# LEARNABILITY IN PROBLEMS OF SEQUENTIAL INFERENCE

1 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
Abstract : Given a growing sequence of observations x_1,...,x_n,..., one is required, at each time step n, to make some inference about the stochastic mechanism generating the sequence. Several problems that have numerous applications in different branches of mathematics and computer science can be formulated in this way. For example, one may want to forecast probabilities of the next outcome x_{n+1} (sequence prediction); to make a decision on whether the mechanism generating the sequence belongs to a certain family $H_0$ versus it belongs to a different family $H_1$ (hypothesis testing); to take an action in order to maximize some utility function. In each of these problems, as well as in many others, in order to be able to make inference, one has to make some assumptions on the probabilistic mechanism generating the data. Typical assumptions are that x_i are independent and identically distributed, or that the distribution generating the sequence belongs to a certain parametric family. The central question addressed in this work is: under which assumptions is inference possible? This question is considered for several problems of inference, including sequence prediction, hypothesis testing, classification and reinforcement learning.
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Habilitation à diriger des recherches
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https://tel.archives-ouvertes.fr/tel-00675680
Contributor : Daniil Ryabko <>
Submitted on : Saturday, December 27, 2014 - 1:31:09 AM
Last modification on : Thursday, February 21, 2019 - 10:52:49 AM
Document(s) archivé(s) le : Saturday, March 28, 2015 - 10:05:52 AM

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• HAL Id : tel-00675680, version 2

### Citation

Daniil Ryabko. LEARNABILITY IN PROBLEMS OF SEQUENTIAL INFERENCE. Machine Learning [cs.LG]. Université des Sciences et Technologie de Lille - Lille I, 2011. ⟨tel-00675680v2⟩

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