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Acta Biotheoretica

, Volume 58, Issue 2–3, pp 191–216 | Cite as

Common Bayesian Models for Common Cognitive Issues

  • Francis ColasEmail author
  • Julien Diard
  • Pierre Bessière
Regular Article

Abstract

How can an incomplete and uncertain model of the environment be used to perceive, infer, decide and act efficiently? This is the challenge that both living and artificial cognitive systems have to face. Symbolic logic is, by its nature, unable to deal with this question. The subjectivist approach to probability is an extension to logic that is designed specifically to face this challenge. In this paper, we review a number of frequently encountered cognitive issues and cast them into a common Bayesian formalism. The concepts we review are ambiguities, fusion, multimodality, conflicts, modularity, hierarchies and loops. First, each of these concepts is introduced briefly using some examples from the neuroscience, psychophysics or robotics literature. Then, the concept is formalized using a template Bayesian model. The assumptions and common features of these models, as well as their major differences, are outlined and discussed.

Keywords

Mixture Model Bayesian Network Bayesian Model Conditional Independence Hide Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Alais D, Burr D (2004) The ventriloquist effect results from near-optimal bimodal integration. Curr Biol 14:257–262Google Scholar
  2. Anastasio TJ, Patton PE, Belkacem-Boussaid K (2000) Using Bayes’ rule to model multisensory enhancement in the superior colliculus. Neural Comput 12(5):1165–1187CrossRefGoogle Scholar
  3. Arulampalam S, Maskell S, Gordon N, Clapp T (2002) A tutorial on particle filter for online nonlinear/non-gaussian Bayesian tracking. IEEE Transact Signal Proc 50(2):174–188Google Scholar
  4. Banks MS (2004) Neuroscience: what you see and hear is what you get. Curr Biol 14(6):236–238CrossRefGoogle Scholar
  5. Battaglia PW, Jacobs RA, Aslin RN (2003) Bayesian integration of visual and auditory signals for spatial localization. J Opt Soc Am A 20(7):1391–1397CrossRefGoogle Scholar
  6. Bengio Y, Frasconi P (1995) An input/output HMM architecture. In: Tesauro G, Touretzky D, Leen T (eds) Advances in neural information processing systems 7. MIT Press, Cambridge, pp 427–434Google Scholar
  7. Bessière P, Ahuactzin J-M, Aycard O, Bellot D, Colas F, Coué C, Diard J, Garcia R, Koike C, Lebeltel O, LeHy R, Malrait O, Mazer E, Mekhnacha K, Pradalier C, Spalanzani A (2003) Survey: Probabilistic methodology and techniques for artefact conception and development. Technical Report RR-4730, INRIA Rhône-Alpes, Montbonnot, FranceGoogle Scholar
  8. Bessière P, Laugier C, Siegwart R (eds) (2008) Probabilistic reasoning and decision making in sensory-motor systems, vol 46 of STAR. Springer, BerlinGoogle Scholar
  9. Bishop CM, Svensén M (2003) Bayesian hierarchical mixtures of experts. In: Proceedings of the ninteenth conference on uncertainty in artificial intelligence. Acapulco, MexicoGoogle Scholar
  10. Boutilier C, Dean T, Hanks S (1999) Decision theoretic planning: Structural assumptions and computational leverage. J Artif Intell Res (JAIR) 11:1–94Google Scholar
  11. Brockwell PJ, Davis RA (2000) Introduction to time series and forecasting, 2nd edn. Springer, BerlinGoogle Scholar
  12. Dean T, Kanazawa K (1989) A model for reasoning about persistence and causation. Comput Intell 5(3):142–150CrossRefGoogle Scholar
  13. Diard J, Bessière P (2008) Bayesian maps: probabilistic and hierarchical models for mobile robot navigation. In: Bessière P, Laugier C, Siegwart R (eds) Probabilistic reasoning and decision making in sensory-motor systems, vol 46. Springer Tracts in Advanced Robotics. Springer, Berlin, pp 153–176Google Scholar
  14. Drewing K, Ernst M (2006) Integration of force and position cues for shape perception through active touch. Brain Res 1078:92–100CrossRefGoogle Scholar
  15. Ernst MO, Banks MS (2002) Humans integrate visual and haptic information in a statistically optimal fashion. Nature 415(6870):429–433CrossRefGoogle Scholar
  16. Frey BJ (1998) Graphical models for machine learning and digital communication. MIT Press, CambridgeGoogle Scholar
  17. Geisler WS, Kersten D (2002) Illusions, perception and Bayes. Nature Neuroscience 5(6):598–604Google Scholar
  18. Gepshtein S, Banks MS (2003) Viewing geometry determines how vision and haptics combine in size perception. Curr Biol 13(6):483–488CrossRefGoogle Scholar
