Pré-Publication, Document De Travail Année : 2024

General oracle inequalities for a penalized log-likelihood criterion based on non-stationary data

Inégalités oracles générales pour un critère par log-vraisemblance pénalisée pour des données non stationnaires

Résumé

We prove oracle inequalities for a penalized log-likelihood criterion that hold even if the data are not independent and not stationary, based on a martingale approach. The assumptions are checked for various contexts: density estimation with independent and identically distributed (i.i.d) data, hidden Markov models, spiking neural networks, adversarial bandits. In each case, we compare our results to the literature, showing that, although we lose some logarithmic factors in the most classical case (i.i.d.), these results are comparable or more general than the existing results in the more dependent cases.

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Dates et versions

hal-04578260 , version 1 (16-05-2024)
hal-04578260 , version 2 (10-10-2024)

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Julien Aubert, Luc Lehéricy, Patricia Reynaud-Bouret. General oracle inequalities for a penalized log-likelihood criterion based on non-stationary data. 2024. ⟨hal-04578260v2⟩
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