Not) Bounding the True Error
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TL;DR
A new approach to bounding the true error rate of a continuous valued classifier based upon PAC-Bayes bounds is presented, with results of a 2 - 3 order of magnitude improvement vs. the best deterministic neural net bounds.
Abstract
We present a new approach to bounding the true error rate of a continuous valued classifier based upon PAC-Bayes bounds. The method first constructs a distribution over classifiers by determining how sensitive each parameter in the model is to noise. The true error rate of the stochastic classifier found with the sensitivity analysis can then be tightly bounded using a PAC-Bayes bound. In this paper we demonstrate the method on artificial neural networks with results of a 2 3 order of magnitude improvement vs. the best deterministic neural net bounds. 1