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 (MCMC) techniques and the recently introduced interacting particle Langevin algorithm (IPLA), we propose several variants within the novel proximal IPLA family, tailored to the problem of estimating parameters in a non-differentiable statistical model. We prove nonasymptotic bounds for the parameter estimates produced by multiple 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 the proposed family of algorithms on a toy hierarchical example where our assumptions can be checked, as well as on the problems of sparse Bayesian logistic regression, sparse Bayesian neural network, and sparse matrix completion. Our theory and experiments together show that PIPLA family can be the de facto choice for parameter estimation problems in latent variable models for non-differentiable models.

翻译：本文提出了一类名为近端交互粒子朗之万算法（PIPLA）的算法，用于联合概率密度不可微的隐变量模型中的推断与学习。结合近端马尔可夫链蒙特卡洛（MCMC）技术与近期提出的交互粒子朗之万算法（IPLA），我们在新颖的近端IPLA框架内提出了多种变体，专门用于估计不可微统计模型中的参数。我们在强对数凹设定下证明了多种算法所产生参数估计的非渐近界，并在多种模型上进行了全面的数值实验以验证所提方法的有效性。特别地，我们通过一个可验证假设的玩具分层示例，以及在稀疏贝叶斯逻辑回归、稀疏贝叶斯神经网络和稀疏矩阵补全问题上的应用，展示了所提算法族的实用性。我们的理论与实验共同表明，PIPLA算法族可成为不可微隐变量模型中参数估计问题的实际首选方法。