One-Way Matching of Datasets with Low Rank Signals

TL;DR

This paper investigates the limits and methods for matching datasets with low rank signals, establishing theoretical bounds and demonstrating practical effectiveness through simulations and single-cell data applications.

Contribution

It introduces a theoretical framework for one-way dataset matching with low rank signals and proposes a linear assignment method that achieves optimal convergence rates.

Findings

Linear assignment with projected data achieves fast convergence.

Theoretical bounds are supported by simulations.

Practical application demonstrated on single-cell datasets.

Abstract

We study one-way matching of a pair of datasets with low rank signals. Under a stylized model, we first derive information-theoretic limits of matching under a mismatch proportion loss. We then show that linear assignment with projected data achieves fast rates of convergence and sometimes even minimax rate optimality for this task. The theoretical error bounds are corroborated by simulated examples. Furthermore, we illustrate practical use of the matching procedure on two single-cell data examples.