Related papers: Sampling from the Mean-Field Stationary Distributi…
A key task in Bayesian machine learning is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). One prevalent example of this is sampling posteriors in parametric distributions,…
We analyze a recently proposed class of algorithms for the problem of sampling from probability distributions $\mu^\ast$ in $\mathbb{R}^d$ with a Lebesgue density of the form $\mu^\ast(x) \propto \exp(-f(Kx)-g(x))$, where $K$ is a linear…
We introduce a novel approach based on stochastic optimization to find the optimal sampling distribution for the data-driven stability analysis of switched linear systems. Our goal is to address limitations of existing approaches, in…
We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or…
The mean-field stochastic partial differential equation (SPDE) corresponding to a mean-field super-Brownian motion (sBm) is obtained and studied. In this mean-field sBm, the branching-particle lifetime is allowed to depend upon the…
Much recent research activity has been devoted to empirical study and theoretical models of complex networks (random graphs) with three qualitative features: power-law degree distribution, local clustering of edges, and small diameter. We…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…
This paper studies a large number of homogeneous Markov decision processes where the transition probabilities and costs are coupled in the empirical distribution of states (also called mean-field). The state of each process is not known to…
We consider the problem of selecting important nodes in a random network, where the nodes connect to each other randomly with certain transition probabilities. The node importance is characterized by the stationary probabilities of the…
In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent…
We study the problem of mean-field control when the state dynamics are given by general systems of forward-backward stochastic differential equations (FBSDEs) with heterogeneous mean-field interactions. Firstly, we introduce a novel…
We consider a distributionally robust stochastic optimization problem and formulate it as a stochastic two-level composition optimization problem with the use of the mean--semideviation risk measure. In this setting, we consider a single…
This paper presents theoretical advances in the application of the Stochastic Partial Differential Equation (SPDE) approach in geostatistics. We show a general approach to construct stationary models related to a wide class of linear SPDEs,…
This paper concerns the nonparametric estimation problem of the distribution-state dependent drift vector field in an interacting $N$-particle system. Observing single-trajectory data for each particle, we derive the mean-field rate of…
We study scaling properties of stochastic aggregation processes in one dimension. Numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent nontrivial exponents…
This paper investigates Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations of stochastic partial differential equations. We establish approximation error guarantees building on the…
This work considers the problem of sampling from a probability distribution known up to a normalization constant while satisfying a set of statistical constraints specified by the expected values of general nonlinear functions. This problem…
Incorporating social interactions is essential to an accurate modeling of epidemic spreading. This work proposes a novel local mean-field density functional theory model by using the sum-of-exponential approximation of convolution kernels…
We propose a new algorithm---Stochastic Proximal Langevin Algorithm (SPLA)---for sampling from a log concave distribution. Our method is a generalization of the Langevin algorithm to potentials expressed as the sum of one stochastic smooth…
The dynamic behaviour of stochastic spreading processes on a network model based on k-regular graphs is investigated. The contact process and the susceptible-infected-susceptible model for the spread of epidemics are considered as prototype…