Probabilistic Graphical Models(Stanford) - 2

notes Probabilistic_Graphical_Models

Week1 Template Models

1. Overview of Template Models

There are some ''patterns'' are sharing between models within this model.

• sharing across pixel
• sharing pair of supperpixels
• sharing between and within a model

examples:

Template Variables:

Template Models:

Which of the following are advantages of using template models?

• CPDs in template models can often be copied many times.
• Template models can often capture events that occur in a time series.
• Template models can capture parameter sharing within a model.

2. Template Models - DBNs

Markov Assumption

The equation above do not make any assumption!!! we only re-expressing the
probability distribution in the way that time flows forward

Add the independent assumption

which means that the next step is independent of the past given the present.

the equation above is acquired based on the independent assumption
An example of showing that the Markov assumption sometimes is too strong.

Time Invariance

Time invariance states that the states of system change from one to another is independent of the current time.
we can enrich the model by including some other conditions.

Dynamic Bayesian Network

Summary

3. Temporal Models - HMMs

Numerous Application

• Robot Localization
  
• Speech Recognition
  
  
  Phones matters much(Phonetic Alphabet).
• Word HMM
  
  
  this is the whole system.

Summary

4. Plate Models

$\theta$ is the actual CPD parameter
$\theta$ is outside the plate which means it is not indexed by $t$ which also means it is the same for all values of $t$.

Nested Plates

The variable in the nested plates are indexed by both.

Overlapping Plates

Plate Dependency Model

Summary