# Constructing confidence sets for the matrix completion problem

## TL;DR

This paper introduces a method for constructing honest and adaptive confidence sets in matrix completion, effectively accounting for unknown matrix rank under Bernoulli noise with known variance.

## Contribution

It presents a realizable approach to create confidence sets that adapt to the unknown rank of the matrix in the Bernoulli noise model.

## Key findings

- Confidence sets adapt to unknown matrix rank
- Method works under Bernoulli noise with known variance
- Provides honest and adaptive inference for matrix completion

## Abstract

In the present note we consider the problem of constructing honest and adaptive confidence sets for the matrix completion problem. For the Bernoulli model with known variance of the noise we provide a realizable method for constructing confidence sets that adapt to the unknown rank of the true matrix.