arXiv subjects

Pervez Ali

Publications and source records attributed to Pervez Ali.

3 recordsLinked to original sources

arXiv2026

Accelerating Non-Smooth and Heavy-Tailed Sampling

Anchored Langevin dynamics (ALD) is useful for non-smooth sampling where the density of the target distribution is possibly non-differentiable and heavy-tailed; reflected anchored Langevin dynamics (RALD) can sample possibly non-differentiable target density on a constrained domain. In this paper, we propose and study non-reversible anchored Langevin dynamics (NALD) for sampling possibly non-differentiable and heavy-tailed target density in the Euclidean space and the non-reversible reflected anchored Langevin dynamics (NRALD) for sampling possibly non-differentiable target density in the constrained space. Our construction adds a circulation drift generated by a possibly state-dependent divergence-free skew-symmetric matrix field and a stream potential. It preserves the target distribution without requiring derivatives of target density, admits a random-time-change representation, and applies both on the whole Euclidean space and on bounded domains with normal reflection. By breaking reversibility, we show that NALD and NRALD can converge to their target distributions faster than their reversible counterparts via finite-time non-asymptotic convergence analysis, a large deviations analysis and asymptotic variance reduction. Numerical experiments demonstrate the efficiency of the proposed algorithms.

stat.ML↗

arXiv2026

Penalized Nonreversible Langevin for Constrained Sampling

We propose penalized nonreversible Langevin algorithms for sampling from $π(x)\propto e^{-f(x)}\mathbf 1_{\mathcal C}(x)$, where $\mathcal C\subset\mathbb R^d$ is a compact convex set. The algorithms combine a squared distance penalty with constant or compatible state dependent skew symmetric perturbations that preserve the penalized Gibbs distribution. For smooth, possibly nonconvex $f$, we derive nonasymptotic total variation bounds for the full gradient algorithm under a log Sobolev inequality. When unbiased stochastic gradients are available, we establish $2$-Wasserstein bounds under global contraction and Lipschitz conditions on the full drift in an adapted quadratic metric. For a fixed penalty parameter, the error relative to the penalized Gibbs distribution decays exponentially to an $\mathcal{O}(\sqrtη)$ neighborhood, where $η$ is the stepsize. We also bound the discrepancy between the penalized Gibbs distribution and the constrained target. In a two dimensional quadratic model, we establish nonreversible acceleration by tuning the skew perturbation to the curvature imbalance induced by penalization. With the target accuracy and smaller curvature fixed and initial Wasserstein distances uniformly bounded, tuning the skew perturbation improves the sufficient Euler iteration bound from linear to logarithmic in the curvature ratio. Numerical experiments evaluate the algorithms on constrained Bayesian regression, classification, neural networks, and truncated sampling, and examine the acceleration mechanism in a stochastic quadratic model.

stat.ML↗

arXiv2026

Accelerating Langevin Monte Carlo Sampling: A Large Deviations Analysis

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 Langevin Monte Carlo algorithm is based on the overdamped Langevin dynamics. There are many variants of Langevin dynamics that often show superior performance in practice. In this paper, we provide a unified approach to study the acceleration of the variants of the overdamped Langevin dynamics through the lens of large deviations theory. Numerical experiments using both synthetic and real data are provided to illustrate the efficiency of these variants.

math.PR↗