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The problem of low-rank matrix completion with heterogeneous andsub-exponential (as opposed to homogeneous and Gaussian) noise is particularlyrelevant to a number of applications in modern commerce. Examples include panelsales data and data collected from web-commerce systems such as recommendationengines. An important unresolved question for this problem is characterizingthe distribution of estimated matrix entries under common low-rank estimators.Such a characterization is essential to any application that requiresquantification of uncertainty in these estimates and has heretofore only beenavailable under the assumption of homogenous Gaussian noise. Here wecharacterize the distribution of estimated matrix entries when the observationnoise is heterogeneous sub-exponential and provide, as an application, explicitformulas for this distribution when observed entries are Poisson or Binarydistributed.

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