Proximal Interacting Particle Langevin Algorithms

Paula Cordero Encinar, Francesca Romana Crucinio, Omer Deniz Akyildiz
Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, PMLR 286:1220-1265, 2025.

Abstract

We introduce a class of algorithms, termed proximal interacting particle Langevin algorithms (PIPLA), for inference and learning in latent variable models whose joint probability density is non-differentiable. Leveraging proximal Markov chain Monte Carlo techniques and interacting particle Langevin algorithms, we propose three algorithms tailored to the problem of estimating parameters in a non-differentiable statistical model. We prove non-asymptotic bounds for the parameter estimates produced by the different algorithms in the strongly log-concave setting and provide comprehensive numerical experiments on various models to demonstrate the effectiveness of the proposed methods. In particular, we demonstrate the utility of our family of algorithms for sparse Bayesian logistic regression, training of sparse Bayesian neural networks or neural networks with non-differentiable activation functions, image deblurring, and sparse matrix completion. Our theory and experiments together show that PIPLA family can be the de facto choice for parameter estimation problems in non-differentiable latent variable models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v286-encinar25a, title = {Proximal Interacting Particle Langevin Algorithms}, author = {Encinar, Paula Cordero and Crucinio, Francesca Romana and Akyildiz, Omer Deniz}, booktitle = {Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence}, pages = {1220--1265}, year = {2025}, editor = {Chiappa, Silvia and Magliacane, Sara}, volume = {286}, series = {Proceedings of Machine Learning Research}, month = {21--25 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v286/main/assets/encinar25a/encinar25a.pdf}, url = {https://proceedings.mlr.press/v286/encinar25a.html}, abstract = {We introduce a class of algorithms, termed proximal interacting particle Langevin algorithms (PIPLA), for inference and learning in latent variable models whose joint probability density is non-differentiable. Leveraging proximal Markov chain Monte Carlo techniques and interacting particle Langevin algorithms, we propose three algorithms tailored to the problem of estimating parameters in a non-differentiable statistical model. We prove non-asymptotic bounds for the parameter estimates produced by the different algorithms in the strongly log-concave setting and provide comprehensive numerical experiments on various models to demonstrate the effectiveness of the proposed methods. In particular, we demonstrate the utility of our family of algorithms for sparse Bayesian logistic regression, training of sparse Bayesian neural networks or neural networks with non-differentiable activation functions, image deblurring, and sparse matrix completion. Our theory and experiments together show that PIPLA family can be the de facto choice for parameter estimation problems in non-differentiable latent variable models.} }
Endnote
%0 Conference Paper %T Proximal Interacting Particle Langevin Algorithms %A Paula Cordero Encinar %A Francesca Romana Crucinio %A Omer Deniz Akyildiz %B Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2025 %E Silvia Chiappa %E Sara Magliacane %F pmlr-v286-encinar25a %I PMLR %P 1220--1265 %U https://proceedings.mlr.press/v286/encinar25a.html %V 286 %X We introduce a class of algorithms, termed proximal interacting particle Langevin algorithms (PIPLA), for inference and learning in latent variable models whose joint probability density is non-differentiable. Leveraging proximal Markov chain Monte Carlo techniques and interacting particle Langevin algorithms, we propose three algorithms tailored to the problem of estimating parameters in a non-differentiable statistical model. We prove non-asymptotic bounds for the parameter estimates produced by the different algorithms in the strongly log-concave setting and provide comprehensive numerical experiments on various models to demonstrate the effectiveness of the proposed methods. In particular, we demonstrate the utility of our family of algorithms for sparse Bayesian logistic regression, training of sparse Bayesian neural networks or neural networks with non-differentiable activation functions, image deblurring, and sparse matrix completion. Our theory and experiments together show that PIPLA family can be the de facto choice for parameter estimation problems in non-differentiable latent variable models.
APA
Encinar, P.C., Crucinio, F.R. & Akyildiz, O.D.. (2025). Proximal Interacting Particle Langevin Algorithms. Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 286:1220-1265 Available from https://proceedings.mlr.press/v286/encinar25a.html.

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