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We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over…
Rhythmic data are ubiquitous in the life sciences. Biologists need reliable statistical tests to identify whether a particular experimental treatment has caused a significant change in a rhythmic signal. When these signals display…
Many spatial processes exhibit nonstationary features. We estimate a variance function from a single process observation where the errors are nonstationary and correlated. We propose a difference-based approach for a one-dimensional…
This manuscript is superseded by Constantine, Dow, and Wang's "Active Subspaces in Theory and Practice: Applications to Kriging Surfaces" [SIAM J. of Sci. Comput., 36 (2014), pp. A1500-A1524]. Many multivariate functions encountered in…
We propose computationally efficient methods for estimating stationary multivariate spatial and spatial-temporal spectra from incomplete gridded data. The methods are iterative and rely on successive imputation of data and updating of model…
In recent years, machine learning has witnessed extensive adoption across various sectors, yet its application in medical image-based disease detection and diagnosis remains challenging due to distribution shifts in real-world data. In…
Many-body localization (MBL), characterized by the absence of thermalization and the violation of conventional thermodynamics, has elicited much interest both as a fundamental physical phenomenon and for practical applications in quantum…
Spatial classification with limited feature observations has been a challenging problem in machine learning. The problem exists in applications where only a subset of sensors are deployed at certain spots or partial responses are collected…
Peebles (1989) showed that in the gravitational instability picture galaxy orbits can be traced back in time from a knowledge of their current positions, via a variational principle. We modify this variational principle so that galaxy…
The present paper is intended to provide the basis for the study of weakly differentiable functions on rectifiable varifolds with locally bounded first variation. The concept proposed here is defined by means of integration by parts…
Nonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for…
'Sharing of statistical strength' is a phrase often employed in machine learning and signal processing. In sensor networks, for example, missing signals from certain sensors may be predicted by exploiting their correlation with observed…
In this paper, we apply a recently developed nonparametric modeling approach, the "diffusion forecast", to predict the time-evolution of Fourier modes of turbulent dynamical systems. While the diffusion forecasting method assumes the…
Diffusion and anomalous diffusion are widely observed and used to study movement across organisms, resulting in extensive use of the mean and mean-squared displacement (MSD). However, these measures - corresponding to specific displacement…
We consider the problem of anomaly detection in images, and present a new detection technique. Given a sample of images, all known to belong to a "normal" class (e.g., dogs), we show how to train a deep neural model that can detect…
Wavelets provide the flexibility to analyse stochastic processes at different scales. Here, we apply them to multivariate point processes as a means of detecting and analysing unknown non-stationarity, both within and across data streams.…
Statisticians have recently developed propensity score methods to improve generalizations from randomized experiments that do not employ random sampling. However, these methods typically rely on assumptions whose plausibility may be…
We introduce a notion of non-local perimeter which is defined through an arbitrary positive Borel measure on $\mathbb{R}^d$ which integrates the function $1\wedge |x|$. Such definition of non-local perimeter encompasses a wide range of…
Existing urban boundaries are usually defined by government agencies for administrative, economic, and political purposes. Defining urban boundaries that consider socio-economic relationships and citizen commute patterns is important for…
We propose a new test of local realism based on correlation measurements of continuum valued functions of positions and momenta, known as modular variables. The Wigner representation of these observables are bounded in phase space, and…