Sharp bounds for population recovery

TL;DR

This paper establishes tight bounds on the sample and algorithmic complexity for the population recovery problem under noisy conditions, providing efficient algorithms that match these bounds.

Contribution

It offers the first comprehensive analysis of the most general population recovery problem with both bit-flip and erasure noise models, including tight bounds and efficient algorithms.

Findings

Matching upper and lower bounds for sample complexity under both noise models

Efficient algorithms that achieve these bounds up to polynomial factors

Extension of results to the most general version of the problem

Abstract

The population recovery problem is a basic problem in noisy unsupervised learning that has attracted significant research attention in recent years [WY12,DRWY12, MS13, BIMP13, LZ15,DST16]. A number of different variants of this problem have been studied, often under assumptions on the unknown distribution (such as that it has restricted support size). In this work we study the sample complexity and algorithmic complexity of the most general version of the problem, under both bit-flip noise and erasure noise model. We give essentially matching upper and lower sample complexity bounds for both noise models, and efficient algorithms matching these sample complexity bounds up to polynomial factors.