2012/02/14 by Haohai Yu, Yu, Haohai, Robert A. van Engelen +2 · 1 citation
Computer Science · Decision Sciences · Mathematics · #Artificial Intelligence (cs.AI) #Artificial intelligence #Bayesian Modeling and Causal Inference #Bayesian average #Bayesian inference #Bayesian linear regression #Bayesian network #Bayesian probability #Bayesian statistics #Computer science #Data Quality and Management #Econometrics #FOS: Computer and information sciences #Importance sampling #Inference #Mathematics #Monte Carlo method #Sampling (signal processing) #Sampling distribution #Statistical Methods and Bayesian Inference #Statistics #cs.AI
paper · pdf · doi:10.48550/arxiv.1202.3773
published in arXiv (Cornell University) (Cornell University)
arxiv created 2012/02/14 · openalex publication_date 2012/02/14 · arxiv updated 2012/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Approximate Bayesian inference is NP-hard. Dagum and Luby defined the Local Variance Bound (LVB) to measure the approximation hardness of Bayesian inference on Bayesian networks, assuming the networks model strictly positive joint probability distributions, i.e. zero probabilities are not permitted. This paper introduces the k-test to measure the approximation hardness of inference on Bayesian networks with deterministic causalities in the probability distribution, i.e. when zero conditional probabilities are permitted. Approximation by stochastic sampling is a widely-used inference method that is known to suffer from inefficiencies due to sample rejection. The k-test predicts when rejection rates of stochastic sampling a Bayesian network will be low, modest, high, or when sampling is intractable.