Multivariate Cluster-Based Discretization for Bayesian Network Structure Learning

Mabrouk, Ahmed; Gonzales, Christophe; Jabet-Chevalier, Karine; Chojnaki, Eric

doi:10.1007/978-3-319-23540-0_11

Cited by 8 publications

(7 citation statements)

References 14 publications

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“…But the expressive power shall be increased. In some sense, a ctdBN learning algorithm has already been provided in [18]. This algorithm raises some issues, notably the fact that computing discretizations conditionally to the nodes in the Markov blankets of each discretized node limits the ctdBNs that can be learnt.…”

Section: Resultsmentioning

confidence: 99%

“…and ii) will the loss of information affect significantly the results of inference? A possible answer to the first question consists of exploiting "conditional truncated densities" [18]. The answer to the second question of course strongly depends on the discretization performed but, as we shall see, conditional truncated densities can limit the discrepancy between the exact a posteriori marginal density functions of the continuous random variables and the approximation they provide.…”

Section: Definition 3 (Discretization) a Discretization Of A Continumentioning

confidence: 99%

“…It represents compactly mixed probability distributions. The model is derived from the result of an algorithm for learning BNs from datasets containing both discrete and continuous random variables [18].…”

Section: Introductionmentioning

confidence: 99%

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On conditional truncated densities Bayesian networks

Cortijo

Gonzales

2018

International Journal of Approximate Reasoning

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The majority of Bayesian networks learning and inference algorithms rely on the assumption that all random variables are discrete, which is not necessarily the case in real-world problems. In situations where some variables are continuous, a trade-off between the expressive power of the model and the computational complexity of inference has to be done: on one hand, conditional Gaussian models are computationally efficient but they lack expressive power; on the other hand, mixtures of exponentials (MTE), basis functions (MTBF) or polynomials (MOP) are expressive but this comes at the expense of tractability. In this paper, we introduce an alternative model called a ctdBN that lies in between. It is composed of a "discrete" Bayesian network (BN) combined with a set of univariate conditional truncated densities modeling the uncertainty over the continuous random variables given their discrete counterpart resulting from a discretization process. We prove that ctdBNs can approximate (arbitrarily well) any Lipschitz mixed probability distribution. They can therefore be exploited in many practical situations. An efficient inference algorithm is also provided and its computational complexity justifies theoretically why inference computation times in ctdBNs are very close to those in discrete BNs. Experiments confirm the tractability of the model and highlight its expressive power, notably by comparing it with BNs on classification problems and with MTEs and MOPs on marginal distributions estimations.

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Section: Resultsmentioning

confidence: 99%

Section: Definition 3 (Discretization) a Discretization Of A Continumentioning

confidence: 99%

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On conditional truncated densities Bayesian networks

Cortijo

Gonzales

2018

International Journal of Approximate Reasoning

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“…We thus propose to discretize in a three-level scale {OK, degraded, KO} each continuous criterion X τ (noting its discretized counterpart X τ d ). Considering the discretization step in the model itself is a usual practice when dealing with probabilistic graphical model (see for instance (Mabrouk et al, 2015)). We then propose in a similar way to deal with this discretization step in the form of a Gaussian mixture model where the parameters are learnt in an unsupervised way by Expectation-Maximization (EM) algorithm (Dempster et al, 1977).…”

Section: Discretizationmentioning

confidence: 99%

“…The grey area is the histogram of the V 120 rms values. The blue and orange lines are the cut points between the three states OK, degraded and KO, a https://www.probayes.com/ determined as proposed by Mabrouk et al (2015). Weakly critical vibrations are considered for this variable when V 120 rms < 429, or strongly critical when V 120 rms > 1735.…”

Section: Discretizationmentioning

confidence: 99%

Unsupervised Co-Training of Bayesian Networks for the Diagnosis of Machining Spindle

Monvoisin¹,

Leray²,

Ritou³

2021

Proceedings of the 31st European Safety and Reliability Conference (ESREL 2021)

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The objective of Smart Manufacturing is to improve productivity and competitiveness in industry, based on in-process data. Indeed, failures can stop the production for a couple of days and generate costs of non-quality. Failures in industry can either damage the machine or the product being produced. In both cases, the earlier the failure is detected, the lower the impact on production. Thus, monitoring both the process and the machine condition is interesting, due to their potential interactions. Besides, the diagnosis of the nature of the incident is also important, in order to react adequately as fast as possible. It requires reliable, explainable and understandable models such as Bayesian networks for performing tasks like condition prediction. Bayesian networks can be learned with incomplete data and in a supervised or unsupervised way, which is very useful because the collect of labelled data is costly and sometimes impossible, especially in industry where problems are, moreover, very rare. In this paper, we propose a generic architecture based on two Bayesian networks and a collaborative learning strategy that improves the condition monitoring of rotating machines in unsupervised context by using information gathered from process monitoring.

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Dealing with Continuous Variables in Graphical Models

Gonzales

2019

Lecture Notes in Computer Science

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Multivariate Cluster-Based Discretization for Bayesian Network Structure Learning

Cited by 8 publications

References 14 publications

On conditional truncated densities Bayesian networks

On conditional truncated densities Bayesian networks

Unsupervised Co-Training of Bayesian Networks for the Diagnosis of Machining Spindle

Dealing with Continuous Variables in Graphical Models

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