PRML閱讀記(3)

繼續啃PRML

第八章：

Basic notation:

• node --> random variable or group of random variables
• link --> probabilistic relation ship
• notation of random var and non-random var, observed and unobserved var

Conditional Independence:

• three example: block means independent conditionally

     1. tail-tail, observed(block), unobserved(unblock)

     2. head-tail, observed(block), unobserved(unblock)

     3. head-head, observed(unblock), unobserved(block)

• D-separation theorm: regrard graph as filter for distribution p(x)
• Markov blanket/Markov boundary

Directed graphical model --> Bayesian Networks:

• Discrete variables: three ways to control number of parameters

     1. chain nodes

     2. sharing parameters

     3. model with latent parameter

• Continues variables: Linear-Gaussian model

Undirected graphical model --> Markov random field：

• conditional independence property in undirected graph
• factorization property in directed graph
• potential function and energy function
• how to convert directed graph to undirected and vice versa
• I map, D map, perfect map

Inference:

• chain: using potential function, local messages pass to get an efficient algorithm
• trees: undirected tree, directed tree, polytree, use efficient algorithm in a broader situation

factor graph:

• translate directed and undirected graph to factor graph to become tree
• sum-product algorithm: read it later
• max-sum algorithm: read it later

important view:

1. Basic notation

2. Conditional property and factorization property

3. Directed graphical model --> Bayesian Networks, Undirected graphical model --> Markov random field

4. Inference in graphical model