Operations for inference in continuous Bayesian networks with linear deterministic variables

An important class of continuous Bayesian networks are those that have linear conditionally deterministic variables (a variable that is a linear deterministic function of its parents). In this case, the joint density function for the variables in the network does not exist. Conditional linear Gaussian (CLG) distributions can handle such cases when all variables are normally distributed. In this paper, we develop operations required for performing inference with linear conditionally deterministic variables in continuous Bayesian networks using relationships derived from joint cumulative distribution functions. These methods allow inference in networks with linear deterministic variables and non-Gaussian distributions.

[1]  Prakash P. Shenoy,et al.  Inference in hybrid Bayesian networks with mixtures of truncated exponentials , 2006, Int. J. Approx. Reason..

[2]  S. Lauritzen.  Propagation of Probabilities, Means, and Variances in Mixed Graphical Association Models , 1992 .

[3]  Patrick Brézillon,et al.  Lecture Notes in Artificial Intelligence , 1999 .

[4]  Steffen L. Lauritzen,et al.  Stable local computation with conditional Gaussian distributions , 2001, Stat. Comput..

[5]  Serafín Moral,et al.  Approximating Conditional MTE Distributions by Means of Mixed Trees , 2003, ECSQARU.

[6]  Prakash P. Shenoy,et al.  Approximating Probability Density Functions with Mixtures of Truncated Exponentials , 2004 .

[7]  Prakash P. Shenoy,et al.  Nonlinear Deterministic Relationships in Bayesian Networks , 2005, ECSQARU.

[8]  Serafín Moral,et al.  Mixtures of Truncated Exponentials in Hybrid Bayesian Networks , 2001, ECSQARU.

[9]  Serafín Moral,et al.  Estimating Mixtures of Truncated Exponentials from Data , 2002, Probabilistic Graphical Models.

[10]  Michael I. Jordan,et al.  Probabilistic Networks and Expert Systems , 1999 .

[11]  Prakash P. Shenoy,et al.  Hybrid Bayesian Networks with Linear Deterministic Variables , 2005, UAI.

[12]  Andrew P. Sage,et al.  Uncertainty in Artificial Intelligence , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[13]  Rafael Rumí Rodríguez.  Modelos de redes bayesianas con variables discretas y continuas , 2003 .

[14]  R. Larsen.  An introduction to mathematical statistics and its applications / Richard J. Larsen, Morris L. Marx , 1986 .