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On the Information Complexity of Proper Learners for VC Classes in the Realizable Case (2011.02970v1)
Published 5 Nov 2020 in cs.LG, cs.IT, and math.IT
Abstract: We provide a negative resolution to a conjecture of Steinke and Zakynthinou (2020a), by showing that their bound on the conditional mutual information (CMI) of proper learners of Vapnik--Chervonenkis (VC) classes cannot be improved from $d \log n +2$ to $O(d)$, where $n$ is the number of i.i.d. training examples. In fact, we exhibit VC classes for which the CMI of any proper learner cannot be bounded by any real-valued function of the VC dimension only.