Direct message passing for hybrid Bayesian networks and performance analysis

Wei Sun; K. C. Chang

doi:10.1117/12.852088

27 April 2010 Direct message passing for hybrid Bayesian networks and performance analysis

Wei Sun, K. C. Chang

Proceedings Volume 7697, Signal Processing, Sensor Fusion, and Target Recognition XIX; 76970S (2010) https://doi.org/10.1117/12.852088
Event: SPIE Defense, Security, and Sensing, 2010, Orlando, Florida, United States

Abstract

Probabilistic inference for hybrid Bayesian networks, which involves both discrete and continuous variables, has been an important research topic over the recent years. This is not only because a number of efficient inference algorithms have been developed and used maturely for simple types of networks such as pure discrete model, but also for the practical needs that continuous variables are inevitable in modeling complex systems. Pearl's message passing algorithm provides a simple framework to compute posterior distribution by propagating messages between nodes and can provides exact answer for polytree models with pure discrete or continuous variables. In addition, applying Pearl's message passing to network with loops usually converges and results in good approximation. However, for hybrid model, there is a need of a general message passing algorithm between different types of variables. In this paper, we develop a method called Direct Message Passing (DMP) for exchanging messages between discrete and continuous variables. Based on Pearl's algorithm, we derive formulae to compute messages for variables in various dependence relationships encoded in conditional probability distributions. Mixture of Gaussian is used to represent continuous messages, with the number of mixture components up to the size of the joint state space of all discrete parents. For polytree Conditional Linear Gaussian (CLG) Bayesian network, DMP has the same computational requirements and can provide exact solution as the one obtained by the Junction Tree (JT) algorithm. However, while JT can only work for the CLG model, DMP can be applied for general nonlinear, non-Gaussian hybrid model to produce approximate solution using unscented transformation and loopy propagation. Furthermore, we can scale the algorithm by restricting the number of mixture components in the messages. Empirically, we found that the approximation errors are relatively small especially for nodes that are far away from the discrete parent nodes. Numerical simulations show encouraging results.

Citation Download Citation

Wei Sun and K. C. Chang "Direct message passing for hybrid Bayesian networks and performance analysis", Proc. SPIE 7697, Signal Processing, Sensor Fusion, and Target Recognition XIX, 76970S (27 April 2010); https://doi.org/10.1117/12.852088

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available