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By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…
In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called…
This manuscript introduces a regression-type formulation for approximating the Perron-Frobenius Operator by relying on distributional snapshots of data. These snapshots may represent densities of particles. The Wasserstein metric is…
We study recursive maximum likelihood estimation for stochastic interacting particle systems based on continuous observation of a single particle. In this regime, consistent estimation of the finite-particle log-likelihood is not possible,…
Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show…
In this paper, we consider a target random variable $Y \sim \CVG$ distributed according to a centered Variance--Gamma distribution. For a generic random element $F=I_2(f)$ in the second Wiener chaos with $\E[F^2]= \E[Y^2]$ we establish a…
We develop a theory of finite-dimensional polyhedral subsets over the Wasserstein space and optimization of functionals over them via first-order methods. Our main application is to the problem of mean-field variational inference, which…
It is well-known that many diffusion equations can be recast as Wasserstein gradient flows. Moreover, in recent years, by modifying the Wasserstein distance appropriately, this technique has been transferred to further evolution equations…
Among dissimilarities between probability distributions, the Kernel Stein Discrepancy (KSD) has received much interest recently. We investigate the properties of its Wasserstein gradient flow to approximate a target probability distribution…
Stein's method is used to study discrete representations of multidimensional distributions that arise as approximations of states of quantum harmonic oscillators. These representations model how quantum effects result from the interaction…
In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…
Recently developed particle flow algorithms provide an alternative to importance sampling for drawing particles from a posterior distribution, and a number of particle filters based on this principle have been proposed. Samples are drawn…
We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport. Unlike previous approaches, our method extends to continuous input distributions and…
Inverse problems in physical or biological sciences often involve recovering an unknown parameter that is random. The sought-after quantity is a probability distribution of the unknown parameter, that produces data that aligns with…
In Bayesian inference, the posterior distributions are difficult to obtain analytically for complex models such as neural networks. Variational inference usually uses a parametric distribution for approximation, from which we can easily…
This paper proposes a stochastic gradient descent method with an adaptive Gaussian noise term for the global minimization of nearly convex functions, which are nonconvex and possess multiple strict local minimizers. The noise term,…
We develop a quantitative statistical theory of transformers in the large-context regime by adopting the abstraction of contextual flow maps (CFMs): dynamical systems that evolve a distinguished token in the presence of a contextual measure…
This paper presents a novel Wasserstein distributionally robust control and state estimation algorithm for partially observable linear stochastic systems, where the probability distributions of disturbances and measurement noises are…
The Wasserstein distance has emerged as a key metric to quantify distances between probability distributions, with applications in various fields, including machine learning, control theory, decision theory, and biological systems.…
Dynamical systems of N particles in \R^{D} interacting by a singular pair potential of mean field type are considered. The systems are assumed to be of gradient type and the existence of a macroscopic limit in the many particle limit is…