Abstract

In this talk, I will summarise recent progress and challenges in maximum marginal likelihood estimation (MMLE) – focusing on the methods based on Langevin diffusions. I will first introduce the problem and the necessary background on Langevin diffusions, together with recent results on Langevin-based MMLE estimators [1-3], detailing the interacting particle Langevin algorithm (IPLA) [3] which is a recent Langevin-based MMLE method with explicit theoretical guarantees akin to Langevin Monte Carlo methods. I will then move on to summarise recent progress, specifically accelerated variants [4] and methods for MMLE in nondifferentiable statistical models [5] with convergence and complexity results. Finally, if time permits, I will talk about the application of IPLA to inverse problems [6].

[1] Kuntz, Juan, Jen Ning Lim, and Adam M. Johansen. “Particle algorithms for maximum likelihood training of latent variable models.” International Conference on Artificial Intelligence and Statistics. PMLR , 2023.

[2] De Bortoli, Valentin, et al. “Efficient stochastic optimisation by unadjusted Langevin Monte Carlo: Application to maximum marginal likelihood and empirical Bayesian estimation.” Statistics and Computing 31 (2021): 1-18.

[3] Akyildiz, Ö. D., Crucinio, F. R., Girolami, M., Johnston, T., & Sabanis, S. (2023). Interacting particle langevin algorithm for maximum marginal likelihood estimation. arXiv preprint arXiv:2303.13429.

[4] Oliva, P. F. V., & Akyildiz, O. D. (2024). Kinetic Interacting Particle Langevin Monte Carlo. arXiv preprint arXiv:2407.05790.

[5] Encinar, P. C., Crucinio, F. R., & Akyildiz, O. D. (2024). Proximal Interacting Particle Langevin Algorithms. arXiv preprint arXiv:2406.14292.

[6] Glyn-Davies, A., Duffin, C., Kazlauskaite, I., Girolami, M., & Akyildiz, Ö. D. (2024). Statistical Finite Elements via Interacting Particle Langevin Dynamics. arXiv preprint arXiv:2409.07101.

This talk is held in person and streamed live on Zoom at https://cam-ac-uk.zoom.us/j/85902531691?pwd=nczVlT9y6odBCF71anusgYotW05M42.1