  19. Ghahramani Z, Wolpert DM, Jordan MI (1997) Computational models of sensorimotor integration. In: Morasso PG, Sanguineti V (eds) Self-organization, computational maps and motor control. Elsevier, Amsterdam, pp 117–147Google Scholar
  20. Gopnik A, Schulz L (2004) Mechanisms of theory formation in young children. Trends Cogn Sci 8(8):371–377CrossRefGoogle Scholar
  21. Haith A, Jackson C, Miall C, Vijayakumar S (2008) Unifying the sensory and motor components of sensorimotor adaptation. In: Advances in neural information processing systems (NIPS 2008)Google Scholar
  22. Harvey AC (1992) Forecasting, structural time series models and the Kalman filter. Cambridge University Press, Cambridge.Google Scholar
  23. Hauskrecht M, Meuleau N, Boutilier L, Kaelbling L, Dean T (1998) Hierarchical solution of markov decision processes using macro-actions. In: Proceedings of the 14-th conference on uncertainty in artificial intelligence. pp 220–229.Google Scholar
  24. Hillis JM, Watt SJ, Landy MS, Banks MS (2004) Slant from texture and disparity cues: optimal cue combination. J Vis 4:967–992Google Scholar
  25. Jacobs RA (1999) Optimal integration of texture and motion cues to depth. Vis Res 39:3621–3629CrossRefGoogle Scholar
  26. Jacobs RA, Jordan MI, Nowlan SJ, Hinton GE (1991) Adaptive mixtures of local experts. Neural Comput 3:79–87CrossRefGoogle Scholar
  27. Jaynes ET (2003) Probability theory: the logic of science. Cambridge University Press, CambridgeGoogle Scholar
  28. Jensen F (1996) An introduction to Bayesian networks. UCL Press, LondonGoogle Scholar
  29. Jordan MI (1999) Learning in graphical models. MIT Press, Cambridge (Edited Volume)Google Scholar
  30. Jürgens R, Becker W (2006) Perception of angular displacement without landmarks: evidence for Bayesian fusion of vestibular, optokinetic, podokinesthetic, and cognitive information. Exp Brain Res 174:528–543CrossRefGoogle Scholar
  31. Kaelbling LP, Littman M, Cassandra A (1998) Planning and acting in partially observable stochastic domain. Artifi Intell 101(1–2):99–134CrossRefGoogle Scholar
  32. Kalman RE (1960) A new approach to linear filtering and prediction problems. Trans ASME–J Basic Eng 82(Series D):35–45Google Scholar
  33. Kemp C, Tenenbaum J (2008) The discovery of structural form. Proc Natl Acad Sci USA 105(31):10687–10692CrossRefGoogle Scholar
  34. Kersten D, Mamassian P, Yuille A (2004) Object perception as Bayesian inference. Ann Rev Psychol 55:271–304CrossRefGoogle Scholar
  35. Kiemel T, Oie K, Jeka J (2002) Multisensory fusion and the stochastic structure of postural sway. Biol Cybern 87:262–277CrossRefGoogle Scholar
  36. Knill DC, Richards W (1996) Perception as Bayesian inference. MIT Press, Cambridge, MAGoogle Scholar
  37. Koike C (2005) Bayesian approach to action selection and attention focusing. Application in autonomous robot programming. Thèse de doctorat, Inst. Nat. Polytechnique de Grenoble, Grenoble (FR)Google Scholar
  38. Koike C, Bessière P, Mazer E (2008) Bayesian approach to action selection and attention focusing. In: Bessière P, Laugier C, Siegwart R (eds) Probabilistic reasoning and decision making in sensory-motor systems, vol 46 of STAR. Springer, BerlinGoogle Scholar
  39. Koller D, Pfeffer A (1997) Object-oriented Bayesian networks. In: Proceedings of the thirteenth conference on uncertainty in artifical intelligence. Morgan Kaufmann publishers, San Francisco, pp 302–313Google Scholar
  40. Körding KP, Beierholm U, Ma WJ, Quartz S, Tenenbaum JB, Shams L (2007) Causal inference in multisensory perception. PLoS one 2(9):e943CrossRefGoogle Scholar
  41. Körding KP, Wolpert DM (2004a) Bayesian integration in sensorimotor learning. Nature 427:244–247CrossRefGoogle Scholar
  42. Körding KP, Wolpert DM (2004b) The loss function of sensorimotor learning. Proc Natl Acad Sci USA 101(26):9839–9842CrossRefGoogle Scholar
  43. Kuipers BJ (2000) The spatial semantic hierarchy. Artifi Intell 119(1–2):191–233CrossRefGoogle Scholar
  44. Landy MS, Maloney LT, Johnston EB, Young M (1995) Measurement and modeling of depth cue combination: in defense of weak fusion. Vis Res 35:389–412CrossRefGoogle Scholar
  45. Laskey KB, Mahoney SM (1997) Network fragments: representing knowledge for constructing probabilistic models. In: Proceedings of the thirteenth conference on uncertainty in artifical intelligence. Morgan Kaufmann publishers, San Francisco, pp 334–341Google Scholar
  46. Laurens J, Droulez J (2007) Bayesian processing of vestibular information. Biol Cybern 96:389–404CrossRefGoogle Scholar
