Communication Dans Un Congrès Année : 2025

Sampling Nonsmooth Log-Concave Densities: A Comparative Study of Primal-Dual Based Proposal Distributions

Résumé

Sampling from a real-valued distribution, whose density is nonsmooth and log-concave, is a computational issue that often arises in Machine Learning and Statistics. Langevin-based Hastings-Metropolis methods were proposed: they extend the Unadjusted Langevin Algorithm by using proximal methods to define a smoothed version of the density of interest. We consider the case when these extensions do not apply: the involved proximal operators do not have closed forms and the density is defined on a subset of the real numbers. We derive new Gaussian proposal mechanisms in a Metropolis Adjusted Langevin Algorithm, which use first-order information about the density function. We numerically compare these strategies and discuss the benefits of a change of geometry. The gain in using partial updates instead of global parameter updates is also illustrated.

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Dates et versions

hal-04824190 , version 1 (06-12-2024)
hal-04824190 , version 2 (08-01-2025)

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  • HAL Id : hal-04824190 , version 2

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Juliette Chevallier, Gersende Fort. Sampling Nonsmooth Log-Concave Densities: A Comparative Study of Primal-Dual Based Proposal Distributions. 2025 IEEE International Conference on Acoustics, Speech, and Signal Processing, Apr 2025, Hyderabad (IN), India. ⟨hal-04824190v2⟩
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