TY - JOUR

T1 - Tuning-Free Maximum Likelihood Training of Latent Variable Models via Coin Betting

AU - Sharrock, Louis

AU - Dodd, Daniel

AU - Nemeth, Christopher

N1 - Conference code: 27

PY - 2024/1/19

Y1 - 2024/1/19

N2 - We introduce two new particle-based algo- rithms 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 discretiza- tion of a gradient flow associated with the free energy. We study one such approach, which resembles an extension of Stein varia- tional 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 learn- ing 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 ex- periments, including several high-dimensional settings. Our results are competitive with existing particle-based methods, without the need for any hyperparameter tuning.

AB - We introduce two new particle-based algo- rithms 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 discretiza- tion of a gradient flow associated with the free energy. We study one such approach, which resembles an extension of Stein varia- tional 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 learn- ing 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 ex- periments, including several high-dimensional settings. Our results are competitive with existing particle-based methods, without the need for any hyperparameter tuning.

M3 - Conference article

JO - Proceedings of Machine Learning Research

JF - Proceedings of Machine Learning Research

SN - 1938-7228

T2 - 27th International Conference on Artificial Intelligence and Statistics, AISTATS 2024

Y2 - 2 May 2024 through 4 May 2024

ER -