Biological Network Inference With GRASP: A Bayesian Network Structure Learning Method Using Adaptive Sequential Monte Carlo

Bayesian networks (BNs) provide a probabilistic, graphical framework for modeling high-dimensional joint distributions with complex correlation structures. BNs have wide applications in many disciplines, including biology, social science, finance and biomedical science. Despite extensive studies in the past, network structure learning from data is still a challenging open question in BN research. In this study, we present a sequential Monte Carlo (SMC)-based three-stage approach, GRowth-based Approach with Staged Pruning (GRASP). A double filtering strategy was first used for discovering the overall skeleton of the target BN. To search for the optimal network structures we designed an adaptive SMC (adSMC) algorithm to increase the quality and diversity of sampled networks which were further improved by a third stage to reclaim edges missed in the skeleton discovery step. GRASP gave very satisfactory results when tested on benchmark networks. Finally, BN structure learning using multiple types of genomics data illustrates GRASP’s potential in discovering novel biological relationships in integrative genomic studies.

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Biological Network Inference with GRASP: A Bayesian Network Structure Learning Method Using Adaptive Sequential Monte Carlo

10.21203/rs.3.rs-148701/v1 ◽

2021 ◽

Author(s):

Kaixian Yu ◽

Zihan Cui ◽

Xin Sui ◽

Xing Qiu ◽

Jinfeng Zhang

Keyword(s):

Monte Carlo ◽

Network Structure ◽

Network Inference ◽

Sequential Monte Carlo ◽

Structure Learning ◽

Biomedical Science ◽

Optimal Network ◽

Genomic Studies ◽

Complex Correlation ◽

Open Question

Abstract Bayesian networks (BNs) provide a probabilistic, graphical framework for modeling high-dimensional joint distributions with complex correlation structures. BNs have wide applications in many disciplines, including biology, social science, finance and biomedical science. Despite extensive studies in the past, network structure learning from data is still a challenging open question in BN research. In this study, we present a sequential Monte Carlo (SMC)-based three-stage approach, GRowth-based Approach with Staged Pruning (GRASP). A double filtering strategy was first used for discovering the overall skeleton of the target BN. To search for the optimal network structures we designed an adaptive SMC (adSMC) algorithm to increase the quality and diversity of sampled networks which were further improved by a third stage to reclaim edges missed in the skeleton discovery step. GRASP gave very satisfactory results when tested on benchmark networks. Finally, BN structure learning using multiple types of genomics data illustrates GRASP’s potential in discovering novel biological relationships in integrative genomic studies.

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GRASP: a Bayesian network structure learning method using adaptive sequential Monte Carlo

10.1101/767327 ◽

2019 ◽

Author(s):

Kaixian Yu ◽

Zihan Cui ◽

Xing Qiu ◽

Jinfeng Zhang

Keyword(s):

Monte Carlo ◽

Network Structure ◽

Biological Networks ◽

Missing Values ◽

Sequential Monte Carlo ◽

Structure Learning ◽

Heterogeneous Data ◽

Optimal Network ◽

Genomic Studies ◽

Open Question

AbstractBayesian networks (BNs) provide a probabilistic, graphical framework for modeling high-dimensional joint distributions with complex dependence structures. BNs can be used to infer complex biological networks using heterogeneous data from different sources with missing values. Despite extensive studies in the past, network structure learning from data is still a challenging open question in BN research. In this study, we present a sequential Monte Carlo (SMC) based three-stage approach, GRowth-based Approach with Staged Pruning (GRASP). A double filtering strategy was first used for discovering the overall skeleton of the target BN. To search for the optimal network structures we designed an adaptive SMC (adSMC) algorithm to increase the diversity of sampled networks which were further improved by a new stage to reclaim edges missed in the skeleton discovery step. GRASP gave very satisfactory results when tested on benchmark networks. Finally, BN structure learning using multiple types of genomics data illustrates GRASP’s potential in discovering novel biological relationships in integrative genomic studies.

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Correctness of Sequential Monte Carlo Inference for Probabilistic Programming Languages

Programming Languages and Systems - Lecture Notes in Computer Science ◽

10.1007/978-3-030-72019-3_15 ◽

2021 ◽

pp. 404-431

Author(s):

Daniel Lundén ◽

Johannes Borgström ◽

David Broman

Keyword(s):

Monte Carlo ◽

Programming Languages ◽

Sequential Monte Carlo ◽

Fundamental Problem ◽

Operational Semantics ◽

Correctness Proof ◽

Probabilistic Programming ◽

Inference Problems ◽

Large Numbers ◽

Open Question

AbstractProbabilistic programming is an approach to reasoning under uncertainty by encoding inference problems as programs. In order to solve these inference problems, probabilistic programming languages (PPLs) employ different inference algorithms, such as sequential Monte Carlo (SMC), Markov chain Monte Carlo (MCMC), or variational methods. Existing research on such algorithms mainly concerns their implementation and efficiency, rather than the correctness of the algorithms themselves when applied in the context of expressive PPLs. To remedy this, we give a correctness proof for SMC methods in the context of an expressive PPL calculus, representative of popular PPLs such as WebPPL, Anglican, and Birch. Previous work have studied correctness of MCMC using an operational semantics, and correctness of SMC and MCMC in a denotational setting without term recursion. However, for SMC inference—one of the most commonly used algorithms in PPLs as of today—no formal correctness proof exists in an operational setting. In particular, an open question is if the resample locations in a probabilistic program affects the correctness of SMC. We solve this fundamental problem, and make four novel contributions: (i) we extend an untyped PPL lambda calculus and operational semantics to include explicit resample terms, expressing synchronization points in SMC inference; (ii) we prove, for the first time, that subject to mild restrictions, any placement of the explicit resample terms is valid for a generic form of SMC inference; (iii) as a result of (ii), our calculus benefits from classic results from the SMC literature: a law of large numbers and an unbiased estimate of the model evidence; and (iv) we formalize the bootstrap particle filter for the calculus and discuss how our results can be further extended to other SMC algorithms.

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Bayesian Estimation of DSGE Models

10.23943/princeton/9780691161082.001.0001 ◽

2015 ◽

Cited By ~ 45

Author(s):

Edward P. Herbst ◽

Frank Schorfheide

Keyword(s):

Monte Carlo ◽

Sequential Monte Carlo ◽

Likelihood Function ◽

Academic Research ◽

Dynamic Stochastic General Equilibrium ◽

Computational Techniques ◽

Dsge Models ◽

Monte Carlo Techniques ◽

Dynamic Stochastic ◽

Theoretical Foundations

Dynamic stochastic general equilibrium (DSGE) models have become one of the workhorses of modern macroeconomics and are extensively used for academic research as well as forecasting and policy analysis at central banks. This book introduces readers to state-of-the-art computational techniques used in the Bayesian analysis of DSGE models. The book covers Markov chain Monte Carlo techniques for linearized DSGE models, novel sequential Monte Carlo methods that can be used for parameter inference, and the estimation of nonlinear DSGE models based on particle filter approximations of the likelihood function. The theoretical foundations of the algorithms are discussed in depth, and detailed empirical applications and numerical illustrations are provided. The book also gives invaluable advice on how to tailor these algorithms to specific applications and assess the accuracy and reliability of the computations. The book is essential reading for graduate students, academic researchers, and practitioners at policy institutions.

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