Related papers: Autoregressive Processes on Stiefel and Grassmann …

The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite…

Vector autoregression model is ubiquitous in classical time series data analysis. With the rapid advance of social network sites, time series data over latent graph is becoming increasingly popular. In this paper, we develop a novel…

We introduce an approach based on the Givens representation for posterior inference in statistical models with orthogonal matrix parameters, such as factor models and probabilistic principal component analysis (PPCA). We show how the Givens…

We study a class of mathematical and statistical algorithms with the aim of establishing a computer-based framework for fast and reliable automatic abnormality detection on landmark represented image templates. Under this framework, we…

This paper introduces an iterative algorithm for training nonparametric additive models that enjoys favorable memory storage and computational requirements. The algorithm can be viewed as the functional counterpart of stochastic gradient…

Calibration is a highly challenging task, in particular in multiple yield curve markets. This paper is a first attempt to study the chances and challenges of the application of machine learning techniques for this. We employ Gaussian…

As a means of improving analysis of biological shapes, we propose an algorithm for sampling a Riemannian manifold by sequentially selecting points with maximum uncertainty under a Gaussian process model. This greedy strategy is known to be…

We use Stein's method to provide non asymptotic $L^1$ bounds to the normal for functionals of associated point processes. As for supporting tools, we use the connection between association and $\alpha$-mixing properties that was recently…

Estimation of actual errors from the residue in iterative solutions is necessary for efficient solution of large problems when their condition number is much larger than one. Such estimators for conjugate gradient algorithms used to solve…

We consider in this work a system of two stochastic differential equations named the perturbed compositional gradient flow. By introducing a separation of fast and slow scales of the two equations, we show that the limit of the slow motion…

The real symplectic Stiefel manifold is the manifold of symplectic bases of symplectic subspaces of a fixed dimension. It features in a large variety of applications in physics and engineering. In this work, we study this manifold with the…

A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…

Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…

We consider the optimization problem with a generally quadratic matrix constraint of the form $X^TAX = J$, where $A$ is a given nonsingular, symmetric $n\times n$ matrix and $J$ is a given $k\times k$ symmetric matrix, with $k\leq n$,…

In this paper we propose a novel approach to identify dynamical systems. The method estimates the model structure and the parameters of the model simultaneously, automating the critical decisions involved in identification such as model…

We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian…

A common task is the determination of system parameters from spectroscopy, where one compares the experimental spectrum with calculated spectra, that depend on the desired parameters. Here we discuss an approach based on a machine learning…

We present a stepwise approach to estimate high dimensional Gaussian graphical models. We exploit the relation between the partial correlation coefficients and the distribution of the prediction errors, and parametrize the model in terms of…

In this paper we propose an identification method for latent-variable graphical models associated to autoregressive (AR) Gaussian stationary processes. The identification procedure exploits the approximation of AR processes through…

Rare transitions in stochastic processes can often be rigorously described via an underlying large deviation principle. Recent breakthroughs in the classification of reversible stochastic processes as gradient flows have led to a connection…