Data MiningData Mining Blog | My personal exploration of data mining

Although time is an important element of artificial intelligence and knowledge representation, it is not included in the Bayesian Network framework. Dynamic Bayesian Networks are actually a special case of singly connected Bayesian Networks specifically aimed at time series modeling.

In this case, we are concerned about modeling systems that vary through time and have an associated uncertainty rather than a static snap shot of time. We want to be able to understand and represent how a system evolves through time and, optionally, provide predictions as to future probabilities.

In the DBN case, we define a state (or set of variables), and examine the relationship between them at successive time points. This introduces an inherent feedback or cyclic flow of influence.

The video above provides an introductory tutorial drawing upon the prior introduction to Bayesian Networks.

One of the interesting applications is scenario testing: What would happen if …. ?

Additional Resources:

Bayes Net Toolbox for Matlab
Dynamic Bayesian Networks (pdf) by Kevin Murphey
State of the Art Dynamic Bayesian Networks by Mihajlovic and Petkovic
Approximate Inference, Dynamic Bayesian Networks, and Hidden Markov Model (pdf tutorial)

Below is an exceptional introduction to Bayesian networks tutorial by the University of Michigan’s Peter Woolf.

There is a relative continuum in the modeling landscape that can be distinguished according to what is known through time. These include:

Topology and parameters are known and stationary
Topology is known and we have data to learn stationary parameters
Only data are known, must learn topology and parameters (stationary)
Only partial data are known, must learn topology and parameter (stationary)
Model is unknown and nonstationary

The Bayesian network is a graphical representation of Bayes rule that enables one to include knowledge of complex relationships between multiple variables. Bayesian networks are useful when there is ambiguity in a system but data exists to infer connections between variables. In particular, the following scenarios indicate a benefit from this type of data mining algorithm:

Inferential sensing – sense the state of something you don’t see
Sensor redundancy – if multiple sensors disagree, what can you say about the state of the system
Nosy System – if you system is highly variable, how can you model it?