Nonparametric Factor Trajectory Learning for Dynamic Tensor Decomposition

TL;DR

This paper introduces NONFAT, a nonparametric method using Gaussian processes in the frequency domain for dynamic tensor decomposition, capturing temporal evolution of factors over long periods with scalable inference.

Contribution

It proposes a novel nonparametric approach with Gaussian process priors in the frequency domain for modeling temporal dynamics in tensor data, overcoming data sparsity and scalability issues.

Findings

Demonstrates superior performance on real-world datasets.

Effectively captures complex temporal variation patterns.

Provides scalable inference for large tensor data.

Abstract

Tensor decomposition is a fundamental framework to analyze data that can be represented by multi-dimensional arrays. In practice, tensor data is often accompanied by temporal information, namely the time points when the entry values were generated. This information implies abundant, complex temporal variation patterns. However, current methods always assume the factor representations of the entities in each tensor mode are static, and never consider their temporal evolution. To fill this gap, we propose NONparametric FActor Trajectory learning for dynamic tensor decomposition (NONFAT). We place Gaussian process (GP) priors in the frequency domain and conduct inverse Fourier transform via Gauss-Laguerre quadrature to sample the trajectory functions. In this way, we can overcome data sparsity and obtain robust trajectory estimates across long time horizons. Given the trajectory values at specific time points, we use a second-level GP to sample the entry values and to capture the temporal relationship between the entities. For efficient and scalable inference, we leverage the matrix Gaussian structure in the model, introduce a matrix Gaussian posterior, and develop a nested sparse variational learning algorithm. We have shown the advantage of our method in several real-world applications.