Probabilistic Graphical Models

[Rishabh Mehrotra]

Hi,

We have decided to cover Probabilistic Graphical Models from the next session onwards. I have tried to summarize and present the bigger picture just to make everyone understand the bigger picture! :P 

Two BIG Machine Learning Themes:

Any problem in ML can be approached from two different perspectives, which we can also term as two themes of Machine Learning:

• Kernel Based Methods
• Graphical Models

We have already discussed a bit about Kernel Based methods in the previous sessions(more on Kernels maybe a little later, once we are comfortable with Convex Optimization). Its time we discuss something about Graphical Models.

Definition:

GMs provide a unifying framework for capturing complex dependencies among random variables, and building large-scale multivariate statistical models.

Why Probabilistic Graphical Models?

• Probabilistic models allow convenient way to represent knowledge as a joint probability distributions. 
• Joint probability distributions support inferences that output probabilities that are useful for decision making.
• But using joint probability distribution tables does not scale. Probabilistic graphical models (PGMs) make them scalable.
• We can learn PGMs from data.

Basic approach towards understanding Graphical Models include understanding the following sub-tasks:

• Representation: Understanding how to represent data in a Graphical Model.
• Inference: Understanding how to draw conclusions/make inferences given a Graphical Model.
• Learning 
• Learning model parameters
• Learning model structure

Some of the famous Graphical Models finding huge applications include:

• Markov Random Fields
• Conditional Random Fields
• Bayesian Networks (Hidden Markov Models can be considered as simplest Bayesian Networks)

We can divide these among ourselves and discuss each of them the next time we meet. 

I am taking up MRFs. :)

--
Rishabh.

[ambarisha b]

I can try and talk about Bayesian Networks.

Ambarish

[Pranav Agarwal]

Need a few pdf's to start with basics of Graphical Models and then the advanced versions. Does anyone have it?

Pranav

[Phaneendra Chiruvella]

Hi Pranav,

Here are a few links I found, haven't gone through any of them yet though, check them out.

1>  There is a single lecture on PGM here with three ppts and a few references

2>  http://pgm.stanford.edu/ has an intro chapter for a text book.

3> PGM Class at CMU here

4> A text book on Bayesian Reasoning and Machine Learning here

Phaneendra Chiruvella
Twitter: @superxor