Tree-structured CPDs Local Structure Representation Probabilistic Graphical Models Local Structure Tree-structured CPDs

Tree CPD A S L s1 a0 a1 s0 l1 l0 (0.8,0.2) (0.9,0.1) (0.4,0.6) (0.1,0.9) s1 a0 a1 s0 l1 l0 Apply Letter SAT Job

Which context-specific independencies are implied by the structure of this CPD? (Mark all that apply.) A S L (0.8,0.2) (0.9,0.1) (0.4,0.6) (0.1,0.9) s1 a0 a1 s0 l1 l0

Tree CPD C L2 L1 c1 c2 l1 l0 (0.8,0.2) (0.1,0.9) (0.9,0.1) (0.3,0.7) Choice Letter1 Letter2 Job

Which non-context-specific independency is implied by the structure of this CPD? (0.9,0.1) (0.3,0.7) l1 l0 L (0.8,0.2) (0.1,0.9) l1 l0 Choice Letter1 Letter2 Job

C L L c1 c2 l1 l0 l1 l0 (0.9,0.1) (0.3,0.7) (0.8,0.2) (0.1,0.9) Choice Letter1 Letter2 Job

Multiplexer CPD . . . Z1 Z2 Zk A Y

Microsoft Troubleshooters # of parameters: 145 to 55