  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 at estimating 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.
In this paper, we nest the uncertainty quantification (UQ) of tensor completion
under a split conformal prediction framework and establish the connection of
the UQ problem to a problem of estimating the missing propensity of each tensor
entry. We model the data missingness of the tensor with a tensor Ising model
parameterized by a low-rank tensor parameter. We propose to estimate the tensor
parameter 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. We apply our method
to the regional total electron content (TEC) reconstruction problem.
