A1483
Title: Generalized tensor completion with non-random missingness
Authors: Biao Cai - City University of Hong Kong (United States) [presenting]
Abstract: Tensor completion plays a crucial role in applications such as recommender systems and medical imaging, where data are often highly incomplete. While extensive prior work has addressed tensor completion with data missingness, most assume that each entry of the tensor is available independently with probability. However, real-world tensor data often exhibit missing-not-at-random (MNAR) patterns, where the probability of missingness depends on the underlying tensor values. A generalized tensor completion framework is introduced for noisy data with MNAR, where the observation probability is modeled as a function of underlying tensor values. The flexible framework accommodates various tensor data types, such as continuous, binary and count data. For model estimation, an alternating maximization algorithm is developed and non-asymptotic error bounds are derived for the estimator at each iteration, under considerably relaxed conditions on the observation probabilities. Additionally, a statistical inference procedure is proposed to test whether observation probabilities depend on underlying tensor values, offering a formal assessment of the missingness assumption within the modeling framework. The utility and efficacy of the approach are demonstrated through comparative simulation studies and analyses of two real-world datasets.
