Sample Amplification: Increasing Dataset Size even when Learning is Impossible

Jul 12, 2020



Given data drawn from an unknown distribution, D, to what extent is it possible to “amplify” this dataset and faithfully output an even larger set of samples that appear to have been drawn from D? We formalize this question as follows: an (n,m) amplification procedure takes as input n independent draws from an unknown distribution D, and outputs a set of m > n “samples” which must be indistinguishable from m samples drawn iid from D. We consider this sample amplification problem in two fundamental settings: the case where D is an arbitrary discrete distribution supported on k elements, and the case where D is a d-dimensional Gaussian with unknown mean, and fixed covariance matrix. Perhaps surprisingly, we show a valid amplification procedure exists for both of these settings, even in the regime where the size of the input dataset, n, is significantly less than what would be necessary to learn distribution D to non-trivial accuracy. We also show that our procedures are optimal up to constant factors. Beyond these results, we describe potential applications of such data amplification, and formalize a number of curious directions for future research along this vein.



About ICML 2020

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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