Analyzing statistical and computational tradeoffs of estimation procedures
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 riskcomputation 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 HodgesLehmann estimators. We conclude with an evaluation of risk associated with early termination of iterative matrix inversion algorithms in the context of linear regression.
 Publication:

arXiv eprints
 Pub Date:
 June 2015
 arXiv:
 arXiv:1506.07925
 Bibcode:
 2015arXiv150607925S
 Keywords:

 Statistics  Computation;
 Statistics  Machine Learning