Pierre-Henri Wuillemin - Academia.edu (original) (raw)
Papers by Pierre-Henri Wuillemin
Le Centre pour la Communication Scientifique Directe - HAL - Diderot, Feb 28, 2018
Proceedings of the AAAI Conference on Artificial Intelligence
We propose a new framework to learn non-parametric graphical models from continuous observational... more We propose a new framework to learn non-parametric graphical models from continuous observational data. Our method is based on concepts from information theory in order to discover independences and causality between variables: the conditional and multivariate mutual information (such as \cite{verny2017learning} for discrete models). To estimate these quantities, we propose non-parametric estimators relying on the Bernstein copula and that are constructed by exploiting the relation between the mutual information and the copula entropy \cite{ma2011mutual, belalia2017testing}. To our knowledge, this relation is only documented for the bivariate case and, for the need of our algorithms, is here extended to the conditional and multivariate mutual information. This framework leads to a new algorithm to learn continuous non-parametric Bayesian network. Moreover, we use this estimator to speed up the BIC algorithm proposed in \cite{elidan2010copula} by taking advantage of the decomposition...
Le Centre pour la Communication Scientifique Directe - HAL - Diderot, Oct 1, 2009
National audienc
Communications in computer and information science, 2022
Le Centre pour la Communication Scientifique Directe - HAL - Université de Nantes, 2000
In complex domains, users need to be able to find causal relations between the different attribut... more In complex domains, users need to be able to find causal relations between the different attributes that compose them. Our work offers a way to help users to uncover such relations by combining the representativity of ontologies and the flexibility of probabilistic relational models, and provides them with an interactive and iterative process in order to validate or modify the obtained results.
La representation de connaissances incertaines est un probleme important dans le domaine de l'... more La representation de connaissances incertaines est un probleme important dans le domaine de l'intelligence artificielle. Les reseaux bayesiens proposent une solution interessante pour de nombreuses raisons tant theoriques que pratiques, mais ont le desavantage d'etre difficiles a creer autant qu'a maintenir. En reponse a ces problematiques, de nouveaux formalismes ont emerges, tels les Probablistic Relational Models. Ces nouveaux modeles sont tous aptes a utiliser les algorithmes d'inference developpes pour les reseaux bayesiens. Cependant ils permettent un passage a l'echelle rendant leurs utilisations tres couteuses et sous-optimales en regard de l'exploitation des informations structurelles de ces modeles. Dans cet article, nous proposons de tirer profit de notre cadre logiciel dans lequel coexistent plusieurs algorithmes d'inference dedies ou non aux PRMs afin de mener une comparaison experimentale du comportement de ces differents algorithmes.
This paper presents the aGrUM framework, a LGPL C++ library providing state-of-the-art implementa... more This paper presents the aGrUM framework, a LGPL C++ library providing state-of-the-art implementations of graphical models for decision making, including Bayesian Networks, Markov Networks (Markov random fields), Influence Diagrams, Credal Networks, Probabilistic Relational Models. The framework also contains a wrapper, pyAgrum for exploiting aGrUM in Python. This framework is the result of an ongoing effort to build an efficient and well maintained open source cross-platform software, running on Linux, MacOS X and Windows, for dealing with graphical models and for providing essential components to build new algorithms for graphical models.
Cet article s'interesse a l'inference probabiliste dans les systemes dynamiques multi-cib... more Cet article s'interesse a l'inference probabiliste dans les systemes dynamiques multi-cibles. Dans un contexte ou les cibles et/ou les observations peuvent evoluer, la plupart des algorithmes ne se servent pas completement de l'incrementalite du systeme pour optimiser les calculs. Cela induit des calculs inutiles et peut augmenter considerablement les temps d'in-ference, particulierement pour les systemes de grande taille. Pour pallier ce probleme, nous proposons un nouvel algorithme d'arbre de jonction utilisant une technique par envoi de messages. Etant donne une nouvelle requete, cet algorithme permet de minimiser les calculs en recalculant uniquement les messages differents des calculs precedents. Nous montrons l'effica-cite de notre approche par des resultats experimentaux. ABSTRACT. This article addresses the question of probabilistic inference in multi-target dynamic systems. In a context where targets and/or evidence may evolve, most of the algorithms...
