Improving Importance Sampling by Adaptive Split-Rejection Control in Bayesian Networks

Yuan, Changhe; Drużdżel, Marek J.

doi:10.1007/978-3-540-72665-4_29

Cited by 6 publications

(3 citation statements)

References 11 publications

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“…However, a biased estimate would be obtained due to the unevenly distributed high-importance weights by the SIR method; that is, a few extremely large weights dominate the entire resampling process, so it is highly unlikely that other small weighted samples will be generated. To avoid the concentration of posterior sets caused by large weights, a wider sample range was explored by splitting the larger weights into smaller ones, which also proved that the results remained unbiased [49]. The process of inferring a posterior based on the ABM method is shown in Figure 1 and listed as follows:…”

Section: An Adaptive Bayesian Melding Methodsmentioning

confidence: 99%

An Adaptive Bayesian Melding Method for Reliability Evaluation Via Limited Failure Data: An Application to the Servo Turret

et al. 2020

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In the early stage of product development, reliability evaluation is an indispensable step before launching a product onto the market. It is not realistic to evaluate the reliability of a new product by a host of reliability tests due to the limiting factors of time and test costs. Evaluating the reliability of products in a short time is a challenging problem. In this paper, an approach is proposed that combines a group of experts’ judgments and limited failure data. Novel features of this approach are that it can reflect various kinds of information without considering the individual weight and reduces aggregation error in the uncertainty quantification of multiple inconsistent pieces of information. First, an expert system is established by the Bayesian best–worst method and fuzzy logic inference, which collects and aggregates a group of expert opinions to estimate the reliability improvement factor. Then, an adaptive Bayesian melding method is investigated to generate a posterior by inaccurate prior knowledge and limited test data; this method is made more computationally efficient by implementing an improved sampling importance resampling algorithm. Finally, an application for the reliability evaluation of a subsystem of a CNC lathe is discussed to illustrate the framework, which is shown to validate the reasonability and robustness of our proposal.

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Section: An Adaptive Bayesian Melding Methodsmentioning

confidence: 99%

An Adaptive Bayesian Melding Method for Reliability Evaluation Via Limited Failure Data: An Application to the Servo Turret

et al. 2020

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“…Therefore, they mirror the Monte Carlo and Markov chain Monte Carlo approaches in the literature: rejection sampling, importance sampling, and sequential Monte Carlo among others. Two state-of-the-art examples are the adaptive importance sampling (AIS-BN) scheme [46] and the evidence pre-propagation importance sampling (EPIS-BN) [47].…”

Section: Inferencementioning

confidence: 99%

Entropy and the Kullback–Leibler Divergence for Bayesian Networks: Computational Complexity and Efficient Implementation

Scutari

2024

Algorithms

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Bayesian networks (BNs) are a foundational model in machine learning and causal inference. Their graphical structure can handle high-dimensional problems, divide them into a sparse collection of smaller ones, underlies Judea Pearl’s causality, and determines their explainability and interpretability. Despite their popularity, there are almost no resources in the literature on how to compute Shannon’s entropy and the Kullback–Leibler (KL) divergence for BNs under their most common distributional assumptions. In this paper, we provide computationally efficient algorithms for both by leveraging BNs’ graphical structure, and we illustrate them with a complete set of numerical examples. In the process, we show it is possible to reduce the computational complexity of KL from cubic to quadratic for Gaussian BNs.

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“…As mentioned above, batch resampling techniques based on rejection control (Liu, Chen, and Wong 1998;Yuan and Druzdzel 2007b) or sequential Monte Carlo (SMC) (Doucet, Godsill, and Andrieu 2000;Fan, Xu, and Shelton 2010), i.e. particle filtering, can mitigate the SIS weight variance problem, but they can lead to reduced particle diversity, especially when many resampling iterations are required.…”

Section: Related Workmentioning

confidence: 99%

Learning to Reject Sequential Importance Steps for Continuous-Time Bayesian Networks

Weiss

Natarajan

Page

2015

AAAI

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Applications of graphical models often require the use of approximate inference, such as sequential importance sampling (SIS), for estimation of the model distribution given partial evidence, i.e., the target distribution. However, when SIS proposal and target distributions are dissimilar, such procedures lead to biased estimates or require a prohibitive number of samples. We introduce ReBaSIS, a method that better approximates the target distribution by sampling variable by variable from existing importance samplers and accepting or rejecting each proposed assignment in the sequence: a choice made based on anticipating upcoming evidence. We relate the per-variable proposal and model distributions by expected weight ratios of sequence completions and show that we can learn accurate models of optimal acceptance probabilities from local samples. In a continuous-time domain, our method improves upon previous importance samplers by transforming an SIS problem into a machine learning one.

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Improving Importance Sampling by Adaptive Split-Rejection Control in Bayesian Networks

Cited by 6 publications

References 11 publications

An Adaptive Bayesian Melding Method for Reliability Evaluation Via Limited Failure Data: An Application to the Servo Turret

An Adaptive Bayesian Melding Method for Reliability Evaluation Via Limited Failure Data: An Application to the Servo Turret

Entropy and the Kullback–Leibler Divergence for Bayesian Networks: Computational Complexity and Efficient Implementation

Learning to Reject Sequential Importance Steps for Continuous-Time Bayesian Networks

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