Analyzing statistical and computational tradeoffs of estimation procedures
This work addresses the challenge of making inference tractable and meaningful in high-dimensional data for practitioners, though it is incremental as it builds on existing tradeoff concepts.
The authors tackled the problem of balancing computational cost and statistical accuracy in data analysis by proposing a framework that allows practitioners to specify acceptable statistical risk for given computational budgets, deriving theoretical risk-computation frontiers. They illustrated this tradeoff in three settings, including analytic risk forms for normal and exponential family parameters, computationally constrained Hodges-Lehmann estimators, and early termination in iterative matrix inversion for linear regression.
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.