Still No Free Lunches: The Price to Pay for Tighter PAC-Bayes Bounds

Autor:	Louis Pujol, Benjamin Guedj
Přispěvatelé:	University College of London [London] (UCL), Computer science department [University College London] (UCL-CS), Inria-CWI (Inria-CWI), Centrum Wiskunde & Informatica (CWI)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)-Université de Lille, Sciences et Technologies, The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris-Saclay, Department of Computer science [University College of London] (UCL-CS), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), ANR-18-CE23-0015,APRIORI,Une Perspective PAC-Bayésienne de l'Apprentissage de Représentations(2018), ANR-18-CE40-0016,BEAGLE,Apprentissage PAC-bayésien agnostique(2018)
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	FOS: Computer and information sciences Computer Science - Machine Learning no free lunch theorems Science QC1-999 Yield (finance) Robust statistics Probably approximately correct learning General Physics and Astronomy PAC-Bayes theory Machine Learning (stat.ML) Mathematics - Statistics Theory Statistics Theory (math.ST) 02 engineering and technology Astrophysics 01 natural sciences Article Machine Learning (cs.LG) 010104 statistics & probability Bayes' theorem statistical learning theory [STAT.ML]Statistics [stat]/Machine Learning [stat.ML] [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG] Statistics - Machine Learning 020204 information systems FOS: Mathematics 0202 electrical engineering electronic engineering information engineering No free lunch in search and optimization Applied mathematics 0101 mathematics Impossibility Mathematics Physics State (functional analysis) [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] QB460-466 Statistical learning theory
Zdroj:	Entropy Volume 23 Issue 11 Entropy, MDPI, 2021, ⟨10.3390/e23111529⟩ Entropy, Vol 23, Iss 1529, p 1529 (2021) Entropy, 2021, ⟨10.3390/e23111529⟩
ISSN:	1099-4300
DOI:	10.3390/e23111529
Popis:	“No free lunch” results state the impossibility of obtaining meaningful bounds on the error of a learning algorithm without prior assumptions and modelling, which is more or less realistic for a given problem. Some models are “expensive” (strong assumptions, such as sub-Gaussian tails), others are “cheap” (simply finite variance). As it is well known, the more you pay, the more you get: in other words, the most expensive models yield the more interesting bounds. Recent advances in robust statistics have investigated procedures to obtain tight bounds while keeping the cost of assumptions minimal. The present paper explores and exhibits what the limits are for obtaining tight probably approximately correct (PAC)-Bayes bounds in a robust setting for cheap models.
Databáze:	OpenAIRE
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