%0 Journal Article %1 haddouche2020pacbayes %A Haddouche, Maxime %A Guedj, Benjamin %A Rivasplata, Omar %A Shawe-Taylor, John %D 2020 %K bayesian bounds generalization objectives readings %T PAC-Bayes unleashed: generalisation bounds with unbounded losses %U http://arxiv.org/abs/2006.07279 %X 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 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.

@article{haddouche2020pacbayes, 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.}, added-at = {2020-06-18T19:37:36.000+0200}, author = {Haddouche, Maxime and Guedj, Benjamin and Rivasplata, Omar and Shawe-Taylor, John}, biburl = {https://www.bibsonomy.org/bibtex/2ae44b740a928ea8357c73ad520e36ece/kirk86}, description = {[2006.07279] PAC-Bayes unleashed: generalisation bounds with unbounded losses}, interhash = {d3fdae9e117bf1a5103144d8d67275df}, intrahash = {ae44b740a928ea8357c73ad520e36ece}, keywords = {bayesian bounds generalization objectives readings}, note = {cite arxiv:2006.07279}, timestamp = {2020-06-18T19:37:36.000+0200}, title = {PAC-Bayes unleashed: generalisation bounds with unbounded losses}, url = {http://arxiv.org/abs/2006.07279}, year = 2020 }