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Still no free lunches: the price to pay for tighter PAC-Bayes bounds

Benjamin Guedj 1, 2, 3, 4, 5 Louis Pujol 6 
4 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, METRICS - Evaluation des technologies de santé et des pratiques médicales - ULR 2694, Polytech Lille - École polytechnique universitaire de Lille
Abstract : "No free lunch" results state the impossibility of obtaining meaningful bounds on the error of a learning algorithm without prior assumptions and modelling. Some models are expensive (strong assumptions, such as as subgaussian 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 minimal. The present paper explores and exhibits what the limits are for obtaining tight PAC-Bayes bounds in a robust setting for cheap models, addressing the question: is PAC-Bayes good value for money?
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Submitted on : Monday, December 9, 2019 - 9:14:20 PM
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Benjamin Guedj, Louis Pujol. Still no free lunches: the price to pay for tighter PAC-Bayes bounds. Entropy, MDPI, 2021, ⟨10.3390/e23111529⟩. ⟨hal-02401286⟩



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