Online Natural Gradient as a Kalman Filter

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
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Contributeur : Yann Ollivier <>
Soumis le : lundi 11 décembre 2017 - 10:50:31
Dernière modification le : jeudi 11 janvier 2018 - 06:27:34


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


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



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