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Publication Detail
PAC-Bayes unleashed: generalisation bounds with unbounded losses
  • Publication Type:
    Journal article
  • Publication Sub Type:
    Article
  • Authors:
    Haddouche M, Guedj B, Rivasplata O, Shawe-Taylor J
  • Publisher:
    MDPI AG
  • Publication date:
    12/10/2021
  • Journal:
    Entropy: international and interdisciplinary journal of entropy and information studies
  • Status:
    Published
  • Print ISSN:
    1099-4300
  • Keywords:
    stat.ML, stat.ML, cs.LG, math.ST, stat.TH
Abstract
We present new PAC-Bayesian generalisation bounds for learning problems with unbounded loss functions. This extends the relevance and applicability of the PAC-Bayes learning framework, where most of the existing literature focuses on supervised learning problems where the loss function is bounded (typically assumed to take values in the interval [0;1]). In order to relax this assumption, we propose a new notion called the \emph{special boundedness condition}, which effectively allows the range of the loss to depend on each predictor. Based on this new notion we derive a novel PAC-Bayesian generalisation bound for unbounded loss functions, and we instantiate it on a linear regression problem. To make our theory usable by the largest audience possible, we include discussions on actual computation, practicality and limitations of our assumptions.
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Dept of Statistical Science
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