Related papers: Regularization of covariance matrices on Riemannia…
We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix…
In this paper the space of images is considered as a Riemannian manifold using the metamorphosis approach, where the underlying Riemannian metric simultaneously measures the cost of image transport and intensity variation. A robust and…
Inferring time-varying graph structures from high-dimensional nodal observations is a fundamental problem arising in neuroscience, finance, climatology, and beyond. Two intrinsic challenges govern this problem: maintaining the…
The advent of data science has provided an increasing number of challenges with high data complexity. This paper addresses the challenge of space-time data where the spatial domain is not a planar surface, a sphere, or a linear network, but…
We develop a new method for visualizing and refining the invariances of learned representations. Specifically, we test for a general form of invariance, linearization, in which the action of a transformation is confined to a low-dimensional…
Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn…
This study develops identification methods for linear continuous-time symmetric systems, such as electrical network systems, multi-agent network systems, and temperature dynamics in buildings. To this end, we formulate three system…
In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the…
The problem of adaptive Kalman filtering for a discrete observable linear time-varying system with unknown noise covariance matrices is addressed in this paper. The measurement difference autocovariance method is used to formulate a linear…
This paper proposes an original Riemmanian geometry for low-rank structured elliptical models, i.e., when samples are elliptically distributed with a covariance matrix that has a low-rank plus identity structure. The considered geometry is…
Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…
This work addresses the problem of vehicle path planning in the presence of obstacles and uncertainties, which is a fundamental problem in robotics. While many path planning algorithms have been proposed for decades, many of them have dealt…
Optimal transport has found widespread applications in signal processing and machine learning. Among its many equivalent formulations, optimal transport seeks to reconstruct a random variable/vector with a prescribed distribution at the…
A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the…
The paper studies identification of linear systems with multiplicative noise from multiple-trajectory data. An algorithm based on the least-squares method and multiple-trajectory data is proposed for joint estimation of the nominal system…
In many applications and physical phenomena, bivariate signals are polarized, i.e. they trace an elliptical trajectory over time when viewed in the 2D planes of their two components. The smooth evolution of this elliptical trajectory,…
We theoretically investigate parameter quantum estimation in quantum chaotic systems. Our analysis is based on an effective description of non-integrable quantum systems in terms of a random matrix Hamiltonian. Based on this approach we…
A non-Bayesian, regression-based or generalized least squares (GLS)-based approach is formally proposed to estimate a class of time-varying AR parameter models. This approach has partly been used by Ito et al. (2014, 2016a,b), and is proven…
In this paper, we study the optimal control problem for steering the state covariance of a discrete-time linear stochastic system over a finite time horizon. First, we establish the existence and uniqueness of the optimal control law for a…
As the benchmark of data-driven control methods, the linear quadratic regulator (LQR) problem has gained significant attention. A growing trend is direct LQR design, which finds the optimal LQR gain directly from raw data and bypassing…