Supervised multiway factorization

TL;DR

SupCP introduces a probabilistic tensor factorization method that incorporates auxiliary covariates, enabling more accurate, interpretable dimension reduction and predictive modeling for multiway data in biomedical and related fields.

Contribution

It generalizes supervised tensor decomposition by integrating covariates into a probabilistic CP factorization with an EM algorithm for estimation.

Findings

SupCP improves latent structure interpretability and accuracy.

The method effectively models multiway data with covariates.

Applications demonstrate enhanced predictive performance.

Abstract

We describe a probabilistic PARAFAC/CANDECOMP (CP) factorization for multiway (i.e., tensor) data that incorporates auxiliary covariates, SupCP. SupCP generalizes the supervised singular value decomposition (SupSVD) for vector-valued observations, to allow for observations that have the form of a matrix or higher-order array. Such data are increasingly encountered in biomedical research and other fields. We describe a likelihood-based latent variable representation of the CP factorization, in which the latent variables are informed by additional covariates. We give conditions for identifiability, and develop an EM algorithm for simultaneous estimation of all model parameters. SupCP can be used for dimension reduction, capturing latent structures that are more accurate and interpretable due to covariate supervision. Moreover, SupCP specifies a full probability distribution for a multiway data observation with given covariate values, which can be used for predictive modeling. We conduct comprehensive simulations to evaluate the SupCP algorithm. We apply it to a facial image database with facial descriptors (e.g., smiling / not smiling) as covariates, and to a study of amino acid fluorescence. Software is available at https://github.com/lockEF/SupCP .