A common decision problem repeats a lot of time with the same kind of alternatives and the same s... more A common decision problem repeats a lot of time with the same kind of alternatives and the same set of criteria, but with a different decision case in each occurrence. The objective of early guidance in this kind of problem is to facilitate the selection of a subset of satisfactory alternatives for each new decision case, without asking the user any knowledge of the problem. This article proposes an early guidance system based on a model of knowledge of the common decision problem. It first presents the construction of a Bayesian network for a common decision problem to embed the knowledge in the aiding framework. Second, the concept of intervention proposed by Pearl is extended to prob-abilistic interventions for a single variable and for a set of variables. Finally the early guidance procedure is presented on the basis of the Bayesian network and using a proba-bilistic intervention to set a decision case even though it is partially observed.
Representing uncertainty in knowledge is a common issue in Artificial Intelligence. Bayesian Netw... more Representing uncertainty in knowledge is a common issue in Artificial Intelligence. Bayesian Networks have been one of the main models used in this field of research. The simplicity of their specification is one of the reason for their success, both in industrial and in theoretical domains. The widespread use of Bayesian Networks brings new challenges in the design and use of large- scale systems, where this very simplicity causes a lack of expressiveness and scalability. To fill this gap, an increasing number of languages emerged as extensions of Bayesian Networks with many approaches: first-order logic, object-oriented, entity-relation, and so on. In this paper we focus on Probabilistic Relational Models, an object-oriented extension. However, Probabilistic Relational Models do not fully exploit the object-oriented paradigm, in particular they lack class inheritance. Using Object-Oriented Bayesian Networks as a basis, we propose to lightly extend PRMs framework resulting in strong...
This paper reports the progress of a project whose goal is to develop a model-driven, contract-ba... more This paper reports the progress of a project whose goal is to develop a model-driven, contract-based SOA testing environment in which grey-box test strategies for large services architectures are driven by stochastic inference. In order to achieve this goal, a Bayesian network is built directly by mapping and model transformation from the services architecture models (MDA approach). As services architectures are complex and large systems, the generated BN and its associated probability tables may also be very large. Nevertheless, the structure of the services architecture, of its design and test models suggests that techniques of compilation of the inference tasks will allow using the BN as a sustainable tool for driving the troubleshooting strategy for large scale systems.
Estimating the prerequisite structure of skills is a crucial issue in domain modeling. Students u... more Estimating the prerequisite structure of skills is a crucial issue in domain modeling. Students usually learn skills in sequence since the preliminary skills need to be learned prior to the complex skills. The prerequisite relations between skills underlie the design of learning sequence and adaptation strategies for tutoring systems. The prerequisite structures of skills are usually studied by human experts, but they are seldom tested empirically. Due to plenty of educational data available, in this paper, we intend to discover the prerequisite structure of skills from student performance data. However, it is a challenging task since skills are latent variables. Uncertainty exists in inferring student knowledge of skills from performance data. Probabilistic Association Rules Mining proposed by Sun et al. (2010) is a novel technique to discover association rules from uncertain data. In this paper, we preprocess student performance data by an evidence model. Then the probabilistic kn...
La representation de connaissances incertaines est un probleme important dans le domaine de l'... more La representation de connaissances incertaines est un probleme important dans le domaine de l'intelligence artificielle. Les reseaux bayesiens proposent une solution interessante pour de nombreuses raisons theoriques et pratiques mais ont le desavantage d'etre difficiles a creer autant qu'a maintenir. Dans cet article, nous comparons trois formalismes qui tentent de repondre a ces problemes en enrichissant les reseaux bayesiens avec des notions issues des paradigmes orientes objets et de la logique du premier ordre. Nous verrons que ces propositions fournissent de nouveaux outils de modelisation des reseaux bayesiens, mais posent de nouveaux problemes propres aux reseaux de grande taille.
