Computational and Statistical Tradeoffs via Convex Relaxation

Venkat Chandrasekaran
California Institute of Technology

In modern data analysis, one is frequently faced with statistical inference problems involving massive datasets. Processing such large datasets is usually viewed as a substantial computational challenge. However, if data are a statistician’s main resource then access to more data should be viewed as an asset rather than as a burden. In this paper we describe a computational framework based on convex relaxation to reduce the computational complexity of an inference procedure when one has access to increasingly larger datasets. Convex relaxation techniques have been widely used in theoretical computer science as they give tractable approximation algorithms to many computationally intractable tasks. We demonstrate the e?cacy of this methodology in statistical estimation in providing concrete time-data tradeo?s in a class of denoising problems. Thus, convex relaxation o?ers a principled approach to exploit the statistical gains from larger datasets to reduce the runtime of inference algorithms. (Joint work with Michael Jordan.)

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