2018 10-708 (CMU) Probabilistic Graphical Models {Lecture 2} [Directed GMs: Bayesian Networks]
https://kayhan.dbmi.pitt.edu/sites/default/files/lecture2.pdf
P(sequence) given both dices are fair
x2 → x4
↗ ↘
x1 x5
↘ ↗
x3
P(x5) = P(X1) P(X2|X1) P(X3|X1) P(X4|X2) P(X5|X3,X4)
Directed Acyclic Graphical (DAG)
Wrong: I(g) = {A ⊥ C | B}
A,B,C has 2^N * 2^N * 2^N ($2^(N^3)$) combinations of graph.
I(G) \subset I(P)
G0's I-map: I(G_0) = {X⊥Y}
G1's I-map: I(G_1) = \O
G2's I-map: I(G_2) = \o
https://www.youtube.com/watch?v=yDs_q6jKHb0
D-Separation
... More examples
https://stats.stackexchange.com/questions/258012/explanation-of-i-map-in-a-markov-bayesian-network
Explanation of I-map in a Markov/Bayesian network
（a） satisfies
BN: Bayesian Network
CPD: conditional probability distribution
\theta_1 and \theta_k are outside of the box
