Minimum Free Energy Principle for Constraint-Based Learning Bayesian Networks

Isozaki, Takashi; Ueno, Maomi

doi:10.1007/978-3-642-04180-8_57

Cited by 3 publications

(4 citation statements)

References 13 publications

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“…In the preliminary paper, 22) a proof for convergence was performed under strong assumption and its practical advantage was shown only in edge-reversed errors for random networks. In addition, for edge-reversed errors, our following speculation is not sufficiently analyzed: many reversed errors occurred in the process of finding v-structures.…”

Section: T Isozakimentioning

confidence: 99%

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Learning Causal Bayesian Networks Using Minimum Free Energy Principle

Isozaki

2012

New Gener. Comput.

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Constraint-based search methods, which are a major approach to learning Bayesian networks, are expected to be effective in causal discovery tasks. However, such methods often suffer from impracticality of classical hypothesis testing for conditional independence when the sample size is insufficiently large. We present a new conditional independence (CI) testing method that is designed to be effective for small samples. Our method uses the minimum free energy principle, which originates from thermodynamics, with the "Data Temperature" assumption recently proposed by us. This CI method incorporates the maximum entropy principle and converges to classical hypothesis tests in asymptotic regions. In our experiments using repository datasets (Alarm/Insurance/Hailfinder/Barley/Mildew), the results show that our method improves the learning performance of the well known PC algorithm in the view of edge-reversed errors in addition to extra/missing errors.Bayesian networks (BNs) 33) are graphical models that are also called directed acyclic graphs (DAGs) and compact representations of joint probability distributions. In a DAG, its nodes and directed edges represent random variables and direct dependencies relative among variables. This combination is suitable for modeling the uncertainty surrounding random variables.

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Section: T Isozakimentioning

confidence: 99%

“…In the preliminary paper, 22) we assumed the exponential model to prove that. However, this proof reduces the necessary assumption.…”

Section: Proofmentioning

confidence: 99%

Learning Causal Bayesian Networks Using Minimum Free Energy Principle

Isozaki

2012

New Gener. Comput.

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“…Such "big data" is gaining greater importance on the future of human society. In Open Systems Data Analytics, we are trying to develop novel analytical tools of massive data that have many variables dependent on each other, using probabilistic graphical models and methodologies of physics [57] [58].…”

Section: Open Systems Data Analyticsmentioning

confidence: 99%

Foundation of CS-DC e-Laboratory: Open Systems Exploration for Ecosystems Leveraging

Funabashi

Hanappe²,

Isozaki

et al. 2016

First Complex Systems Digital Campus World E-Conference 2015

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Abstract. We established a Complex Systems Digital Campus(CS-DC) e-laboratory "Open Systems Exploration for Ecosystems Leveraging" in view of redesigning sustainable social-ecological systems related to food production ranging over food, health, community, economy, and environment. 6 projects have begun to collaborate in e-laboratory, namely Synecoculture, P2P Food Lab, Open Systems Data Analytics, The Bee Laboratory, Open Systems Simulation and One-Health Food Lab. As a transversal methodology we apply open systems science to deepen scientific understanding and for a continuous amelioration of the management. The projects involve scientists, engineers, artists, citizens and are open to collaboration inside and outside of the e-laboratory. This article summarizes foundational principles of these projects and reports initial steps in operation.

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“…We expect to employ their method to address much larger number of variables in our method. • Isozaki et al [51,52], Isozaki and Ueno [53] proposed an effective learning Bayesian network method by adjusting the hyperparameter for small data. We expect to employ their method instead of the BDeu to improve the classification accuracy for small data.…”

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confidence: 99%

Bayesian Network Model Averaging Classifiers by Subbagging

Sugahara

Aomi²,

Ueno

2022

Entropy

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When applied to classification problems, Bayesian networks are often used to infer a class variable when given feature variables. Earlier reports have described that the classification accuracy of Bayesian network structures achieved by maximizing the marginal likelihood (ML) is lower than that achieved by maximizing the conditional log likelihood (CLL) of a class variable given the feature variables. Nevertheless, because ML has asymptotic consistency, the performance of Bayesian network structures achieved by maximizing ML is not necessarily worse than that achieved by maximizing CLL for large data. However, the error of learning structures by maximizing the ML becomes much larger for small sample sizes. That large error degrades the classification accuracy. As a method to resolve this shortcoming, model averaging has been proposed to marginalize the class variable posterior over all structures. However, the posterior standard error of each structure in the model averaging becomes large as the sample size becomes small; it subsequently degrades the classification accuracy. The main idea of this study is to improve the classification accuracy using subbagging, which is modified bagging using random sampling without replacement, to reduce the posterior standard error of each structure in model averaging. Moreover, to guarantee asymptotic consistency, we use the K-best method with the ML score. The experimentally obtained results demonstrate that our proposed method provides more accurate classification than earlier BNC methods and the other state-of-the-art ensemble methods do.

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Minimum Free Energy Principle for Constraint-Based Learning Bayesian Networks

Cited by 3 publications

References 13 publications

Learning Causal Bayesian Networks Using Minimum Free Energy Principle

Learning Causal Bayesian Networks Using Minimum Free Energy Principle

Foundation of CS-DC e-Laboratory: Open Systems Exploration for Ecosystems Leveraging

Bayesian Network Model Averaging Classifiers by Subbagging

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