# Tuning-Free Maximum Likelihood Training of Latent Variable Models via Coin Betting

arXiv: https://arxiv.org/abs/2305.14916 · HTML: https://mlsanity.com/paper/2305.14916/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 90 references that are in the map.
- First posted on arXiv 24 May 2023.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [Statistical guarantees for the EM algorithm: From population to sample-based analysis](https://mlsanity.com/paper/1408.2156/) (2014)
- [Coin Betting and Parameter-Free Online Learning](https://mlsanity.com/paper/1602.04128/) (2016)
- [Black-Box Reductions for Parameter-free Online Learning in Banach Spaces](https://mlsanity.com/paper/1802.06293/) (2018)
- [Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1512.07666/) (2015)
- [On the geometry of Stein variational gradient descent](https://mlsanity.com/paper/1912.00894/) (2019)
- [A Non-Asymptotic Analysis for Stein Variational Gradient Descent](https://mlsanity.com/paper/2006.09797/) (2020)
- [A Stein variational Newton method](https://mlsanity.com/paper/1806.03085/) (2018)
- [Stacking for Non-mixing Bayesian Computations: The Curse and Blessing of Multimodal Posteriors](https://mlsanity.com/paper/2006.12335/) (2020)
- [Parameter-Free Online Convex Optimization with Sub-Exponential Noise](https://mlsanity.com/paper/1902.01500/) (2019)
- [A Finite-Particle Convergence Rate for Stein Variational Gradient Descent](https://mlsanity.com/paper/2211.09721/) (2022)
- [A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1](https://mlsanity.com/paper/2106.03076/) (2021)
- [Better Parameter-free Stochastic Optimization with ODE Updates for Coin-Betting](https://mlsanity.com/paper/2006.07507/) (2020)
- [Bridging the Gap between Stochastic Gradient MCMC and Stochastic Optimization](https://mlsanity.com/paper/1512.07962/) (2015)
- [Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimation](https://mlsanity.com/paper/2303.13429/) (2023)
- [Online Learning for Changing Environments using Coin Betting](https://mlsanity.com/paper/1711.02545/) (2017)
- [Efficient and Generalizable Tuning Strategies for Stochastic Gradient MCMC](https://mlsanity.com/paper/2105.13059/) (2021)
- [A stochastic version of Stein Variational Gradient Descent for efficient sampling](https://mlsanity.com/paper/1902.03394/) (2019)
- [Implicit Parameter-free Online Learning with Truncated Linear Models](https://mlsanity.com/paper/2203.10327/) (2022)
- [Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates](https://mlsanity.com/paper/2301.11294/) (2023)
- [Latent Space Modelling of Hypergraph Data](https://mlsanity.com/paper/1909.00472/) (2019)
- [Stochastic Approximate Gradient Descent via the Langevin Algorithm](https://mlsanity.com/paper/2002.05519/) (2020)
- [A Bayesian Nonparametric Latent Space Approach to Modeling Evolving Communities in Dynamic Networks](https://mlsanity.com/paper/2003.07404/) (2020)

## Built on by (most cited first, 11 of 11)

- [Implicit Diffusion: Efficient Optimization through Stochastic Sampling](https://mlsanity.com/paper/2402.05468/) (2024)
- [Error bounds for particle gradient descent, and extensions of the log-Sobolev and Talagrand inequalities](https://mlsanity.com/paper/2403.02004/) (2024)
- [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)
- [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)
- [Learning Latent Variable Models via Jarzynski-adjusted Langevin Algorithm](https://mlsanity.com/paper/2505.18427/) (2025)
- [Learning-Rate-Free Stochastic Optimization over Riemannian Manifolds](https://mlsanity.com/paper/2406.02296/) (2024)
- [Tempered Guided Diffusion](https://mlsanity.com/paper/2605.03712/) (2026)
- [Momentum SVGD-EM for Accelerated Maximum Marginal Likelihood Estimation](https://mlsanity.com/paper/2603.08676/) (2026)
- [Hypergraph Generation via Structured Stochastic Diffusion](https://mlsanity.com/paper/2605.05024/) (2026)

## Abstract (arXiv)

We introduce two new particle-based algorithms for learning latent variable models via marginal maximum likelihood estimation, including one which is entirely tuning-free. Our methods are based on the perspective of marginal maximum likelihood estimation as an optimization problem: namely, as the minimization of a free energy functional. One way to solve this problem is via the discretization of a gradient flow associated with the free energy. We study one such approach, which resembles an extension of Stein variational gradient descent, establishing a descent lemma which guarantees that the free energy decreases at each iteration. This method, and any other obtained as the discretization of the gradient flow, necessarily depends on a learning rate which must be carefully tuned by the practitioner in order to ensure convergence at a suitable rate. With this in mind, we also propose another algorithm for optimizing the free energy which is entirely learning rate free, based on coin betting techniques from convex optimization. We validate the performance of our algorithms across several numerical experiments, including several high-dimensional settings. Our results are competitive with existing particle-based methods, without the need for any hyperparameter tuning.