A Survey of Probabilistic Models Using the Bayesian Programming Methodology as a Unifying Framework

This paper presents a survey of the most common probabilistic models for artefact conception. We use a generic formalism called Bayesian Programming, which we introduce briefly, for reviewing the main probabilistic models found in the literature. Indeed, we show that Bayesian Networks, Markov Localization, Kalman filters, etc., can all be captured under this single formalism. We believe it offers the novice reader a good introduction to these models, while still providing the experience reader an enriching global view of the field.

[1]  Padhraic Smyth,et al.  Belief networks, hidden Markov models, and Markov random fields: A unifying view , 1997, Pattern Recognit. Lett..

[2]  Brendan J. Frey,et al.  Graphical Models for Machine Learning and Digital Communication , 1998 .

[3]  J. L. Roux An Introduction to the Kalman Filter , 2003 .

[4]  Zoubin Ghahramani,et al.  Learning Dynamic Bayesian Networks , 1997, Summer School on Neural Networks.

[5]  L. Kaelbling,et al.  Toward Hierachical Decomposition for Planning in Uncertain Environments , 2001 .

[6]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..

[7]  Keiji Kanazawa,et al.  A model for reasoning about persistence and causation , 1989 .

[8]  Julien Diard,et al.  La carte bayésienne : un modèle probabiliste hiérarchique pour la navigation en robotique mobile. (The Bayesian map - A hierarchical probabilistic model for mobile robot navigation) , 2003 .

[9]  Zoubin Ghahramani,et al.  An Introduction to Hidden Markov Models and Bayesian Networks , 2001, Int. J. Pattern Recognit. Artif. Intell..

[10]  Wolfram Burgard,et al.  Estimating the Absolute Position of a Mobile Robot Using Position Probability Grids , 1996, AAAI/IAAI, Vol. 2.

[11]  Stuart J. Russell,et al.  Stochastic simulation algorithms for dynamic probabilistic networks , 1995, UAI.

[12]  A. Jazwinski Stochastic Processes and Filtering Theory , 1970 .

[13]  Yoshua Bengio,et al.  An Input Output HMM Architecture , 1994, NIPS.

[14]  Craig Boutilier,et al.  Decision-Theoretic Planning: Structural Assumptions and Computational Leverage , 1999, J. Artif. Intell. Res..

[15]  Stuart J. Russell,et al.  Dynamic bayesian networks: representation, inference and learning , 2002 .

[16]  ierre,et al.  Bayesian Robot Programming , 2022 .

[17]  Hagai Attias,et al.  Planning by Probabilistic Inference , 2003, AISTATS.

[18]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[19]  G Roup,et al.  Survey: Probabilistic Methodology and Techniques for Artefact Conception and Development , 2002 .

[20]  Joelle Pineau,et al.  An integrated approach to hierarchy and abstraction for pomdps , 2002 .

[21]  Michael I. Jordan Graphical Models , 2003 .

[22]  Zoubin Ghahramani,et al.  A Unifying Review of Linear Gaussian Models , 1999, Neural Computation.

[23]  P. Gehler,et al.  An introduction to graphical models , 2001 .

[24]  Milos Hauskrecht,et al.  Hierarchical Solution of Markov Decision Processes using Macro-actions , 1998, UAI.

[25]  Michael I. Jordan,et al.  Probabilistic Independence Networks for Hidden Markov Probability Models , 1997, Neural Computation.

[26]  Michael I. Jordan,et al.  Learning Fine Motion by Markov Mixtures of Experts , 1995, NIPS.

[27]  Wolfram Burgard,et al.  A Probabilistic Approach to Concurrent Mapping and Localization for Mobile Robots , 1998, Auton. Robots.

[28]  Sebastian Thrun,et al.  Probabilistic Algorithms in Robotics , 2000, AI Mag..

[29]  A. L. Barker,et al.  Bayesian Estimation and the Kalman Filter , 1994 .

[30]  Sebastian Thrun,et al.  Robotic mapping: a survey , 2003 .

[31]  P. Bessière,et al.  Hierarchies of probabilistic models of space for mobile robots: the bayesian map and the abstraction operator , 2003 .

[32]  Pierre Bessiere,et al.  Probabilistic Methodology and Techniques for Artefact Conception and Development , 2003 .

[33]  Steven J. Nowlan,et al.  Mixtures of Controllers for Jump Linear and Non-Linear Plants , 1993, NIPS.

[34]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[35]  Lawrence R. Rabiner,et al.  A tutorial on hidden Markov models and selected applications in speech recognition , 1989, Proc. IEEE.

[36]  Julien Diard,et al.  Programmation bayésienne des robots , 2004, Rev. d'Intelligence Artif..

[37]  Leslie Pack Kaelbling,et al.  Planning and Acting in Partially Observable Stochastic Domains , 1998, Artif. Intell..

[38]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..