A0715
Title: Uncertainty quantification of spatiotemporal tensor completion
Authors: Hu Sun - University of Michigan, Ann Arbor (United States) [presenting]
Yang Chen - University of Michigan (United States)
Abstract: Tensor data, or multi-dimensional array, is a data format popular in multiple fields, such as social network analysis, recommender systems, and brain imaging. It is not uncommon to observe tensor data containing missing values, and tensor completion aims to estimate the missing values given the partially observed tensor. Sufficient efforts have been spared on devising scalable tensor completion algorithms but few on quantifying the uncertainty of the estimator. The uncertainty quantification (UQ) of tensor completion is nested under a split conformal prediction framework, and the connection of the UQ problem to a problem of estimating the missing propensity of each tensor entry is established. A novel tensor Ising model, parametrized by a low-rank tensor parameter, is introduced to model the locally-dependent data missingness, which is common for spatiotemporal tensor data. Estimating the tensor parameter is proposed by maximum pseudo-likelihood estimation (MPLE) with a Riemannian gradient descent algorithm. Extensive simulation studies have been conducted to justify the validity of the resulting conformal interval. The method is applied to the regional total electron content (TEC) reconstruction problem in geophysics.
