixture Models (FMM) GMM with independence assumption Block diagonal co-variable matrix Graphical Model
Finite mixture models Latent class models (lcm): Discrete attributes Graphical Model P(x)=P(AA2…An)=∑P(2=k)ⅡP(4z=k) Distribution for cluster k: IIP(A)z Product multinomial distribution =1 All FMMs One latent variable Yielding one partition of data AAAl2014 Tutorial Nevin L Zhang HKUST 10
AAAI 2014 Tutorial Nevin L. Zhang HKUST 10 Finite Mixture Models Latent class models (LCM): Discrete attributes Distribution for cluster k: Product multinomial distribution: All FMMs One latent variable Yielding one partition of data Graphical Model