Non-negative Tensor Mixture Learning for Discrete Density Estimation

Kazu Ghalamkari, Jesper Løve Hinrich, Morten Mørup

Keywords: Tensor factorization, EM algorithm, Low-rank approximation

TL;DR: EM-based unified framework for non-negative tensor decomposition that can accommodate a mixture of low-rank tensors and adaptive noise terms

Abstract: We present an expectation-maximization (EM) based unified framework for non-negative tensor decomposition that optimizes the Kullback-Leibler divergence. To avoid iterations in each M-step and learning rate tuning, we establish a general relationship between low-rank decomposition and many-body approximation. Using this connection, we exploit that the closed-form solution of the many-body approximation can be used to update all parameters simultaneously in the M-step. Our framework offers not only a unified methodology for a variety of low-rank structures, including CP, Tucker, and Train decompositions but also their combinations forming mixtures of tensors. The weights of each low-rank tensor in the mixture can be learned from the data, which eliminates the need to carefully choose a single low-rank structure in advance. We empirically demonstrate that our framework provides superior generalization for discrete density estimation compared to conventional tensor-based approaches.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Submission Number: 6148