Coresets for Regressions with Panel Data

TL;DR

This paper develops algorithms to create small, efficient coresets for regression problems in panel data, enabling faster computations without significant loss of accuracy.

Contribution

It introduces a novel framework for constructing coresets in panel data regression, with size bounds independent of data size, based on the Feldman-Langberg sensitivity approach.

Findings

Coreset sizes are significantly smaller than full datasets.

Coresets accelerate regression computations.

Empirical results validate the effectiveness of the approach.

Abstract

This paper introduces the problem of coresets for regression problems to panel data settings. We first define coresets for several variants of regression problems with panel data and then present efficient algorithms to construct coresets of size that depend polynomially on 1/$\varepsilon$ (where $\varepsilon$ is the error parameter) and the number of regression parameters - independent of the number of individuals in the panel data or the time units each individual is observed for. Our approach is based on the Feldman-Langberg framework in which a key step is to upper bound the "total sensitivity" that is roughly the sum of maximum influences of all individual-time pairs taken over all possible choices of regression parameters. Empirically, we assess our approach with synthetic and real-world datasets; the coreset sizes constructed using our approach are much smaller than the full dataset and coresets indeed accelerate the running time of computing the regression objective.