E$^2$M: Double Bounded $α$-Divergence Optimization for Tensor-based Discrete Density Estimation
Primary research
#1380
- Canonical URL
- http://arxiv.org/abs/2405.18220v4
- Topic
- unassigned (set during synthesis)
- First seen
- 2026-08-06 07:16:10
- Last seen
- 2026-08-06 07:16:10
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- arXiv2026-08-06 07:15:25E$^2$M: Double Bounded $α$-Divergence Optimization for Tensor-based Discrete Density Estimation
Tensor-based discrete density estimation requires flexible modeling and proper divergence criteria to enable effective learning; however, traditional approaches using $α$-divergence face analytical challenges due to the $α$-power terms in the objective function, which hinder the derivation of closed-form update rules. We present a generalization of the expectation-maximization (EM) algorithm, called the E$^2$M algorithm. It circumvents this issue by first relaxing the optimization into the minimization of a surrogate objective based on the Kullback-Leibler (KL) divergence, which is tractable via the standard EM algorithm, and subsequently applying a tensor many-body approximation in the M-step to enable simultaneous closed-form updates of all parameters. Our approach offers flexible modeling for not only a variety of low-rank structures, including the CP, Tucker, and Tensor Train formats, but also their mixtures, thus allowing us to leverage the strengths of different low-rank structures. We evaluate the effectiveness of our approach on synthetic and real datasets, highlighting its comparable convergence to gradient-based procedures, robustness to outliers, and favorable density estimation performance compared to prominent existing tensor-based methods.