We construct and implement a family of digital signature schemes, named BLISS (Bimodal Lattice Signature Scheme) for security levels of 128, 160, and 192 bits.Expand

In this paper, we study a method to sample from a target distribution $\pi$ over $\mathbb{R}^d$ having a positive density with respect to the Lebesgue measure, known up to a normalisation factor.… Expand

This paper presents a new and efficient Markov chain Monte Carlo methodology to perform Bayesian computation for high-dimensional models that are log-concave and nonsmooth, a class of models that is central in imaging sciences.Expand

We show that this method can be formulated as a first order optimization algorithm of an objective functional defined on the Wasserstein space of order $2$.Expand

We consider in this paper the problem of sampling a probability distribution π having a density w.r.t. the Lebesgue measure on $\mathbb{R}^d$, known up to a normalisation factor $x \mapsto… Expand

In this work, we establish $\mathrm{L}^2$-exponential convergence for a broad class of Piecewise Deterministic Markov Processes recently proposed in the context of Markov process Monte Carlo methods and covering in particular the Randomized Hamiltonian Monte Carlo, the Zig-Zag process and the Bouncy Particle Sampler.Expand

We consider the minimization of an objective function given access to unbiased estimates of its gradient through stochastic gradient descent (SGD) with constant step-size. While the detailed analysis… Expand

We show that the SGLD algorithm has an invariant probability measure which significantly departs from the target posterior and behaves like as Stochastic Gradient Descent.Expand

We establish explicit convergence rates for Markov chains in Wasserstein distance by analyzing Exponential Integrator version of the Metropolis Adjusted Langevin Algorithm.Expand