Related papers: Improvements to exact Boltzmann sampling using pro…
We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples…
The paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete, and the binary aggregation alone governs the time evolution of the systems. By considering the growth…
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…
Various bias-correction methods such as EXTRA, gradient tracking methods, and exact diffusion have been proposed recently to solve distributed {\em deterministic} optimization problems. These methods employ constant step-sizes and converge…
Sampling is an important tool for estimating large, complex sums and integrals over high dimensional spaces. For instance, important sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we…
Monte Carlo methods -- such as Markov chain Monte Carlo (MCMC) and piecewise deterministic Markov process (PDMP) samplers -- provide asymptotically exact estimators of expectations under a target distribution. There is growing interest in…
We formulate pure characteristics demand models under uncertainties of probability distributions as distributionally robust mathematical programs with stochastic complementarity constraints (DRMP-SCC). For any fixed first-stage variable and…
We consider the reconstruction of moving sources using partial measured data. A two-step deterministic-statistical approach is proposed. In the first step, an approximate direct sampling method is developed to obtain the locations of the…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
Learning the parameters of graphical models using the maximum likelihood estimation is generally hard which requires an approximation. Maximum composite likelihood estimations are statistical approximations of the maximum likelihood…
Model comparison for the purposes of selection, averaging and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of models within a…
Advances in information technology have led to extremely large datasets that are often kept in different storage centers. Existing statistical methods must be adapted to overcome the resulting computational obstacles while retaining…
We formulate a novel approach to solve a class of stochastic problems, referred to as data-consistent inverse (DCI) problems, which involve the characterization of a probability measure on the parameters of a computational model whose…
This paper focuses on variational inference with intractable likelihood functions that can be unbiasedly estimated. A flexible variational approximation based on Gaussian mixtures is developed, by adopting the mixture population Monte Carlo…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
The state-of-the-art methods for solving optimization problems in big dimensions are variants of randomized coordinate descent (RCD). In this paper we introduce a fundamentally new type of acceleration strategy for RCD based on the…
This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of…
This paper explores the process of optimal quantization for several types of discrete probability distributions. Quantization is a technique used to approximate a complex distribution with a smaller set of representative points, which is…
In recent years, an increasing amount of data is collected in different and often, not cooperative, databases. The problem of privacy-preserving, distributed calculations over separated databases and, a relative to it, issue of private data…
High-dimensional partial-differential equations (PDEs) arise in a number of fields of science and engineering, where they are used to describe the evolution of joint probability functions. Their examples include the Boltzmann and…