# Momentum SVGD-EM for Accelerated Maximum Marginal Likelihood Estimation

arXiv: https://arxiv.org/abs/2603.08676 · HTML: https://mlsanity.com/paper/2603.08676/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 9 Mar 2026.

## Builds on (most cited first, 14 of 14)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Statistical exploration of the Manifold Hypothesis](https://mlsanity.com/paper/2208.11665/) (2022)
- [Particle algorithms for maximum likelihood training of latent variable models](https://mlsanity.com/paper/2204.12965/) (2022)
- [Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimation](https://mlsanity.com/paper/2303.13429/) (2023)
- [Algorithmic Instabilities of Accelerated Gradient Descent](https://mlsanity.com/paper/2102.02167/) (2021)
- [Error bounds for particle gradient descent, and extensions of the log-Sobolev and Talagrand inequalities](https://mlsanity.com/paper/2403.02004/) (2024)
- [Momentum Particle Maximum Likelihood](https://mlsanity.com/paper/2312.07335/) (2023)
- [Tuning-Free Maximum Likelihood Training of Latent Variable Models via Coin Betting](https://mlsanity.com/paper/2305.14916/) (2023)
- [Proximal Interacting Particle Langevin Algorithms](https://mlsanity.com/paper/2406.14292/) (2024)
- [Kinetic Interacting Particle Langevin Monte Carlo](https://mlsanity.com/paper/2407.05790/) (2024)
- [Accelerated Stein Variational Gradient Flow](https://mlsanity.com/paper/2503.23462/) (2025)
- [Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamics](https://mlsanity.com/paper/2510.12311/) (2025)
- [Training Latent Diffusion Models with Interacting Particle Algorithms](https://mlsanity.com/paper/2505.12412/) (2025)

## Abstract (arXiv)

Maximum marginal likelihood estimation (MMLE) can be formulated as the optimization of a free energy functional. From this viewpoint, the Expectation-Maximisation (EM) algorithm admits a natural interpretation as a coordinate descent method over the joint space of model parameters and probability measures. Recently, a significant body of work has adopted this perspective, leading to interacting particle algorithms for MMLE. In this paper, we propose an accelerated version of one such procedure, based on Stein variational gradient descent (SVGD), by introducing Nesterov acceleration in both the parameter updates and in the space of probability measures. The resulting method, termed Momentum SVGD-EM, consistently accelerates convergence in terms of required iterations across various tasks of increasing difficulty, demonstrating effectiveness in both low- and high-dimensional settings.