Three rates of convergence or separation via U-statistics in a dependent framework
| Autor: | Quentin Duchemin, Yohann De Castro, Claire Lacour |
|---|---|
| Přispěvatelé: | Duchemin, Quentin, Laboratoire Analyse et Mathématiques Appliquées (LAMA), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
FOS: Computer and information sciences
[STAT.TH] Statistics [stat]/Statistics Theory [stat.TH] Machine Learning (stat.ML) Mathematics - Statistics Theory Statistics Theory (math.ST) [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG] [STAT.OT]Statistics [stat]/Other Statistics [stat.ML] [STAT.OT] Statistics [stat]/Other Statistics [stat.ML] [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG] [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] Statistics - Machine Learning FOS: Mathematics [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST] |
| Zdroj: | HAL Journal of Machine Learning Research Journal of Machine Learning Research, Microtome Publishing, 2022, 23 (201), pp.1-59 |
| ISSN: | 1532-4435 1533-7928 |
| Popis: | Despite the ubiquity of U-statistics in modern Probability and Statistics, their non-asymptotic analysis in a dependent framework may have been overlooked. In a recent work, a new concentration inequality for U-statistics of order two for uniformly ergodic Markov chains has been proved. In this paper, we put this theoretical breakthrough into action by pushing further the current state of knowledge in three different active fields of research. First, we establish a new exponential inequality for the estimation of spectra of trace class integral operators with MCMC methods. The novelty is that this result holds for kernels with positive and negative eigenvalues, which is new as far as we know. In addition, we investigate generalization performance of online algorithms working with pairwise loss functions and Markov chain samples. We provide an online-to-batch conversion result by showing how we can extract a low risk hypothesis from the sequence of hypotheses generated by any online learner. We finally give a non-asymptotic analysis of a goodness-of-fit test on the density of the invariant measure of a Markov chain. We identify some classes of alternatives over which our test based on the $L_2$ distance has a prescribed power. arXiv admin note: substantial text overlap with arXiv:2011.11435 |
| Databáze: | OpenAIRE |
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