When using Bayesian networks for modelling the behavior of man-made machinery, it usually happen... more When using Bayesian networks for modelling the behavior of man-made machinery, it usually happens that a large part of the model is deterministic. For such Bayesian networks the deterministic part of the model can be represented as a Boolean function, and a central part of belief updating reduces to the task of calculating the number of satisfying configurations in a Boolean function. In this paper we explore how advances in the calculation of Boolean functions can be adopted for belief updating, in particular within the context of troubleshooting. We present experimental results indicating a substantial speed-up compared to traditional junction tree propagation.
Entropy, 2021
Causal inference methods based on conditional independence construct Markov equivalent graphs and... more Causal inference methods based on conditional independence construct Markov equivalent graphs and cannot be applied to bivariate cases. The approaches based on independence of cause and mechanism state, on the contrary, that causal discovery can be inferred for two observations. In our contribution, we pose a challenge to reconcile these two research directions. We study the role of latent variables such as latent instrumental variables and hidden common causes in the causal graphical structures. We show that methods based on the independence of cause and mechanism indirectly contain traces of the existence of the hidden instrumental variables. We derive a novel algorithm to infer causal relationships between two variables, and we validate the proposed method on simulated data and on a benchmark of cause-effect pairs. We illustrate by our experiments that the proposed approach is simple and extremely competitive in terms of empirical accuracy compared to the state-of-the-art methods.
Probabilistic Graphical Models form a class of compact representations of high-dimensional probab... more Probabilistic Graphical Models form a class of compact representations of high-dimensional probability distributions by decomposing these distributions in a set of multivariate factors (potentials). Every exact algorithm (for probabilistic inference, MAP, etc.) operates on a specific representation of these potentials. However complex probabilistic models often lead to very large potentials which dramatically impact both the space and time complexities of these algorithms and which can make inference in complex models intractable. In this paper we propose a new approach based on low-rank tensor representation to approximate and operate with these potentials. The low-rank tensor representation is used for the approximation of potentials with controlled precision and an important reduction in the number of parameters. Every operator used in such algorithms (multiplication, addition, projection, etc.) can be defined within this representation, leading to an approximation framework wher...
Le Centre pour la Communication Scientifique Directe - HAL - Diderot, Feb 28, 2018
Proceedings of the AAAI Conference on Artificial Intelligence
We propose a new framework to learn non-parametric graphical models from continuous observational... more We propose a new framework to learn non-parametric graphical models from continuous observational data. Our method is based on concepts from information theory in order to discover independences and causality between variables: the conditional and multivariate mutual information (such as \cite{verny2017learning} for discrete models). To estimate these quantities, we propose non-parametric estimators relying on the Bernstein copula and that are constructed by exploiting the relation between the mutual information and the copula entropy \cite{ma2011mutual, belalia2017testing}. To our knowledge, this relation is only documented for the bivariate case and, for the need of our algorithms, is here extended to the conditional and multivariate mutual information. This framework leads to a new algorithm to learn continuous non-parametric Bayesian network. Moreover, we use this estimator to speed up the BIC algorithm proposed in \cite{elidan2010copula} by taking advantage of the decomposition...
Le Centre pour la Communication Scientifique Directe - HAL - Diderot, Oct 1, 2009
National audienc
Communications in computer and information science, 2022
Le Centre pour la Communication Scientifique Directe - HAL - Université de Nantes, 2000
In complex domains, users need to be able to find causal relations between the different attribut... more In complex domains, users need to be able to find causal relations between the different attributes that compose them. Our work offers a way to help users to uncover such relations by combining the representativity of ontologies and the flexibility of probabilistic relational models, and provides them with an interactive and iterative process in order to validate or modify the obtained results.
