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The Pseudo-Marginal (PM) algorithm is a popular Markov chain Monte Carlo (MCMC) method used to sample from a target distribution when its density is inaccessible, but can be estimated with a non-negative unbiased estimator. Its performance…
Reliable density estimation is fundamental for numerous applications in statistics and machine learning. In many practical scenarios, data are best modeled as mixtures of component densities that capture complex and multimodal patterns.…
This paper studies the problem of distributionally robust model predictive control (MPC) using total variation distance ambiguity sets. For a discrete-time linear system with additive disturbances, we provide a conditional value-at-risk…
We study the maximum likelihood estimator of density of $n$ independent observations, under the assumption that it is well approximated by a mixture with a large number of components. The main focus is on statistical properties with respect…
We analyze statistical features of the ``optimization landscape'' in a random version of one of the simplest constrained optimization problems of the least-square type: finding the best approximation for the solution of an overcomplete…
The paper studies the optimal density steering problem for nonlinear continuous-time stochastic systems. To accurately capture nonlinear dynamics in high-uncertainty regions that deviate significantly from a nominal linearization point, we…
This paper investigates the convergence of density approximations for stochastic heat equation in both uniform convergence topology and total variation distance. The convergence order of the densities in uniform convergence topology is…
This paper outlines an approach to the approximation of probability density functions by quadratic forms of weighted orthonormal basis functions with positive semi-definite Hermitian matrices of unit trace. Such matrices are called…
The problem of nearest neighbor condensing has enjoyed a long history of study, both in its theoretical and practical aspects. In this paper, we introduce the problem of weighted distance nearest neighbor condensing, where one assigns…
Sampling from multimodal distributions is a challenging task in scientific computing. When a distribution has an exact symmetry between the modes, direct jumps among them can accelerate the samplings significantly. However, the…
The most efficient way to pack equally sized spheres isotropically in 3D is known as the random close packed state, which provides a starting point for many approximations in physics and engineering. However, the particle size distribution…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
This paper investigates two fundamental descriptors of data, i.e., density distribution versus mass distribution, in the context of clustering. Density distribution has been the de facto descriptor of data distribution since the…
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially heterogeneous manner. Mathematical models of these…
This work studies how to estimate the mean-field density of large-scale systems in a distributed manner. Such problems are motivated by the recent swarm control technique that uses mean-field approximations to represent the collective…
This paper focuses on radar waveform optimization for minimizing the Cram\'er-Rao bound (CRB) in a multiple-input multiple-output (MIMO) radar system. In contrast to conventional approaches relying on semi-definite programming (SDP) and…
We propose extensions and improvements of the statistical analysis of distributed multipoles (SADM) algorithm put forth by Chipot et al. in [6] for the derivation of distributed atomic multipoles from the quantum-mechanical electrostatic…
This paper deals with nonparametric estimation of conditional den-sities in mixture models in the case when additional covariates are available. The proposed approach consists of performing a prelim-inary clustering algorithm on the…
This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…
In this paper, by means of a standard model problem, we devise an approach to computing approximate dual bounds for use in global optimization of coefficient identification in partial differential equations (PDEs) by, e.g., (spatial)…