Statistical Inference with Limited Memory: A Survey
It addresses the problem of memory limitations in statistical inference for researchers and practitioners, but as a survey, it is incremental in summarizing existing work.
The paper surveys the state-of-the-art in statistical inference under memory constraints, covering problems like hypothesis testing and parameter estimation, and identifies fundamental algorithmic building blocks and techniques for lower bounds.
The problem of statistical inference in its various forms has been the subject of decades-long extensive research. Most of the effort has been focused on characterizing the behavior as a function of the number of available samples, with far less attention given to the effect of memory limitations on performance. Recently, this latter topic has drawn much interest in the engineering and computer science literature. In this survey paper, we attempt to review the state-of-the-art of statistical inference under memory constraints in several canonical problems, including hypothesis testing, parameter estimation, and distribution property testing/estimation. We discuss the main results in this developing field, and by identifying recurrent themes, we extract some fundamental building blocks for algorithmic construction, as well as useful techniques for lower bound derivations.