9 papers
Stochastic Transition-Map Distillation for Fast Probabilistic Inference
George Rapakoulias, Peter Garud, Lingjiong Zhu +1
Diffusion models achieve strong generation quality, diversity, and distribution coverage, but their performance often comes with expensive inference. In this work, we propose Stoch…
Decentralized Proximal Stochastic Gradient Langevin Dynamics
Mohammad Rafiqul Islam, Lingjiong Zhu
We propose Decentralized Proximal Stochastic Gradient Langevin Dynamics (DE-PSGLD), a decentralized Markov chain Monte Carlo (MCMC) algorithm for sampling from a log-concave probab…
Rényi Differential Privacy for Heavy-Tailed SDEs via Fractional Poincaré Inequalities
Benjamin Dupuis, Mert Gürbüzbalaban, Umut Şimşekli +3
Characterizing the differential privacy (DP) of learning algorithms has become a major challenge in recent years. In parallel, many studies suggested investigating the behavior of…
DIGing--SGLD: Decentralized and Scalable Langevin Sampling over Time--Varying Networks
Waheed U. Bajwa, Mert Gurbuzbalaban, Mustafa Ali Kutbay +2
Sampling from a target distribution induced by training data is central to Bayesian learning, with Stochastic Gradient Langevin Dynamics (SGLD) serving as a key tool for scalable p…
Anchored Langevin Algorithms
Mert Gurbuzbalaban, Hoang M. Nguyen, Xicheng Zhang +1
Standard first-order Langevin algorithms such as the unadjusted Langevin algorithm (ULA) are obtained by discretizing the Langevin diffusion and are widely used for sampling in mac…
High-Order Langevin Monte Carlo Algorithms
Thanh Dang, Mert Gurbuzbalaban, Mohammad Rafiqul Islam +2
Langevin algorithms are popular Markov chain Monte Carlo (MCMC) methods for large-scale sampling problems that often arise in data science. We propose Monte Carlo algorithms based…
Accelerating Langevin Monte Carlo Sampling: A Large Deviations Analysis
Nian Yao, Pervez Ali, Xihua Tao +1
Langevin algorithms are popular Markov chain Monte Carlo methods that are often used to solve high-dimensional large-scale sampling problems in machine learning. The most classical…
Algorithmic Stability of Stochastic Gradient Descent with Momentum under Heavy-Tailed Noise
Thanh Dang, Melih Barsbey, A K M Rokonuzzaman Sonet +3
Understanding the generalization properties of optimization algorithms under heavy-tailed noise has gained growing attention. However, the existing theoretical results mainly focus…
Gradient estimates for semigroups associated with stochastic differential equations driven by cylindrical Lévy processes
Thanh Dang, Lingjiong Zhu
Via a Bismut-Elworthy-Li formula from [KPP23], we derive uniform gradient estimates for transition semigroups associated with stochastic differential equations driven by a large cl…