A unifying framework for exact and approximate Bayesian inference

Abstract : We present a unifying framework for exact and approximate inference in Bayesian networks. This framework has been used to design a general purpose Bayesian inference engine, called ``ProBT'', for probabilistic reasoning and incremental model construction. This paper is not intended to present ProBT but to describe its underlying algorithms for both exact and approximate inference problems. The main idea of the ProBT inference engine is to use ``probability expressions'' as basic bricks to build more complex probabilistic models incrementally. The numerical evaluation of these expressions is accomplished just-in-time. Indeed, a probability expression is a symbolic representation of an inferred distribution. Probability expressions are manipulated in the same way as numerical distributions, such as probability tables and standard parametric distributions. A probability expression is said to be an ``exact'' or an ``approximate'' depending on the inference method (exact or approximate) used to evaluate it. For exact inference, we describe the ``Successive Restrictions Algorithm'' (SRA). Given a target distribution, the goal of the SRA is to construct a symbolic evaluation tree by finding a corresponding sum/product ordering that takes into account the computational constraints of the application (computation time and/or memory size). The optimality considerations of the SRA are also discussed. For the approximate inference part, several approximation schemes and the corresponding algorithms are presented. An original algorithm called ``MCSEM'' (for Monte Carlo Simultaneous Estimation and Maximization) is proposed. This algorithm aims at solving the problem of maximizing a posteriori high-dimensional distributions containing (in the general case) high-dimensional integrals (or sums).
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Submitted on : Friday, May 19, 2006 - 7:36:04 PM
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Kamel Mekhnacha, Linda Smail, Juan-Manuel Ahuactzin, Pierre Bessière, Emmanuel Mazer. A unifying framework for exact and approximate Bayesian inference. [Research Report] RR-5797, INRIA. 2006, pp.44. ⟨inria-00070226⟩



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