## The Rescorla-Wagner algorithm and Maximum Likelihood estimation of causal parameters”. NIPS (2004)

Venue: | In L |

Citations: | 5 - 4 self |

### BibTeX

@INPROCEEDINGS{Yuille04therescorla-wagner,

author = {Alan Yuille},

title = {The Rescorla-Wagner algorithm and Maximum Likelihood estimation of causal parameters”. NIPS},

booktitle = {In L},

year = {2004}

}

### OpenURL

### Abstract

This paper analyzes generalization of the classic Rescorla-Wagner (R-W) learning algorithm and studies their relationship to Maximum Likelihood estimation of causal parameters. We prove that the parameters of two popular causal models, ∆P and P C, can be learnt by the same generalized linear Rescorla-Wagner (GLRW) algorithm provided genericity conditions apply. We characterize the fixed points of these GLRW algorithms and calculate the fluctuations about them, assuming that the input is a set of i.i.d. samples from a fixed (unknown) distribution. We describe how to determine convergence conditions and calculate convergence rates for the GLRW algorithms under these conditions. 1

### Citations

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A theory of Pavlovian conditioning: Variations in the effectiveness of reinforcement and nonreinforcement
- Rescorla, Wagner
- 1972
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Citation Context ...emp(E = 1|C1 = 0, C2) 1 − Pemp(E = 1|C1 = 0, C2)} ω2 = Pemp(E = 1|C1, C2 = 1) − Pemp(E = 1|C1, C2 = 0) . (5) 1 − Pemp(E = 1|C1, C2 = 0)} 3 Generalized Linear Rescorla-Wagner The Rescorla-Wagner model =-=[7]-=- is an alternative way to account for human learning. This iterative algorithm specifies an update rule for weights. These weights could measure the strength of a cause, such as the parameters of the ... |

259 |
From covariation to causation: a causal power theory
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- 1997
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Citation Context ... calculate convergence rates for the GLRW algorithms under these conditions. 1 Introduction There has recently been growing interest in models of causal learning formulated as probabilistic inference =-=[1,2,3,4,5]-=-. There has also been considerable interest in relating this work to the Rescorla-Wagner learning model [3,5,6] (also known as the delta rule). In addition, there are studies of the equilibria of the ... |

50 |
Crediting causality
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- 1997
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Citation Context ... calculate convergence rates for the GLRW algorithms under these conditions. 1 Introduction There has recently been growing interest in models of causal learning formulated as probabilistic inference =-=[1,2,3,4,5]-=-. There has also been considerable interest in relating this work to the Rescorla-Wagner learning model [3,5,6] (also known as the delta rule). In addition, there are studies of the equilibria of the ... |

50 |
Stochastic Approximation for constrained and unconstrained systems
- Clark, Kushner
- 1978
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Citation Context ...from an unknown empirical distribution Pemp(E, � C). Observe that the fluctuations of GLRW can be removed by introducing damping coefficients which decrease over time. Stochastic approximation theory =-=[8]-=- can then be used to give conditions for convergence. More recent work (Yuille in preparation) clarifies the class of maximum likelihood inference problems that can be “solved” by GLRW and by non-line... |

30 | Equilibria of the Rescorla-Wagner model
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Citation Context ... growing interest in models of causal learning formulated as probabilistic inference [1,2,3,4,5]. There has also been considerable interest in relating this work to the Rescorla-Wagner learning model =-=[3,5,6]-=- (also known as the delta rule). In addition, there are studies of the equilibria of the Rescorla-Wagner model [6]. This paper proves mathematical results about these related topics. In Section (2), w... |

27 | Causal induction: The power PC theory versus the Rescorla-Wagner model - Buehner, Cheng - 1997 |

26 | Explaining away in weight space
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Citation Context ... GLRW and by non-linear GLRW. In particular, we show that a non-linear RW can perform ML estimation for the non-generic case studied by Cheng. We also investigate similarities to Kalman filter models =-=[9]-=-.sAcknowledgements I thank Patricia Cheng, Peter Dayan and Yingnian Wu for helpfell discussions. Anonymous referees gave useful feedback that has motivated a follow-up paper. This work was partially s... |