Related papers: Autoregressive Processes on Stiefel and Grassmann …

This paper presents a model of asymmetric bifurcating autoregressive process with random coefficients. We couple this model with a Galton Watson tree to take into account possibly missing observations. We propose least-squares estimators…

In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue…

We propose a recursive Bayesian estimation procedure for multivariate autoregressive models with exogenous inputs based on message passing in a factor graph. Unlike recursive least-squares, our method produces full posterior distributions…

Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…

The concept of a random process has been recently extended to graph signals, whereby random graph processes are a class of multivariate stochastic processes whose coefficients are matrices with a \textit{graph-topological} structure. The…

An ensemble method is introduced that utilizes randomization and loss function gradients to compute a prediction. Multiple weakly-correlated estimators approximate the gradient at randomly sampled points on the error surface and are…

Autoregressive models are ubiquitous tools for the analysis of time series in many domains such as computational neuroscience and biomedical engineering. In these domains, data is, for example, collected from measurements of brain activity.…

In this paper, we investigate a class of spherical functional autoregressive processes, and we discuss the estimation of the corresponding autoregressive kernels. In particular, we first establish a consistency result (in sup and…

A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…

We propose a novel recursive system identification algorithm for linear autoregressive systems with skewed innovations. The algorithm is based on the variational Bayes approximation of the model with a multivariate normal prior for the…

Motivated by a variety of applications, high-dimensional time series have become an active topic of research. In particular, several methods and finite-sample theories for individual stable autoregressive processes with known lag have…

Random orthogonal matrices play an important role in probability and statistics, arising in multivariate analysis, directional statistics, and models of physical systems, among other areas. Calculations involving random orthogonal matrices…

Considering orthogonal Stiefel manifolds as constraint manifolds, we give an explicit description of a set of local coordinates that also generate a basis for the tangent space in any point of the orthogonal Stiefel manifolds. We show how…

A parameter estimation method is devised for a slow-fast stochastic dynamical system, where often only the slow component is observable. By using the observations only on the slow component, the system parameters are estimated by working on…

A generalized Stiefel manifold is the manifold of orthonormal frames in a vector space with a non-degenerated bilinear or hermitian form. In this article, the Isometry group of the generalized Stiefel manifolds are computed at least up to…

An autoregressive-moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models are useful for…

Gaussian processes are used in machine learning to learn input-output mappings from observed data. Gaussian process regression is based on imposing a Gaussian process prior on the unknown regressor function and statistically conditioning it…

The aim of this paper is to define a nonlinear least squares estimator for the spectral parameters of a spherical autoregressive process of order 1 in a parametric setting. Furthermore, we investigate on its asymptotic properties, such as…

Polygons are compound geometric objects, but when trying to understand the expected behavior of a large collection of random polygons -- or even to formalize what a random polygon is -- it is convenient to interpret each polygon as a point…

In this paper, we propose a simple acceleration scheme for Riemannian gradient methods by extrapolating iterates on manifolds. We show when the iterates are generated from Riemannian gradient descent method, the accelerated scheme achieves…