TERM Model: Tensor Ring Mixture Model for Density Estimation

Probabilistic modeling is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches and allow tractable inference (e.g., marginal inference and conditional inference). In this paper, we introduce tensor ring decomposition for density estimation, which reduces the number of permutation candidates compared to existing methods, while simultaneously enhancing expressive power and maintaining tractable inference. Different non-negative strategies for density function results in two variants: Born TRDE offers simpler inference and sampling but with slightly lower accuracy, while Energy TRDE, though more complex, achieves superior performance. Furthermore, a mixture model that incorporates multiple permutation candidates with adaptive weights is designed, resulting in increased expressive flexibility and comprehensiveness. Unlike existing methods that focus on finding a single optimal permutation, our approach, inspired by ensemble learning, demonstrates that combining multiple suboptimal permutations can yield superior results. Experiments demonstrate that the proposed approach excels in estimating probability density functions and sampling, capturing intricate details with competitive or superior performance compared to existing state-of-the-art (SOTA) tractable density methods.