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Paper Detail

Paper IDD2-S7-T3.1
Paper Title Fast-Rate Loss Bounds via Conditional Information Measures with Applications to Neural Networks
Authors Fredrik Hellström, Giuseppe Durisi, Chalmers University of Technology, Sweden
Session D2-S7-T3: Neural Networks II
Chaired Session: Wednesday, 14 July, 00:00 - 00:20
Engagement Session: Wednesday, 14 July, 00:20 - 00:40
Abstract We present a framework to derive bounds on the test loss of randomized learning algorithms for the case of bounded loss functions. Drawing from Steinke \& Zakynthinou (2020), this framework leads to bounds that depend on the conditional information density between the output hypothesis and the choice of the training set, given a larger set of data samples from which the training set is formed. Furthermore, the bounds pertain to the average test loss as well as to its tail probability, both for the PAC-Bayesian and the single-draw settings. If the conditional information density is bounded uniformly in the size $n$ of the training set, our bounds decay as $1/n$. This is in contrast with the tail bounds involving conditional information measures available in the literature, which have a less benign $1/\sqrt{n}$ dependence. We demonstrate the usefulness of our tail bounds by showing that they lead to nonvacuous estimates of the test loss achievable with some neural network architectures trained on MNIST and Fashion-MNIST.