Abstract
PAC-Bayes is a useful framework for deriving generalization bounds which was introduced by McAllester (’98). This framework has the flexibility of deriving distribution- and algorithm-dependent bounds, which are often tighter than VC-related uniform convergence bounds. In this manuscript we present a limitation for the PAC-Bayes framework. We demonstrate an easy learning task which is not amenable to a PAC-Bayes analysis. Specifically, we consider the task of linear classification in 1D; it is well-known that this task is learnable using just O(log(1/d)/e) examples. On the other hand, we show that this fact can not be proved using a PAC-Bayes analysis: for any algorithm that learns 1-dimensional linear classifiers there exists a (realizable) distribution for which the PAC-Bayes bound is arbitrarily large.
Original language | English |
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Journal | Advances in Neural Information Processing Systems |
Volume | 2020-December |
State | Published - 2020 |
Event | 34th Conference on Neural Information Processing Systems, NeurIPS 2020 - Virtual, Online Duration: 6 Dec 2020 → 12 Dec 2020 |
Funding
Funders | Funder number |
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Google Research | |
United States - Israel Binational Science Foundation | |
United States-Israel Binational Science Foundation | |
Israel Science Foundation | 1225/20, 2188/20 |