Related papers: Nonparametric Measure-Transportation-Based Methods…
Nonlinear statistics (i.e. statistics of permanents) on the eigenvalues of invariant random matrix models are considered for the three Dyson's symmetry classes $\beta=1,2,4$. General formulas in terms of hyperdeterminants are found for…
This survey explores the foundational theory and recent developments in the study of hyperuniformity. We present a comprehensive mathematical framework in the context of weakly stationary random measures, emphasizing spectral…
We study a class of nonlinear nonparametric inverse problems. Specifically, we propose a nonparametric estimator of the dynamics of a monotonically increasing trajectory defined on a finite time interval. Under suitable regularity…
Optimal transport (OT) is a popular and powerful tool for comparing probability measures. However, OT suffers a few drawbacks: (i) input measures required to have the same mass, (ii) a high computational complexity, and (iii) indefiniteness…
Superdiffusion is an anomalous transport behavior. Recently, a new mechanism, termed the ``nodal mechanism," has been proposed to induce superdiffusion in quantum models. However, existing realizations of the nodal mechanism have so far…
We introduce a new non-linear optimal transport formulation for a pair of probability measures on $\mathbb{R}^d$ sharing a common barycentre, in which admissible transference plans satisfy two martingale-type constraints. This bi-martingale…
A novel algorithm is proposed to solve the sample-based optimal transport problem. An adversarial formulation of the push-forward condition uses a test function built as a convolution between an adaptive kernel and an evolving probability…
Non-parametric representations of dynamical systems based on the image of a Hankel matrix of data are extensively used for data-driven control. However, if samples of data are missing, obtaining such representations becomes a difficult…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
We consider the testing and estimation of change-points, locations where the distribution abruptly changes, in a sequence of multivariate or non-Euclidean observations. We study a nonparametric framework that utilizes similarity information…
We consider settings where data are available on a nonparametric function and various partial derivatives. Such circumstances arise in practice, for example in the joint estimation of cost and input functions in economics. We show that when…
We propose nonparametric open-end sequential testing procedures that can detect all types of changes in the contemporary distribution function of possibly multivariate observations. Their asymptotic properties are theoretically investigated…
Existing measures and representations for trajectories have two longstanding fundamental shortcomings, i.e., they are computationally expensive and they can not guarantee the `uniqueness' property of a distance function: dist(X,Y) = 0 if…
In the context of regressing a response $Y$ on a predictor $X$, we consider estimating the local modes of the distribution of $Y$ given $X=x$ when $X$ is prone to measurement error. We propose two nonparametric estimation methods, with one…
Data-Driven Computational Mechanics is a novel computing paradigm that enables the transition from standard data-starved approaches to modern data-rich approaches. At this early stage of development, one can distinguish two mainstream…
We consider optimal transportation of measures on metric and topological spaces in the case where the cost function and marginal distributions depend on a parameter with values in a metric space. The Hausdorff distance between the sets of…
We study the transport property of Gaussian measures on Sobolev spaces of periodic functions under the dynamics of the one-dimensional cubic fractional nonlinear Schr\"{o}dinger equation. For the case of second-order dispersion or greater,…
The parameter space of nonnegative trigonometric sums (NNTS) models for circular data is the surface of a hypersphere; thus, constructing regression models for a circular-dependent variable using NNTS models can comprise fitting great…
This work presents a non-parametric spatio-temporal model for mapping human activity by mobile autonomous robots in a long-term context. Based on Variational Gaussian Process Regression, the model incorporates prior information of spatial…
This paper employs techniques from metric geometry and optimal transport theory to address questions related to the analysis of functional data on metric or metric-measure spaces, which we refer to as fields. Formally, fields are viewed as…