Structured probabilistic inference in object-oriented probabilistic graphical models. (Inférence probabiliste structurée dans les modèles graphiques probabilistes orientés-objet)

Troubleshooting, risk management and reliability are important use of Probabilistic Graphical Models (PGM). In these domains, Bayesian Networks BNs) are favored, as they offer a sound framework for knowledge representation and probabilistic reason- ing. However, when used to model complex systems, BNs lack both scalability and reusability. In the late 90s, several BN extensions inspired by object-oriented program- ing languages appeared. These new frameworks were the first of a growing list of exten- sions that lead to First-Order Probabilistic Models (FOPMs). Yet, as the AI community set its focus on merging first-order logic with PGMs, BN’s modeling issues were set aside. Nonetheless, there are still many unanswered questions regarding object-oriented PGMs: can we extend inheritance ? How can we implement object-oriented concepts such as subtype polymorphisms, prototyping or abstraction ? What are the differences between FOPMs and object-oriented PGMs? In domains were expert knowledge is used to model systems, probabilistic inference is the principal use of BNs. There exists a wide variety of probabilistic inference al- gorithms, each exploiting different aspects of BNs (conditioning, junction trees, CNF, etc.). But, when we consider BNs extensions, there a few dedicated inference algo- rithms. Indeed, most extensions rely on ground inference, ie. , on transforming their model into a BN and apply classic probabilistic inference algorithms. Among the few dedicated inference algorithms, Structured Variable Elimination (SVE, Pfeffer 1999) exploits object-oriented models to prevent redundant computations in networks with structural repetitions. However, SVE has several flaws preventing its use in systems designed by experts in which there is no structural uncertainty, ie. , in closed world systems. This thesis purpose was to develop a complete object-oriented framework for di- rected PGMs and generalize the concepts of structured inference. After describing the current state-of-the-art, we propose a discussion about the different representation paradigms used in BN extensions (object-oriented, entity-relationship, first-order). Then we present the first contribution of this thesis: a fully object-oriented framework for di- rected PGMs. Using Probabilistic Relational Models (PRMs) as a starting point, we extend them to include features such as multiple inheritance, abstraction, subtype poly- morphisms and attribute typing inheritance. The second contribution of this thesis is the study and generalization of SVE. In- deed, SVE exploits the structural information encoded by classes to prevent redundant computations. We propose a reformulation of SVE and point out several flaws in the algorithm. We then generalize SVE by extending the concept of structured inference to our framework, resulting in a new probabilistic inference scheme called Structured Probabilistic Inference (SPI). Finally, we show how d-separation analysis and SPI can both be used conjointly to speed-up probabilistic inference in PRMs. The third contribution of this thesis push structured inference a step further. We exploit subgraphs mining to discover repeated patterns in a system. Such patterns define hight level structural repetitions, called dynamic classes, and can be exploited to speed- up SPI. We propose a complexity analysis of this problem and provide an approximate algorithm to discover "good" dynamic classes. We provide experimental results proving the efficiency of our approach.