Family learning: nonparametric statistical inference with parametric efficiency

TL;DR

This paper introduces a spectral method for nonparametric inference that learns low-dimensional exponential families from related samples, enabling efficient hypothesis testing with potential power gains.

Contribution

It proposes a novel spectral approach to learn parametric families from data, improving inference when the true model is unknown.

Findings

Method achieves asymptotic optimal power when the model fits well.

Computationally efficient and scalable to real-world data.

Demonstrates substantial power gains in simulations and A/B tests.

Abstract

Hypothesis testing and other statistical inference procedures are most efficient when a reliable low-dimensional parametric family can be specified. We propose a method that learns such a family when one exists but its form is not known a priori, by examining samples from related populations and fitting a low-dimensional exponential family that approximates all the samples as well as possible. We propose a computationally efficient spectral method that allows us to carry out hypothesis tests that are valid whether or not the fit is good, and recover asymptotically optimal power if it is. Our method is computationally efficient and can produce substantial power gains in simulation and real-world A/B testing data.