  47. Laurens J, Droulez J (2008) Bayesian modeling of visuo-vestibular interactions. In: Bessière P, Laugier C, Siegwart R (eds) Probabilistic reasoning and decision making in sensory-motor systems, vol 46 of STAR. Springer, BerlinGoogle Scholar
  48. Lebeltel O, Bessière P, Diard J, Mazer E (2004) Bayesian robot programming. Adv Robot 16(1):49–79Google Scholar
  49. Leonard J, Durrant-Whyte H, Cox I (1992) Dynamic map-building for an autonomous mobile robot. Intl J Robot Res 11(4):286–298CrossRefGoogle Scholar
  50. Maeda S (1990) Compensatory articulation during speech: evidence from the analysis and synthesis of vocal-tract shapes using an articulatory model. In: Hardcastle WJ, Marchal A (eds) Speech production and speech modelling. Kluwer, Dordrecht, pp 131–149Google Scholar
  51. Mitchell TM (1997) Machine Learning. McGraw-Hill, HallGoogle Scholar
  52. Murphy K (2002) Dynamic Bayesian networks: Representation, Inference and Learning. Ph.D. thesis, University of California, Berkeley, Berkeley, CAGoogle Scholar
  53. Neal RM, Beal MJ, and Roweis ST (2003) Inferring state sequences for non-linear systems with embedded hidden Markov models. In: Thrun S, and al, (eds), Advances in neural information processing systems 16. MIT Press, CambridgeGoogle Scholar
  54. Nefian A, Hayes M (1999) Face recognition using an embedded hmm. In: Proceedings of the IEEE conference on audio and video-based biometric person authentication. pp 19–24Google Scholar
  55. Pearl J (1988) Probabilistic reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San MateoGoogle Scholar
  56. Pineau J, Thrun S (2002) High-level robot behaviour control with POMDPs. In: AAAI workshop on cognitive roboticsGoogle Scholar
  57. Pizlo Z (2001) Perception viewed as an inverse problem. Vision Research 41(24):3141–3161CrossRefGoogle Scholar
  58. Poggio T (1984) Vision by man and machine. Sci Am 250:106–116Google Scholar
  59. Pradalier C, Colas F, Bessière P (2003) Expressing Bayesian fusion as a product of distributions: applications in robotics. In: Proceedings IEEE international conference on intelligent robots and systemsGoogle Scholar
  60. Rabiner LR (1989) A tutorial on hidden markov models and selected applications in speech recognition. Proc IEEE 77(2):257–286CrossRefGoogle Scholar
  61. Rabiner LR, Juang B-H (1993) Fundamentals of speech recognition, chapter theory and implementation of Hidden Markov Models. Prentice Hall, Englewood Cliffs, pp 321–389Google Scholar
  62. Robinson JA (1979) Logic: form and function. North-Holland, New YorkGoogle Scholar
  63. Sato Y, Toyoizumi T, Aihara K (2007) Bayesian inference explains perception of unity and ventriloquism aftereffect: Identification of common sources of audiovisual stimuli. Neural Comput 19(12):3335–3355CrossRefGoogle Scholar
  64. Stocker A, Simoncelli E (2008) A Bayesian model of conditioned perception. In: Platt J, Koller D, Singer Y, Roweis S (eds) Advances in neural information processing systems 20. MIT Press, Cambridge, pp 1409–1416Google Scholar
  65. Thrun S (2000) Probabilistic algorithms in robotics. AI Magazine 21(4):93–109Google Scholar
  66. Thrun S, Burgard W, Fox D (2005) Probabilistic robotics. MIT Press, CambridgeGoogle Scholar
  67. van der Kooij H, Jacobs R, Koopman B, Grootenboer H (1999) A multisensory integration model of human stance control. Biol Cybern 80:299–308CrossRefGoogle Scholar
  68. Waterhouse S, MacKay D, Robinson T (1996) Bayesian methods for mixtures of experts. In: Touretzky DS, Mozer MC, Hasselmo ME (eds) Advances in neural information processing systems, vol 8. The MIT Press, Cambridge, pp 351–357Google Scholar
  69. Weiss Y, Simoncelli EP, Adelson EH (2002) Motion illusions as optimal percepts. Nature Neurosci 5(6):598–604CrossRefGoogle Scholar
  70. Wolpert D (2007) Probabilistic models in human sensorimotor control. Hum Movement Sci 26:511–24CrossRefGoogle Scholar
  71. Yuille AL, Bülthoff HH (1996) Bayesian decision theory and psychophysics. In: Knill DC, Richards W (eds) Perception as Bayesian inference. MIT Press, Cambridge, pp 123–161Google Scholar
  72. Zupan LH, Merfeld DM, Darlot C (2002) Using sensory weighting to model the influence of canal, otolith and visual cues on spatial orientation and eye movements. Biol Cybern 86(3):209–230CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.ASL, ETH ZurichZurichSwitzerland
  2. 2.LPNC, CNRS, UPMF, Bâtiment Sciences de l’Homme et MathématiqueGrenoble Cedex 9France
  3. 3.E-Motion, LIG, CNRSMontbonnot Saint-IsmierFrance

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