Related papers: Stochastic Nonparametric Estimation of the Density…

Estimating the expectation of a real-valued function of a random variable from sample data is a critical aspect of statistical analysis, with far-reaching implications in various applications. Current methodologies typically assume…

Estimating density functionals of analog sources is an important problem in statistical signal processing and information theory. Traditionally, estimating these quantities requires either making parametric assumptions about the underlying…

In the setting of a recently developed cellular stochastic traffic flow model, it has shown that the joint per-cell vehicle densities, as a function of time, can be accurately approximated by a Gaussian process, which has the attractive…

Accurately estimating data density is crucial for making informed decisions and modeling in various fields. This paper presents a novel nonparametric density estimation procedure that utilizes bivariate penalized spline smoothing over…

This article deals with the observation problem in traffic flow theory. The model used is the semilinear viscous Burgers equation. Instead of using the traditional fixed sensors to estimate the state of the traffic at given points, the…

Stochastic evolution equations describing the dynamics of systems under the influence of both deterministic and stochastic forces are prevalent in all fields of science. Yet, identifying these systems from sparse-in-time observations…

We prove existence and uniqueness of solutions to a transport equation modelling vehicular traffic in which the velocity field depends non-locally on the downstream traffic density via a discontinuous anisotropic kernel. The result is…

Modes and ridges of the probability density function behind observed data are useful geometric features. Mode-seeking clustering assigns cluster labels by associating data samples with the nearest modes, and estimation of density ridges…

Most car-following models show a transition from laminar to ``congested'' flow and vice versa. Deterministic models often have a density range where a disturbance needs a sufficiently large critical amplitude to move the flow from the…

Normalizing flows provide an elegant approach to generative modeling that allows for efficient sampling and exact density evaluation of unknown data distributions. However, current techniques have significant limitations in their…

We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in…

Simulating turbulent fluid flows is a computationally prohibitive task, as it requires the resolution of fine-scale structures and the capture of complex nonlinear interactions across multiple scales. This is particularly the case in direct…

Estimation of unsteady flow fields around flight vehicles may improve flow interactions and lead to enhanced vehicle performance. Although flow-field representations can be very high-dimensional, their dynamics can have low-order…

Equilibrium modeling is common in a variety of fields such as game theory and transportation science. The inputs for these models, however, are often difficult to estimate, while their outputs, i.e., the equilibria they are meant to…

Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…

Machine learning offers an intriguing alternative to first-principles analysis for discovering new physics from experimental data. However, to date, purely data-driven methods have only proven successful in uncovering physical laws…

Temporal coherence is a valuable source of information in the context of optical flow estimation. However, finding a suitable motion model to leverage this information is a non-trivial task. In this paper we propose an unsupervised online…

This paper proposes a novel approach to the statistical characterization of non-central complex Gaussian quadratic forms (CGQFs). Its key strategy is the generation of an auxiliary random variable (RV) that converges in distribution to the…

Flexibly modeling how an entire density changes with covariates is an important but challenging generalization of mean and quantile regression. While existing methods for density regression primarily consist of covariate-dependent discrete…

Tuning of measurement models is challenging in real-world applications of sequential Monte Carlo methods. Recent advances in differentiable particle filters have led to various efforts to learn measurement models through neural networks.…