High Dimensional Data Enrichment: Interpretable, Fast, and Data-Efficient

Abstract

We consider the problem of multi-task learning in the high dimensional setting. In particular, we introduce an estimator and investigate its statistical and computational properties for the problem of multiple connected linear regressions known as Data Enrichment/Sharing. The between-tasks connections are captured by a cross-tasks common parameter, which gets refined by per-task individual parameters. Any convex function, e.g., norm, can characterize the structure of both common and individual parameters. We delineate the sample complexity of our estimator and provide a high probability non-asymptotic bound for estimation error of all parameters under a geometric condition. We show that the recovery of the common parameter benefits from all of the pooled samples. We propose an iterative estimation algorithm with a geometric convergence rate and supplement our theoretical analysis with experiments on synthetic data. Overall, we present a first thorough statistical and computational analysis of inference in the data-sharing model.

Tasks

Reproductions