Analyzing statistical and computational tradeoffs of estimation procedures

TL;DR

This paper introduces a framework to explicitly balance statistical risk and computational cost in data inference, providing a risk-computation frontier across various estimation scenarios.

Contribution

It develops a theoretical framework for quantifying and trading off statistical risk against computational effort in diverse inference problems.

Findings

Derived analytic risk forms for normal and exponential family parameters.

Analyzed risk of early termination in iterative matrix inversion.

Illustrated the risk-computation frontier in three distinct inference settings.

Abstract

The recent explosion in the amount and dimensionality of data has exacerbated the need of trading off computational and statistical efficiency carefully, so that inference is both tractable and meaningful. We propose a framework that provides an explicit opportunity for practitioners to specify how much statistical risk they are willing to accept for a given computational cost, and leads to a theoretical risk-computation frontier for any given inference problem. We illustrate the tradeoff between risk and computation and illustrate the frontier in three distinct settings. First, we derive analytic forms for the risk of estimating parameters in the classical setting of estimating the mean and variance for normally distributed data and for the more general setting of parameters of an exponential family. The second example concentrates on computationally constrained Hodges-Lehmann estimators. We conclude with an evaluation of risk associated with early termination of iterative matrix inversion algorithms in the context of linear regression.