Kinetic Interacting Particle Langevin Monte Carlo

2026-04-17 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

This paper introduces and analyzes Kinetic Interacting Particle Langevin Monte Carlo (KIPLMC) methods, which are interacting underdamped Langevin algorithms designed for statistical inference in latent variable models. The authors propose a novel diffusion process, Kinetic Interacting Particle Langevin Diffusion (KIPLD), that evolves jointly in parameter and latent variable spaces, with its stationary distribution concentrating around the maximum marginal likelihood estimate (MMLE) of the parameters. Two explicit discretizations of this diffusion, KIPLMC1 (an exponential integrator) and KIPLMC2 (a splitting scheme), are presented as practical algorithms. The paper provides nonasymptotic convergence rates for both algorithms in Wasserstein-2 distance, assuming strong concavity of the joint log-likelihood. Numerical experiments on synthetic data and the Wisconsin Cancer Dataset demonstrate the effectiveness of KIPLD for statistical inference and highlight the superior stability of KIPLMC2 compared to KIPLMC1 and the Momentum Particle Gradient Descent (MPGD) algorithm.

Key takeaway

Research Scientists working on maximum marginal likelihood estimation in latent variable models should consider adopting KIPLMC2. This algorithm offers enhanced stability and smoother convergence paths compared to existing methods like MPGD, especially when dealing with larger step-sizes. Its theoretical guarantees, including exponential convergence and concentration around the MMLE, provide a robust framework for parameter estimation, potentially improving performance in both convex and non-convex problem settings.

Key insights

KIPLMC methods offer accelerated, stable maximum marginal likelihood estimation using underdamped Langevin dynamics.

Principles

• Underdamped Langevin diffusions can accelerate convergence rates.
• Interacting particle systems approximate intractable integrals.
• Noise injection can improve robustness in non-convex settings.

Method

KIPLMC methods discretize a kinetic interacting particle Langevin diffusion (KIPLD) to jointly evolve parameters and latent variables, concentrating on the MMLE. KIPLMC2 uses a splitting scheme for enhanced stability.

In practice

• Use KIPLMC2 for improved stability with larger step-sizes.
• Tune the friction coefficient (γ) to optimize convergence behavior.
• Consider KIPLMC for unsupervised learning and inverse problems.

Topics

• Kinetic Interacting Particle Langevin Monte Carlo
• Latent Variable Models
• Maximum Marginal Likelihood Estimation
• Underdamped Langevin Diffusion
• Nonasymptotic Convergence Analysis

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.