mlsanityData to 14 Oct 2026

Uncertainty Quantification For Low-Rank Matrix Completion With Heterogeneous and Sub-Exponential Noise

arXiv 2110.12046 ↗First posted 22 Oct 2021stat.ML cs.LGcited by 1

Not on the map. Why?

Abstract (arXiv)

The problem of low-rank matrix completion with heterogeneous and sub-exponential (as opposed to homogeneous and Gaussian) noise is particularly relevant to a number of applications in modern commerce. Examples include panel sales data and data collected from web-commerce systems such as recommendation engines. An important unresolved question for this problem is characterizing the distribution of estimated matrix entries under common low-rank estimators. Such a characterization is essential to any application that requires quantification of uncertainty in these estimates and has heretofore only been available under the assumption of homogenous Gaussian noise. Here we characterize the distribution of estimated matrix entries when the observation noise is heterogeneous sub-exponential and provide, as an application, explicit formulas for this distribution when observed entries are Poisson or Binary distributed.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 15 of its 60 references that are in the map. First posted on arXiv 22 Oct 2021.

Builds on

15 of 60 references.

References · 15

  1. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,926
  2. 2015An Introduction to Matrix Concentration Inequalitiescited by 397
  3. 2016Matrix Completion has No Spurious Local Minimumcited by 125
  4. 2014Guaranteed Matrix Completion via Non-convex Factorizationcited by 82
  5. 2017Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolutioncited by 63
  6. 2019Noisy Matrix Completion: Understanding Statistical Guarantees for Convex Relaxation via Nonconvex Optimizationcited by 58
  7. 2019Inference and Uncertainty Quantification for Noisy Matrix Completioncited by 39
  8. 2018Heteroskedastic PCA: Algorithm, Optimality, and Applicationscited by 34
  9. 2020Low-Rank Matrix Recovery with Scaled Subgradient Methods: Fast and Robust Convergence Without the Condition Numbercited by 28
  10. 2017The Global Optimization Geometry of Low-Rank Matrix Optimizationcited by 25
  11. 2019Statistical Inferences of Linear Forms for Noisy Matrix Completioncited by 18
  12. 2019Low-rank matrix completion and denoising under Poisson noisecited by 6
3 more
  1. 2021Learning Treatment Effects in Panels with General Intervention Patternscited by 5
  2. 2017Deep density networks and uncertainty in recommender systemscited by 4
  3. 2019Bayesian Matrix Completion Approach to Causal Inference with Panel Datacited by 1

Built on by

Cited by year

Citing papers per year: 2022: 1.

1 paper.

  1. 2022Speed Up the Cold-Start Learning in Two-Sided Bandits with Many Armscited by 4