Related papers: Autoregressive Processes on Stiefel and Grassmann …

Graded Lagrangian formalism in terms of a Grassmann-graded variational bicomplex on graded manifolds is developed in a very general setting. This formalism provides the comprehensive description of reducible degenerate Lagrangian systems,…

Gaussian processes (GPs) provide a powerful non-parametric framework for reasoning over functions. Despite appealing theory, its superlinear computational and memory complexities have presented a long-standing challenge. State-of-the-art…

In this paper we propose a recursive online algorithm for estimating the parameters of a time-varying ARCH process. The estimation is done by updating the estimator at time point $t-1$ with observations about the time point $t$ to yield an…

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…

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…

In this work, the Einstein notation is utilized to synthesize state and parameter transition matrices, by solving a set of ordinary differential equations. Additionally, for the system identification problem, it has been demonstrated that…

Non linear regression models are a standard tool for modeling real phenomena, with several applications in machine learning, ecology, econometry... Estimating the parameters of the model has garnered a lot of attention during many years. We…

Vector autoregressive models characterize a variety of time series in which linear combinations of current and past observations can be used to accurately predict future observations. For instance, each element of an observation vector…

The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems,…

Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian…

Dynamic systems described by differential equations often involve feedback among system components. When there are time delays for components to sense and respond to feedback, delay differential equation (DDE) models are commonly used. This…

As is well known, both sampling from the posterior and computing the mean of the posterior in Gaussian process regression reduces to solving a large linear system of equations. We study the use of stochastic gradient descent for solving…

We propose to use stochastic Riemannian coordinate descent on the orthogonal group for recurrent neural network training. The algorithm rotates successively two columns of the recurrent matrix, an operation that can be efficiently…

Many machine learning applications are naturally formulated as optimization problems on Riemannian manifolds. The main idea behind Riemannian optimization is to maintain the feasibility of the variables while moving along a descent…

Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…

A method for determining the orbital parameters of interacting pairs of galaxies is presented and evaluated using artificial data. The method consists of a genetic algorithm which can search efficiently through the very large space of…

We study fast approximation of integrals with respect to stationary probability measures associated to iterated functions systems on the unit interval. We provide an algorithm for approximating the integrals under certain conditions on the…

This paper proposes a gradient descent based optimization method that relies on automatic differentiation for the computation of gradients. The method uses tools and techniques originally developed in the field of artificial neural networks…

Gaussian processes (GPs) are Bayesian nonparametric models for function approximation with principled predictive uncertainty estimates. Deep Gaussian processes (DGPs) are multilayer generalizations of GPs that can represent complex marginal…

Many collective systems exist in nature far from equilibrium, ranging from cellular sheets up to flocks of birds. These systems reflect a form of active matter, whereby individual material components have internal energy. Under specific…