3 citations · 4 across the 10 of their papers we have counts for
12 papers
Dimension-free regimes for unadjusted Langevin in ridge-separable models: A subspace robust Wasserstein analysis
Yuansi Chen, Francesco Pedrotti, Peter A. Whalley
The Unadjusted Langevin Algorithm (ULA) is widely used for high-dimensional Bayesian inference. Classical analyses in Wasserstein-2 distance predict an asymptotic bias and a mixing…
Wasserstein mixing time of the unadjusted Langevin algorithm
Francesco Pedrotti, Peter A. Whalley
We provide new estimates in Wasserstein distance for the asymptotic bias of the unadjusted Langevin algorithm, in the classical setting of log-smooth strongly log-concave measures.…
The local product condition implies cutoff
Francesco Pedrotti, Justin Salez
In the theory of mixing times, a famously wrong conjecture predicts that a sequence of Markov processes exhibits cutoff as soon as the product of their Poincaré constant and mixing…
Entropy-Wasserstein regularization, defective local concentration and a cutoff criterion beyond non-negative curvature
Francesco Pedrotti
Notions of positive curvature have been shown to imply many remarkable properties for Markov processes, in terms, e.g., of regularization effects, functional inequalities, mixing t…
A transport approach to the cutoff phenomenon
Francesco Pedrotti, Justin Salez
Substantial progress has recently been made in the understanding of the cutoff phenomenon for Markov processes, using an information-theoretic statistics known as varentropy [Sal23…
A new cutoff criterion for non-negatively curved chains
Francesco Pedrotti, Justin Salez
The cutoff phenomenon was recently shown to systematically follow from non-negative curvature and the product condition, for all Markov diffusions. The proof crucially relied on a…
Concentration of information on discrete groups
Jonathan Hermon, Xiangying Huang, Francesco Pedrotti +1
Motivated by the Asymptotic Equipartition Property and its recently discovered role in the cutoff phenomenon, we initiate the systematic study of varentropy on discrete groups. Our…
Heat flow, log-concavity, and Lipschitz transport maps
Giovanni Brigati, Francesco Pedrotti
In this paper we derive estimates for the Hessian of the logarithm (log-Hessian) for solutions to the heat equation. For initial data in the form of log-Lipschitz perturbation of s…
-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher's infinitesimal model
Ksenia A. Khudiakova, Jan Maas, Francesco Pedrotti
We prove upper bounds on the -Wasserstein distance from optimal transport between strongly log-concave probability densities and log-Lipschitz perturbations. In the simpl…
Contractive coupling rates and curvature lower bounds for Markov chains
Francesco Pedrotti
Contractive coupling rates have been recently introduced by Conforti as a tool to establish convex Sobolev inequalities (including modified log-Sobolev and Poincaré inequality) for…
Improved Convergence of Score-Based Diffusion Models via Prediction-Correction
Francesco Pedrotti, Jan Maas, Marco Mondelli
Score-based generative models (SGMs) are powerful tools to sample from complex data distributions. Their underlying idea is to (i) run a forward process for time by adding no…
Local Conditions for Global Convergence of Gradient Flows and Proximal Point Sequences in Metric Spaces
Lorenzo Dello Schiavo, Jan Maas, Francesco Pedrotti
This paper deals with local criteria for the convergence to a global minimiser for gradient flow trajectories and their discretisations. To obtain quantitative estimates on the spe…