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Many computer vision applications involve modeling complex spatio-temporal patterns in high-dimensional motion data. Recently, restricted Boltzmann machines (RBMs) have been widely used to capture and represent spatial patterns in a single…
State estimation that combines observational data with mathematical models is central to many applications and is commonly addressed through filtering methods, such as ensemble Kalman filters. In this article, we examine the signal-tracking…
The present paper introduces a data-driven framework for describing the time-varying nature of an SIRD model in the context of COVID-19. By embedding a rolling regression in a mixed integer bilevel nonlinear programming problem, our aim is…
We consider the statistical problem of estimating constituent curves from observations of their aggregated curves, referred to as aggregated functional data, in models with additive errors. A typical model arises in chemometrics via the…
In many areas of science one aims to estimate latent sub-population mean curves based only on observations of aggregated population curves. By aggregated curves we mean linear combination of functional data that cannot be observed…
We study the boundary rigidity problem with partial data consisting of determining locally the Riemannian metric of a Riemannian manifold with boundary from the distance function measured at pairs of points near a fixed point on the…
Dynamic functional connectivity analysis provides valuable information for understanding brain functional activity underlying different cognitive processes. Besides sliding window based approaches, a variety of methods have been developed…
Data depth is a well-known and useful nonparametric tool for analyzing functional data. It provides a novel way of ranking a sample of curves from the center outwards and defining robust statistics, such as the median or trimmed means. It…
Stochastic-gradient sampling methods are often used to perform Bayesian inference on neural networks. It has been observed that the methods in which notions of differential geometry are included tend to have better performances, with the…
Understanding pedestrian dynamics is critical for mitigating crowd-related risks and improving public safety. In this work, we propose a data-driven mesoscopic modeling framework that combines the kinetic theory of active particles with…
Curve fitting is a fundamental technique in engineering and scientific research, serving as a critical tool for extracting insights from data. This study explores the application of various statistical equations to estimate outcomes in…
We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…
A novel elastic time distance for sparse multivariate functional data is proposed and used to develop a robust distance-based two-layer partition clustering method. With this proposed distance, the new approach not only can detect correct…
Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…
In this work we propose a novel approach for modeling spatio-temporal data characterized by group structures. In particular, we extend classical mixed effect regression models by introducing a space-time nonparametric component, regularized…
The EM algorithm is one of many important tools in the field of statistics. While often used for imputing missing data, its widespread applications include other common statistical tasks, such as clustering. In clustering, the EM algorithm…
Samples of curves, or functional data, usually present phase variability in addition to amplitude variability. Existing functional regression methods do not handle phase variability in an efficient way. In this paper we propose a functional…
This paper develops a theory of clustering and coding which combines a geometric model with a probabilistic model in a principled way. The geometric model is a Riemannian manifold with a Riemannian metric, ${g}_{ij}({\bf x})$, which we…
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…
Generating realistic brain connectivity matrices is key to analyzing population heterogeneity in brain organization, understanding disease, and augmenting data in challenging classification problems. Functional connectivity matrices lie in…