Algorithms and Complexity Results for #SAT and Bayesian Inference
نویسندگان
چکیده
Bayesian inference is an important problem with numerous applications in probabilistic reasoning. Counting satisfying assignments is a closely related problem of fundamental theoretical importance. In this paper, we show that plain old DPLL equipped with memoization (an algorithm we call #DPLLCache) can solve both of these problems with time complexity that is at least as good as state-of-the-art exact algorithms, and that it can also achieve the best known time-space tradeoff. We then proceed to show that there are instances where #DPLLCache can achieve an exponential speedup over existing algorithms.
منابع مشابه
An Introduction to Inference and Learning in Bayesian Networks
Bayesian networks (BNs) are modern tools for modeling phenomena in dynamic and static systems and are used in different subjects such as disease diagnosis, weather forecasting, decision making and clustering. A BN is a graphical-probabilistic model which represents causal relations among random variables and consists of a directed acyclic graph and a set of conditional probabilities. Structure...
متن کاملA Bayesian Networks Approach to Reliability Analysis of a Launch Vehicle Liquid Propellant Engine
This paper presents an extension of Bayesian networks (BN) applied to reliability analysis of an open gas generator cycle Liquid propellant engine (OGLE) of launch vehicles. There are several methods for system reliability analysis such as RBD, FTA, FMEA, Markov Chains, and etc. But for complex systems such as LV, they are not all efficiently applicable due to failure dependencies between compo...
متن کاملModel Counting
Propositional model counting or #SAT is the problem of computing the number of models for a given propositional formula, i.e., the number of distinct truth assignments to variables for which the formula evaluates to true. For a proposi-tional formula F , we will use #F to denote the model count of F. This problem is also referred to as the solution counting problem for SAT. It generalizes SAT a...
متن کاملA Bayesian approach for image denoising in MRI
Magnetic Resonance Imaging (MRI) is a notable medical imaging technique that is based on Nuclear Magnetic Resonance (NMR). MRI is a safe imaging method with high contrast between soft tissues, which made it the most popular imaging technique in clinical applications. MR Imagechr('39')s visual quality plays a vital role in medical diagnostics that can be severely corrupted by existing noise duri...
متن کاملAlgorithms of the LDA model [REPORT]
We review three algorithms for Latent Dirichlet Allocation (LDA). Two of them are variational inference algorithms: Variational Bayesian inference and Online Variational Bayesian inference and one is Markov Chain Monte Carlo (MCMC) algorithm – Collapsed Gibbs sampling. We compare their time complexity and performance. We find that online variational Bayesian inference is the fastest algorithm a...
متن کامل