TY - GEN
T1 - Sampling Nonsmooth Log-Concave Densities
T2 - 2025 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2025
AU - Chevallier, Juliette
AU - Fort, Gersende
N1 - Publisher Copyright:
© 2025 IEEE.
PY - 2025/1/1
Y1 - 2025/1/1
N2 - Sampling from a distribution on the real d-space, 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-form expressions and the density is defined on a subset of the real d-space. 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 of the parameter instead of global updates is also illustrated.
AB - Sampling from a distribution on the real d-space, 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-form expressions and the density is defined on a subset of the real d-space. 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 of the parameter instead of global updates is also illustrated.
KW - Epidemiological model
KW - Langevin-based algorithms
KW - Monte Carlo Sampling
KW - Proximal and Subgradient methods
UR - https://www.scopus.com/pages/publications/105003889549
U2 - 10.1109/ICASSP49660.2025.10887998
DO - 10.1109/ICASSP49660.2025.10887998
M3 - Conference contribution
AN - SCOPUS:105003889549
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
BT - 2025 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2025 - Proceedings
A2 - Rao, Bhaskar D
A2 - Trancoso, Isabel
A2 - Sharma, Gaurav
A2 - Mehta, Neelesh B.
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 6 April 2025 through 11 April 2025
ER -