Related papers: Data-Efficient Non-Gaussian Semi-Nonparametric Den…
This paper presents novel method for distribution-free robust trajectory optimization and control of discrete-time, nonlinear, and non-Gaussian stochastic systems, with closed-loop guarantees on chance constraint satisfaction. Our framework…
This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this…
In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate…
This paper generalizes stochastic collocation methods to handle correlated non-Gaussian random parameters. The key challenge is to perform a multivariate numerical integration in a correlated parameter space when computing the coefficient…
Discrete data are abundant and often arise as counts or rounded data. These data commonly exhibit complex distributional features such as zero-inflation, over-/under-dispersion, boundedness, and heaping, which render many parametric models…
We present a novel distributed Gauss-Newton method for the non-linear state estimation (SE) model based on a probabilistic inference method called belief propagation (BP). The main novelty of our work comes from applying BP sequentially…
We consider nonparametric invariant density and drift estimation for a class of multidimensional degenerate resp. hypoelliptic diffusion processes, so-called stochastic damping Hamiltonian systems or kinetic diffusions, under anisotropic…
Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function.…
We present an efficient nodal discontinuous Galerkin method for approximating nearly incompressible flows using the Boltzmann equations. The equations are discretized with Hermite polynomials in velocity space yielding a first order…
A common challenge in estimating parameters of probability density functions is the intractability of the normalizing constant. While in such cases maximum likelihood estimation may be implemented using numerical integration, the approach…
The paper addresses the problem of passivation of a class of nonlinear systems where the dynamics are unknown. For this purpose, we use the highly flexible, data-driven Gaussian process regression for the identification of the unknown…
We propose the K-series estimation approach for the recovery of unknown univariate and multivariate distributions given knowledge of a finite number of their moments. Our method is directly applicable to the probabilistic analysis of…
Graph neural networks are often used to model interacting dynamical systems since they gracefully scale to systems with a varying and high number of agents. While there has been much progress made for deterministic interacting systems,…
A stationary Gaussian process is said to be long-range dependent (resp., anti-persistent) if its spectral density $f(\lambda)$ can be written as $f(\lambda)=|\lambda|^{-2d}g(|\lambda|)$, where $0<d<1/2$ (resp., $-1/2<d<0$), and $g$ is…
This paper addresses the synthesis of interval observers for partially unknown nonlinear systems subject to bounded noise, aiming to simultaneously estimate system states and learn a model of the unknown dynamics. Our approach leverages…
Probabilistic prediction of stochastic dynamical systems (SDSs) aims to accurately predict the conditional probability distributions of future states. However, accurate probabilistic predictions tightly hinge on accurate distributional…
This article presents a rigorous analysis for efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures.…
We propose a nonparametric density estimator based on the Gaussian process (GP) and derive three novel closed form learning algorithms based on Fisher divergence (FD) score matching. The density estimator is formed by multiplying a base…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
An important question in deep learning is how higher-order optimization methods affect generalization. In this work, we analyze a stochastic Gauss-Newton (SGN) method with Levenberg-Marquardt damping and mini-batch sampling for training…