Computing upper and lower bounds on likelihoods in intractable networks

We present deterministic techniques for computing upper and lower bounds on marginal probabilities in sigmoid and noisy-OR networks. These techniques become useful when the size of the network (or clique size) precludes exact computations. We illustrate the tightness of the bounds by numerical experiments.

[1]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[2]  David J. Spiegelhalter,et al.  Local computations with probabilities on graphical structures and their application to expert systems , 1990 .

[3]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .

[4]  David Heckerman,et al.  A Tractable Inference Algorithm for Diagnosing Multiple Diseases , 2013, UAI.

[5]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[6]  Steffen L. Lauritzen,et al.  Bayesian updating in causal probabilistic networks by local computations , 1990 .

[7]  D. Heckerman,et al.  ,81. Introduction , 2022 .

[8]  Radford M. Neal.  Connectionist Learning of Belief Networks , 1992, Artif. Intell..

[9]  Michael Luby,et al.  Approximating Probabilistic Inference in Bayesian Belief Networks is NP-Hard , 1993, Artif. Intell..

[10]  Bruce D'Ambrosio,et al.  Symbolic Probabilistic Inference in Large BN20 Networks , 1994, UAI.

[11]  Michael I. Jordan,et al.  MASSACHUSETTS INSTITUTE OF TECHNOLOGY ARTIFICIAL INTELLIGENCE LABORATORY and CENTER FOR BIOLOGICAL AND COMPUTATIONAL LEARNING DEPARTMENT OF BRAIN AND COGNITIVE SCIENCES , 1996 .

[12]  Geoffrey E. Hinton,et al.  The Helmholtz Machine , 1995, Neural Computation.

[13]  Geoffrey E. Hinton,et al.  The "wake-sleep" algorithm for unsupervised neural networks. , 1995, Science.

[14]  Michael I. Jordan,et al.  Exploiting Tractable Substructures in Intractable Networks , 1995, NIPS.

[15]  Michael I. Jordan,et al.  Mean Field Theory for Sigmoid Belief Networks , 1996, J. Artif. Intell. Res..