We introduce a class of algorithms, termed proximal interacting particle Langevin algorithms (PI-PLA), 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 nonasymptotic 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 fam-
ily 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.