# Time-series information and learning

1 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal, Inria Lille - Nord Europe
Abstract : Given a time series $X_1,\dots,X_n,\dots$ taking values in a large (high-dimensional) space $\cX$, we would like to find a function $f$ from $\cX$ to a small (low-dimensional or finite) space $\cY$ such that the time series $f(X_1),\dots,f(X_n),\dots$ retains all the information about the time-series dependence in the original sequence, or as much as possible thereof. This goal is formalized in this work, and it is shown that the target function $f$ can be found as the one that maximizes a certain quantity that can be expressed in terms of entropies of the series $(f(X_i))_{i\in\N}$. This quantity can be estimated empirically, and does not involve estimating the distribution on the original time series $(X_i)_{i\in\N}$.
Type de document :
Communication dans un congrès
ISIT - International Symposium on Information Theory, 2013, Istanbul, Turkey. pp.1392-1395, 2013

https://hal.inria.fr/hal-00823233
Contributeur : Daniil Ryabko <>
Soumis le : jeudi 16 mai 2013 - 13:55:47
Dernière modification le : jeudi 11 janvier 2018 - 06:22:13

### Identifiants

• HAL Id : hal-00823233, version 1

### Citation

Daniil Ryabko. Time-series information and learning. ISIT - International Symposium on Information Theory, 2013, Istanbul, Turkey. pp.1392-1395, 2013. 〈hal-00823233〉

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