相关论文: Dynamic Elliptical Graph Factor Models via Riemann…

This paper describes an approach for fitting an immersed submanifold of a finite-dimensional Euclidean space to random samples. The reconstruction mapping from the ambient space to the desired submanifold is implemented as a composition of…

Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…

Decentralized optimization on Riemannian manifolds is foundational for many modern machine learning and signal processing applications in which data are non-Euclidean and generated and processed in a distributed manner. Although intrinsic…

In this work we study the non-parametric reconstruction of spatio-temporal dynamical Gaussian processes (GPs) via GP regression from sparse and noisy data. GPs have been mainly applied to spatial regression where they represent one of the…

The performance of space-time adaptive processing (STAP) is often degraded by factors such as limited sample size and moving targets. Traditional clutter covariance matrix (CCM) estimation relies on Euclidean metrics, which fail to capture…

Understanding the dynamic processes of the glassy system continues to be challenging. Recent advances have shown the power of graph neural networks (GNNs) for determining the correlation between structure and dynamics in the glassy system.…

We consider a class of nonsmooth optimization problems over the Stiefel manifold, in which the objective function is weakly convex in the ambient Euclidean space. Such problems are ubiquitous in engineering applications but still largely…

This paper introduces sparse dynamic chain graph models for network inference in high dimensional non-Gaussian time series data. The proposed method parametrized by a precision matrix that encodes the intra time-slice conditional…

We study optimization over Riemannian embedded submanifolds, where the objective function is relatively smooth in the ambient Euclidean space. Such problems have broad applications but are still largely unexplored. We introduce two…

We present Riemannian Gaussian Variational Flow Matching (RG-VFM), a geometric extension of Variational Flow Matching (VFM) for generative modeling on manifolds. Motivated by the benefits of VFM, we derive a variational flow matching…

Stochastic gradient descent is a simple approach to find the local minima of a cost function whose evaluations are corrupted by noise. In this paper, we develop a procedure extending stochastic gradient descent algorithms to the case where…

This paper considers the problem of decentralized optimization on compact submanifolds, where a finite sum of smooth (possibly non-convex) local functions is minimized by $n$ agents forming an undirected and connected graph. However, the…

Discrete time spatial time series data arise routinely in meteorological and environmental studies. Inference and prediction associated with them are mostly carried out using any of the several variants of the linear state space model that…

This paper considers a distributed convex optimization problem with inequality constraints over time-varying unbalanced digraphs, where the cost function is a sum of local objectives, and each node of the graph only knows its local…

The time-evolving precision matrix of a piecewise-constant Gaussian graphical model encodes the dynamic conditional dependency structure of a multivariate time-series. Traditionally, graphical models are estimated under the assumption that…

We analyse three related preconditioned steepest descent algorithms, which are partially popular in Hartree-Fock and Kohn-Sham theory as well as invariant subspace computations, from the viewpoint of minimization of the corresponding…

We propose a novel framework for learning time-varying graphs from spatiotemporal measurements. Given an appropriate prior on the temporal behavior of signals, our proposed method can estimate time-varying graphs from a small number of…

We consider the problem of learning a graph from a finite set of noisy graph signal observations, the goal of which is to find a smooth representation of the graph signal. Such a problem is motivated by the desire to infer relational…

Assuming Temporal and Configurational Relationalism, GR as Geometrodynamic's DeWitt supermetric alongside local Lorentzian Relativity with its universal finite maximum propagation speed arises as one of very few options from Feeding…

The study of transport and mixing processes in dynamical systems is particularly important for the analysis of mathematical models of physical systems. We propose a novel, direct geometric method to identify subsets of phase space that…