TNSPC: Learning from Partially Observed Data Using Tensor Network Structured Probabilistic Circuits

Partially observed and heterogeneous data pose significant challenges in machine learning and statistical analysis, often leading to biased results or reduced model performance. While various imputation methods exist, they typically struggle with high-dimensional and mixed data types. To address these limitations, we introduce a flexible framework that leverages tensor network structures and probabilistic circuits (TNSPC) to provide an analytically tractable and scalable solution for imputing high-dimensional and mixed data types. Within the TNSPC framework, we systematically contrast the canonical polyadic (CP), tensor train (TT), and tensor tree network (TTN) structures to prominent probabilistic circuit structures not relying on tensor networks and find that the considered TNSPCs in general provide comparable performance and on some of the considered datasets even best performance. We further highlight the versatility of the TNSPC framework and its limitations.