Balanced Tuning of Multi-dimensional Bayesian Network Classifiers

Bolt, Janneke H.; Gaag, Linda C. van der

doi:10.1007/978-3-319-20807-7_19

Cited by 5 publications

(5 citation statements)

References 6 publications

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“…Then, given this algebraic characterization, we demonstrate that one-way sensitivity methods defined for BNs can be generalized to single full CPT analyses for any model whose interpolating polynomial is multilinear, for example context-specific BNs [3] and stratified chain event graphs [12,39]. Because of both the lack of theoretical results justifying their use and the increase in computational complexity, multi-way methods have not been extensively discussed in the literature: see [2,7,21] for some exceptions. This paper aims at providing a comprehensive theoretical toolbox to start applying such analyses in practice.…”

Section: Introductionmentioning

confidence: 99%

Sensitivity analysis in multilinear probabilistic models

Leonelli

Görgen

Smith

2017

Information Sciences

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Sensitivity methods for the analysis of the outputs of discrete Bayesian networks have been extensively studied and implemented in different software packages. These methods usually focus on the study of sensitivity functions and on the impact of a parameter change to the Chan-Darwiche distance. Although not fully recognized, the majority of these results rely heavily on the multilinear structure of atomic probabilities in terms of the conditional probability parameters associated with this type of network. By defining a statistical model through the polynomial expression of its associated defining conditional probabilities, we develop here a unifying approach to sensitivity methods applicable to a large suite of models including extensions of Bayesian networks, for instance context-specific ones. Our algebraic approach enables us to prove that for models whose defining polynomial is multilinear both the Chan-Darwiche distance and any divergence in the family of φ-divergences are minimized for a certain class of multi-parameter contemporaneous variations when parameters are proportionally covaried.

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Section: Introductionmentioning

confidence: 99%

Sensitivity analysis in multilinear probabilistic models

Leonelli

Görgen

Smith

2017

Information Sciences

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“…Renooji (2014) studied the properties of the co-variation schemes for parametrization of BNs. Bolt & van der Gaag (2015 proposed balanced and combined tuning heuristics for parametrization that are interesting for future work.…”

Section: Related Workmentioning

confidence: 99%

“…Such parametric BNs are very useful in situations where probabilities are unknown, or partially known. They received a lot of attention, see e.g., (Coupé & Van der Gaag, 1998;Coupé et al, 2000;Druzdzel & Van der Gaag, 2000;Jensen, 1999;Laskey, 1995;Castillo et al, 1995Castillo et al, , 1996Castillo et al, , 1997aKjaerulff & Van der Gaag, 2000;Chan & Darwiche, 2002, 2004Coupé & Van der Gaag, 2002;Renooij, 2014;Bolt & Van der Gaag, 2015). Important objectives on parametric BNs are e.g., to provide a symbolic expression in terms of the model parameters p and q for inference queries, sensitivity analysis, or determining whether there exists a concrete set of parameter values such that a given threshold on an inference query holds.…”

Section: Introductionmentioning

confidence: 99%

Automatically Finding the Right Probabilities in Bayesian Networks

Salmani,

Katoen

2023

jair

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This paper presents alternative techniques for inference on classical Bayesian networks in which all probabilities are fixed, and for synthesis problems when conditional probability tables (CPTs) in such networks contain symbolic parameters rather than concrete probabilities. The key idea is to exploit probabilistic model checking as well as its recent extension to parameter synthesis techniques for parametric Markov chains. To enable this, the Bayesian networks are transformed into Markov chains and their objectives are mapped onto probabilistic temporal logic formulas. For exact inference, we compare probabilistic model checking to weighted model counting on various Bayesian network benchmarks. We contrast symbolic model checking using multi-terminal binary (aka: algebraic) decision diagrams to symbolic inference using proba- bilistic sentential decision diagrams, symbolic data structures that are tailored to Bayesian networks. For the parametric setting, we describe how our techniques can be used for various synthesis problems such as computing sensitivity functions (and values), simple and difference parameter tuning and ratio parameter tuning. Our parameter synthesis techniques are applicable to arbitrarily many, possibly dependent, parameters that may occur in multiple CPTs. This lifts restrictions, e.g., on the number of parametrized CPTs, or on parameter dependencies between several CPTs, that exist in the literature. Experiments on several benchmarks show that our parameter synthesis techniques can treat parameter synthesis for Bayesian networks (with hundreds of unknown parameters) that are out of reach for existing techniques.

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“…Early MDC researches mainly focus on solving MDC problem via Bayesian techniques [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] which have been reviewed [49]. In recent years, especially during the past five years, more and more attentions have been attracted from machine learning community and many MDC algorithms based on non-Bayesian techniques are proposed.…”

Section: Introductionmentioning

confidence: 99%

Multi-dimensional classification: paradigm, algorithms and beyond

Jia,

Zhang

2024

Vicinagearth

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Multi-dimensional classification (MDC) aims at learning from objects where each of them is represented by a single instance while associated with multiple class variables. In recent years, this practical learning paradigm has attracted increasing attentions in machine learning community. In this paper, a timely review on this topic is provided with emphasis on representative algorithms. Firstly, the MDC learning framework, commonly used evaluation metrics and publicly available MDC datasets are given. Then, eight state-of-the-art MDC algorithms are scrutinized as the representatives of three categories. After that, several related learning settings are briefly summarized. Finally, this paper is concluded with discussing some open problems to be studied in the future.

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Balanced Tuning of Multi-dimensional Bayesian Network Classifiers

Cited by 5 publications

References 6 publications

Sensitivity analysis in multilinear probabilistic models

Sensitivity analysis in multilinear probabilistic models

Automatically Finding the Right Probabilities in Bayesian Networks

Multi-dimensional classification: paradigm, algorithms and beyond

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