La representation de connaissances incertaines est un probleme important dans le domaine de l'... more La representation de connaissances incertaines est un probleme important dans le domaine de l'intelligence artificielle. Les reseaux bayesiens proposent une solution interessante pour de nombreuses raisons tant theoriques que pratiques, mais ont le desavantage d'etre difficiles a creer autant qu'a maintenir. En reponse a ces problematiques, de nouveaux formalismes ont emerges, tels les Probablistic Relational Models. Ces nouveaux modeles sont tous aptes a utiliser les algorithmes d'inference developpes pour les reseaux bayesiens. Cependant ils permettent un passage a l'echelle rendant leurs utilisations tres couteuses et sous-optimales en regard de l'exploitation des informations structurelles de ces modeles. Dans cet article, nous proposons de tirer profit de notre cadre logiciel dans lequel coexistent plusieurs algorithmes d'inference dedies ou non aux PRMs afin de mener une comparaison experimentale du comportement de ces differents algorithmes.
This paper presents the aGrUM framework, a LGPL C++ library providing state-of-the-art implementa... more This paper presents the aGrUM framework, a LGPL C++ library providing state-of-the-art implementations of graphical models for decision making, including Bayesian Networks, Markov Networks (Markov random fields), Influence Diagrams, Credal Networks, Probabilistic Relational Models. The framework also contains a wrapper, pyAgrum for exploiting aGrUM in Python. This framework is the result of an ongoing effort to build an efficient and well maintained open source cross-platform software, running on Linux, MacOS X and Windows, for dealing with graphical models and for providing essential components to build new algorithms for graphical models.
Cet article s'interesse a l'inference probabiliste dans les systemes dynamiques multi-cib... more Cet article s'interesse a l'inference probabiliste dans les systemes dynamiques multi-cibles. Dans un contexte ou les cibles et/ou les observations peuvent evoluer, la plupart des algorithmes ne se servent pas completement de l'incrementalite du systeme pour optimiser les calculs. Cela induit des calculs inutiles et peut augmenter considerablement les temps d'in-ference, particulierement pour les systemes de grande taille. Pour pallier ce probleme, nous proposons un nouvel algorithme d'arbre de jonction utilisant une technique par envoi de messages. Etant donne une nouvelle requete, cet algorithme permet de minimiser les calculs en recalculant uniquement les messages differents des calculs precedents. Nous montrons l'effica-cite de notre approche par des resultats experimentaux. ABSTRACT. This article addresses the question of probabilistic inference in multi-target dynamic systems. In a context where targets and/or evidence may evolve, most of the algorithms...
A common decision problem repeats a lot of time with the same kind of alternatives and the same s... more A common decision problem repeats a lot of time with the same kind of alternatives and the same set of criteria, but with a different decision case in each occurrence. The objective of early guidance in this kind of problem is to facilitate the selection of a subset of satisfactory alternatives for each new decision case, without asking the user any knowledge of the problem. This article proposes an early guidance system based on a model of knowledge of the common decision problem. It first presents the construction of a Bayesian network for a common decision problem to embed the knowledge in the aiding framework. Second, the concept of intervention proposed by Pearl is extended to prob-abilistic interventions for a single variable and for a set of variables. Finally the early guidance procedure is presented on the basis of the Bayesian network and using a proba-bilistic intervention to set a decision case even though it is partially observed.
Representing uncertainty in knowledge is a common issue in Artificial Intelligence. Bayesian Netw... more Representing uncertainty in knowledge is a common issue in Artificial Intelligence. Bayesian Networks have been one of the main models used in this field of research. The simplicity of their specification is one of the reason for their success, both in industrial and in theoretical domains. The widespread use of Bayesian Networks brings new challenges in the design and use of large- scale systems, where this very simplicity causes a lack of expressiveness and scalability. To fill this gap, an increasing number of languages emerged as extensions of Bayesian Networks with many approaches: first-order logic, object-oriented, entity-relation, and so on. In this paper we focus on Probabilistic Relational Models, an object-oriented extension. However, Probabilistic Relational Models do not fully exploit the object-oriented paradigm, in particular they lack class inheritance. Using Object-Oriented Bayesian Networks as a basis, we propose to lightly extend PRMs framework resulting in strong...
