Computational Implications of Reducing Data to Sufficient Statistics

TL;DR

Reducing data to sufficient statistics can transform a computationally feasible estimation problem into an intractable one, challenging common assumptions about data simplification in statistical analysis.

Contribution

The paper reveals that data reduction to sufficient statistics may lead to computational intractability, highlighting a critical consideration in statistical and computational methods.

Findings

Sufficient statistics can cause intractability in estimation tasks.

Connections established between statistical data reduction and computational complexity.

Implications for estimating graphical models are discussed.

Abstract

Given a large dataset and an estimation task, it is common to pre-process the data by reducing them to a set of sufficient statistics. This step is often regarded as straightforward and advantageous (in that it simplifies statistical analysis). I show that -on the contrary- reducing data to sufficient statistics can change a computationally tractable estimation problem into an intractable one. I discuss connections with recent work in theoretical computer science, and implications for some techniques to estimate graphical models.