Online Natural Gradient as a Kalman Filter

Yann Ollivier 1, 2, 3
1 TAU - TAckling the Underspeficied
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : We establish a full relationship between Kalman filtering and Amari's natural gradient in statistical learning. Namely, using an online natural gradient descent on data log-likelihood to evaluate the parameter of a probabilistic model from a series of observations, is exactly equivalent to using an extended Kalman filter to estimate the parameter (assumed to have constant dynamics). In the i.i.d. case, this relation is a consequence of the "information filter" phrasing of the extended Kalman filter. In the recurrent (state space, non-i.i.d.) case, we prove that the joint Kalman filter over states and parameters is a natural gradient on top of real-time recurrent learning (RTRL), a classical algorithm to train recurrent models. This exact algebraic correspondence provides relevant settings for natural gradient hyperparameters such as learning rates or initialization and regularization of the Fisher information matrix.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.inria.fr/hal-01660622
Contributeur : Yann Ollivier <>
Soumis le : lundi 11 décembre 2017 - 10:50:31
Dernière modification le : mardi 17 avril 2018 - 09:05:05

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  • HAL Id : hal-01660622, version 1
  • ARXIV : 1703.00209

Citation

Yann Ollivier. Online Natural Gradient as a Kalman Filter. 2017. 〈hal-01660622〉

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