Learning to learn from data: Using deep adversarial learning to construct optimal statistical procedures | MATHEMATICS - Science Advances

Optimal statistical procedures are constructed using deep adversarial learning to optimize play in a two-player game by Science Advances.
 

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Abstract

Traditionally, statistical procedures have been derived via analytic calculations whose validity often relies on sample size growing to infinity. We use tools from deep learning to develop a new approach, adversarial Monte Carlo meta-learning, for constructing optimal statistical procedures. Statistical problems are framed as two-player games in which Nature adversarially selects a distribution that makes it difficult for a statistician to answer the scientific question using data drawn from this distribution. The players’ strategies are parameterized via neural networks, and optimal play is learned by modifying the network weights over many repetitions of the game. Given sufficient computing time, the statistician’s strategy is (nearly) optimal at the finite observed sample size, rather than in the hypothetical scenario where sample size grows to infinity. In numerical experiments and data examples, this approach performs favorably compared to standard practice in point estimation, individual-level predictions, and interval estimation.

INTRODUCTION
Motivation and background

In most scientific disciplines, hypotheses are evaluated by applying statistical tools to experimental or observational data. Hence, the science of statistics plays a fundamental role in the process of scientific discovery, and innovations in statistical methodology have the potential to enable advances in the broader sciences.

Two distinct paradigms dominate the statistical landscape: the frequentist and Bayesian approaches. In the frequentist paradigm, probability statements describe the behavior of statistical procedures over independent repetitions of an experiment.
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Additional resources 
Science Advances  26 Feb 2020:
Vol. 6, no. 9, eaaw2140
DOI: 10.1126/sciadv.aaw2140

Source: Science Advances