Infinite Tucker Decomposition: Nonparametric Bayesian Models for Multiway Data Analysis

TL;DR

This paper introduces InfTucker, a nonparametric Bayesian tensor decomposition model that effectively captures complex interactions, handles various data types, and improves prediction accuracy for multiway data analysis.

Contribution

The paper presents a novel infinite feature space tensor decomposition model using nonparametric Bayesian methods, enabling better modeling of complex data interactions and types.

Findings

Achieved significantly higher prediction accuracy than state-of-the-art tensor methods.

Reduced time and space complexity by several orders of magnitude.

Demonstrated effectiveness on chemometrics and social network datasets.

Abstract

Tensor decomposition is a powerful computational tool for multiway data analysis. Many popular tensor decomposition approaches---such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)---amount to multi-linear factorization. They are insufficient to model (i) complex interactions between data entities, (ii) various data types (e.g. missing data and binary data), and (iii) noisy observations and outliers. To address these issues, we propose tensor-variate latent nonparametric Bayesian models, coupled with efficient inference methods, for multiway data analysis. We name these models InfTucker. Using these InfTucker, we conduct Tucker decomposition in an infinite feature space. Unlike classical tensor decomposition models, our new approaches handle both continuous and binary data in a probabilistic framework. Unlike previous Bayesian models on matrices and tensors, our models are based on latent Gaussian or $t$ processes with nonlinear covariance functions. To efficiently learn the InfTucker from data, we develop a variational inference technique on tensors. Compared with classical implementation, the new technique reduces both time and space complexities by several orders of magnitude. Our experimental results on chemometrics and social network datasets demonstrate that our new models achieved significantly higher prediction accuracy than the most state-of-art tensor decomposition