This paper reports the progress of a project whose goal is to develop a model-driven, contract-ba... more This paper reports the progress of a project whose goal is to develop a model-driven, contract-based SOA testing environment in which grey-box test strategies for large services architectures are driven by stochastic inference. In order to achieve this goal, a Bayesian network is built directly by mapping and model transformation from the services architecture models (MDA approach). As services architectures are complex and large systems, the generated BN and its associated probability tables may also be very large. Nevertheless, the structure of the services architecture, of its design and test models suggests that techniques of compilation of the inference tasks will allow using the BN as a sustainable tool for driving the troubleshooting strategy for large scale systems.
Estimating the prerequisite structure of skills is a crucial issue in domain modeling. Students u... more Estimating the prerequisite structure of skills is a crucial issue in domain modeling. Students usually learn skills in sequence since the preliminary skills need to be learned prior to the complex skills. The prerequisite relations between skills underlie the design of learning sequence and adaptation strategies for tutoring systems. The prerequisite structures of skills are usually studied by human experts, but they are seldom tested empirically. Due to plenty of educational data available, in this paper, we intend to discover the prerequisite structure of skills from student performance data. However, it is a challenging task since skills are latent variables. Uncertainty exists in inferring student knowledge of skills from performance data. Probabilistic Association Rules Mining proposed by Sun et al. (2010) is a novel technique to discover association rules from uncertain data. In this paper, we preprocess student performance data by an evidence model. Then the probabilistic kn...
La representation de connaissances incertaines est un probleme important dans le domaine de l'... more La representation de connaissances incertaines est un probleme important dans le domaine de l'intelligence artificielle. Les reseaux bayesiens proposent une solution interessante pour de nombreuses raisons theoriques et pratiques mais ont le desavantage d'etre difficiles a creer autant qu'a maintenir. Dans cet article, nous comparons trois formalismes qui tentent de repondre a ces problemes en enrichissant les reseaux bayesiens avec des notions issues des paradigmes orientes objets et de la logique du premier ordre. Nous verrons que ces propositions fournissent de nouveaux outils de modelisation des reseaux bayesiens, mais posent de nouveaux problemes propres aux reseaux de grande taille.
When using Bayesian networks for modelling the behavior of man-made machinery, it usually happen... more When using Bayesian networks for modelling the behavior of man-made machinery, it usually happens that a large part of the model is deterministic. For such Bayesian networks the deterministic part of the model can be represented as a Boolean function, and a central part of belief updating reduces to the task of calculating the number of satisfying configurations in a Boolean function. In this paper we explore how advances in the calculation of Boolean functions can be adopted for belief updating, in particular within the context of troubleshooting. We present experimental results indicating a substantial speed-up compared to traditional junction tree propagation.
Entropy, 2021
Causal inference methods based on conditional independence construct Markov equivalent graphs and... more Causal inference methods based on conditional independence construct Markov equivalent graphs and cannot be applied to bivariate cases. The approaches based on independence of cause and mechanism state, on the contrary, that causal discovery can be inferred for two observations. In our contribution, we pose a challenge to reconcile these two research directions. We study the role of latent variables such as latent instrumental variables and hidden common causes in the causal graphical structures. We show that methods based on the independence of cause and mechanism indirectly contain traces of the existence of the hidden instrumental variables. We derive a novel algorithm to infer causal relationships between two variables, and we validate the proposed method on simulated data and on a benchmark of cause-effect pairs. We illustrate by our experiments that the proposed approach is simple and extremely competitive in terms of empirical accuracy compared to the state-of-the-art methods.
Probabilistic Graphical Models form a class of compact representations of high-dimensional probab... more Probabilistic Graphical Models form a class of compact representations of high-dimensional probability distributions by decomposing these distributions in a set of multivariate factors (potentials). Every exact algorithm (for probabilistic inference, MAP, etc.) operates on a specific representation of these potentials. However complex probabilistic models often lead to very large potentials which dramatically impact both the space and time complexities of these algorithms and which can make inference in complex models intractable. In this paper we propose a new approach based on low-rank tensor representation to approximate and operate with these potentials. The low-rank tensor representation is used for the approximation of potentials with controlled precision and an important reduction in the number of parameters. Every operator used in such algorithms (multiplication, addition, projection, etc.) can be defined within this representation, leading to an approximation framework wher...