# Constructing confidence sets for the matrix completion problem

@inproceedings{Carpentier2017ConstructingCS, title={Constructing confidence sets for the matrix completion problem}, author={Alexandra Carpentier and Olga Klopp and Matthias Loffler}, year={2017} }

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.

## 6 Citations

Matrix completion with data-dependent missingness probabilities

- Computer Science, MathematicsArXiv
- 2021

Two new estimators are proposed, based on singular value thresholding and nuclear norm minimization, to recover the matrix under this assumption of a single number p such that each entry of the matrix is available independently with probability p and missing otherwise.

Inference and uncertainty quantification for noisy matrix completion

- Computer Science, MathematicsProceedings of the National Academy of Sciences
- 2019

A simple procedure to compensate for the bias of the widely used convex and nonconvex estimators and derive distributional characterizations for the resulting debiased estimators, which enable optimal construction of confidence intervals/regions for the missing entries and the low-rank factors.

Matrix Completion with Quantified Uncertainty through Low Rank Gaussian Copula

- Computer ScienceNeurIPS
- 2020

A probabilistic and scalable framework for missing value imputation with quantified uncertainty, augments a standard probabilism model, Probabilistic Principal Component Analysis, with marginal transformations for each column that allow the model to better match the distribution of the data.

Inference for linear forms of eigenvectors under minimal eigenvalue separation: Asymmetry and heteroscedasticity

- Computer ScienceArXiv
- 2020

This work develops algorithms that produce confidence intervals for linear forms of individual eigenvectors, based on eigen-decomposition of the asymmetric data matrix followed by a careful de-biasing scheme, and establishes procedures to construct optimalconfidence intervals for the eigenvalues of interest.

Tackling Small Eigen-Gaps: Fine-Grained Eigenvector Estimation and Inference Under Heteroscedastic Noise

- Computer ScienceIEEE Transactions on Information Theory
- 2021

Based on eigen-decomposition of the asymmetric data matrix, this paper proposes estimation and uncertainty quantification procedures for an unknown eigenvector, which further allow us to reason about linear functionals of an unknown Eigenvector.

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