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This paper deals with the following problem: modify a Bayesian network to satisfy a given set of probability constraints by only change its conditional probability tables, and the probability distribution of the resulting network should be as close as possible to that of the original network. We propose to solve this problem by extending IPFP (iterative proportional fitting procedure) to probability distributions represented by Bayesian networks. The resulting algorithm E-IPFP is further developed to D-IPFP, which reduces the computational cost by decomposing a global EIPFP into a set of smaller local E-IPFP problems. Limited analysis is provided, including the convergence proofs of the two algorithms. Computer experiments were conducted to validate the algorithms. The results are consistent with the theoretical analysis.
Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we derive a ge
We develop the theory and practice of an approach to modelling and probabilistic inference in causal networks that is suitable when application-specific or analysis-specific constraints should inform such inference or when little or no data for the l
This paper proposes various new analysis techniques for Bayes networks in which conditional probability tables (CPTs) may contain symbolic variables. The key idea is to exploit scalable and powerful techniques for synthesis problems in parametric Mar
Domains where supervised models are deployed often come with task-specific constraints, such as prior expert knowledge on the ground-truth function, or desiderata like safety and fairness. We introduce a novel probabilistic framework for reasoning wi
The modified first laws of thermodynamics at the black hole horizon and the cosmological horizon of the Schwarzschild de Sitter black hole and the apparent horizon of the Friedmann-Robertson-Walker cosmology are derived by the surface tensions, respe