14 citations · 33 across the 24 of their papers we have counts for
22 papers · 1 filter
Non-asymptotic convergence bounds for Sinkhorn iterates and their gradients: a coupling approach
Giacomo Greco, Maxence Noble, Giovanni Conforti +1
Computational optimal transport (OT) has recently emerged as a powerful framework with applications in various fields. In this paper we focus on a relaxation of the original OT pro…
Quantitative contraction rates for Sinkhorn's algorithm: beyond bounded costs and compact marginals
Giovanni Conforti, Alain Durmus, Giacomo Greco
We show non-asymptotic exponential convergence of Sinkhorn iterates to the Schrödinger potentials, solutions of the quadratic Entropic Optimal Transport problem on .…
Mean Field Optimization Problem Regularized by Fisher Information
Julien Claisse, Giovanni Conforti, Zhenjie Ren +1
Recently there is a rising interest in the research of mean field optimization, in particular because of its role in analyzing the training of neural networks. In this paper by add…
Weak semiconvexity estimates for Schrödinger potentials and logarithmic Sobolev inequality for Schrödinger bridges
Giovanni Conforti
We investigate the quadratic Schrödinger bridge problem, a.k.a. Entropic Optimal Transport problem, and obtain weak semiconvexity and semiconcavity bounds on Schrödinger potentials…
Gradient estimates for the Schrödinger potentials: convergence to the Brenier map and quantitative stability
Alberto Chiarini, Giovanni Conforti, Giacomo Greco +1
We show convergence of the gradients of the Schrödinger potentials to the Brenier map in the small-time limit under general assumptions on the marginals, which allow for unbounded…
Entropic turnpike estimates for the kinetic Schrödinger problem
Alberto Chiarini, Giovanni Conforti, Giacomo Greco +1
We investigate the kinetic Schrödinger problem, obtained considering Langevin dynamics instead of Brownian motion in Schrödinger's thought experiment. Under a quasilinearity assump…
Time reversal of Markov processes with jumps under a finite entropy condition
Giovanni Conforti, Christian Léonard
Motivated by entropic optimal transport, time reversal of Markov jump processes in is investigated. Relying on an abstract integration by parts formula for the carré…
Time reversal of diffusion processes under a finite entropy condition
Patrick Cattiaux, Giovanni Conforti, Ivan Gentil +1
Motivated by entropic optimal transport, time reversal of diffusion processes is revisited. An integration by parts formula is derived for the carré du champ of a Markov process in…
A probabilistic approach to convex -entropy decay for Markov chains
Giovanni Conforti
We study the exponential dissipation of entropic functionals for continuous time Markov chains and the associated convex Sobolev inequalities, including MLSI and Beckner inequaliti…
A formula for the time derivative of the entropic cost and applications
Giovanni Conforti, Luca Tamanini
In the recent years the Schrödinger problem has gained a lot of attention because of the connection, in the small-noise regime, with the Monge-Kantorovich optimal transport problem…
The mean field Schrödinger problem: ergodic behavior, entropy estimates and functional inequalities
Julio Backhoff-Veraguas, Giovani Conforti, Ivan Gentil +1
We study the mean field Schrödinger problem (MFSP), that is the problem of finding the most likely evolution of a cloud of interacting Brownian particles conditionally on the obser…
Around the entropic Talagrand inequality
Giovanni Conforti, Luigia Ripani
In this article we study generalization of the classical Talagrand transport-entropy inequality in which the Wasserstein distance is replaced by the entropic transportation cost. T…
Conditioned point processes with application to Lévy bridges
Giovanni Conforti, Tetiana Kosenkova, Sylvie Roelly
Our first result concerns a characterisation by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalised…
Approximating conditional distributions
Alberto Chiarini, Alessandra Cipriani, Giovanni Conforti
In this article, we discuss the basic ideas of a general procedure to adapt the Stein-Chen method to bound the distance between conditional distributions. From an integration-by-pa…
A second order equation for Schrödinger bridges with applications to the hot gas experiment and entropic transportation cost
Giovanni Conforti
The \emph{Schrödinger problem} is obtained by replacing the mean square distance with the relative entropy in the Monge-Kantorovich problem. It was first addressed by Schrödinger a…
Couplings, gradient estimates and logarithmic Sobolev inequality for Langevin bridges
Giovanni Conforti, Max Von Renesse
In this paper we establish quantitative results about the bridges of the Langevin dynamics and the associated reciprocal processes. They include an equivalence between gradient est…
Fluctuations of bridges, reciprocal characteristics, and concentration of measure
Giovanni Conforti
Conditions on the generator of a Markov process to control the fluctuations of its bridges are found. In particular, continuous time random walks on graphs and gradient diffusions…
Bridges of Markov counting processes: quantitative estimates
Giovanni Conforti
In this paper we investigate the behavior of the bridges of a Markov counting process in several directions. We first characterize convexity(concavity) in time of the mean value in…
Reciprocal classes of random walks on graphs
Giovanni Conforti, Christian Léonard
The reciprocal class of a Markov path measure is the set of all mixtures of its bridges. We give characterizations of the reciprocal class of a continuous-time Markov random walk o…
Bridges of Markov counting processes. Reciprocal classes and duality formulas
Giovanni Conforti, Christian Léonard, Rüdiger Murr +1
Processes having the same bridges are said to belong to the same reciprocal class. In this article we analyze reciprocal classes of Markov counting processes by identifying their r…
Reciprocal class of jump processes
Giovanni Conforti, Paolo Dai Pra, Sylvie Roelly
Processes having the same bridges as a given reference Markov process constitute its {\it reciprocal class}. In this paper we study the reciprocal class of compound Poisson process…
On small-noise equations with degenerate limiting system arising from volatility models
Giovanni Conforti, Stefano De Marco, Jean-Dominique Deuschel
The one-dimensional SDE with non Lipschitz diffusion coefficient is widely studied in mathematical finance. Several works…