arXiv subjects

Jialun Zhou

Publications and source records attributed to Jialun Zhou.

3 recordsLinked to original sources

arXiv2020

Riemannian information gradient methods for the parameter estimation of ECD: Some applications in image processing

Elliptically-contoured distributions (ECD) play a significant role, in computer vision, image processing, radar, and biomedical signal processing. Maximum likelihood. estimation (MLE) of ECD leads to a system of non-linear equations, most-often addressed using fixed-point (FP) methods. Unfortunately, the computation time required for these methods is unacceptably long, for large-scale or high-dimensional datasets. To overcome this difficulty, the present work introduces a Riemannian optimisation method, the information stochastic gradient (ISG). The ISG is an online (recursive) method, which achieves the same performance as MLE, for large-scale datasets, while requiring modest memory and time resources. To develop the ISG method, the Riemannian information gradient is derived taking into account the product manifold associated to the underlying parameter space of the ECD. From this information gradient definition, we define also, the information deterministic gradient (IDG), an offline (batch) method, which is an alternative, for moderate-sized datasets. The present work formulates these two methods, and demonstrates their performance through numerical simulations. Two applications, to image re-colorization, and to texture classification, are also worked out.

eess.SP↗

arXiv2020

Riemannian geometry for Compound Gaussian distributions: application to recursive change detection

A new Riemannian geometry for the Compound Gaussian distribution is proposed. In particular, the Fisher information metric is obtained, along with corresponding geodesics and distance function. This new geometry is applied on a change detection problem on Multivariate Image Times Series: a recursive approach based on Riemannian optimization is developed. As shown on simulated data, it allows to reach optimal performance while being computationally more efficient.

stat.ML↗

arXiv2018

Fast, asymptotically efficient, recursive estimation in a Riemannian manifold

Stochastic optimisation in Riemannian manifolds, especially the Riemannian stochastic gradient method, has attracted much recent attention. The present work applies stochastic optimisation to the task of recursive estimation of a statistical parameter which belongs to a Riemannian manifold. Roughly, this task amounts to stochastic minimisation of a statistical divergence function. The following problem is considered : how to obtain fast, asymptotically efficient, recursive estimates, using a Riemannian stochastic optimisation algorithm with decreasing step sizes? In solving this problem, several original results are introduced. First, without any convexity assumptions on the divergence function, it is proved that, with an adequate choice of step sizes, the algorithm computes recursive estimates which achieve a fast non-asymptotic rate of convergence. Second, the asymptotic normality of these recursive estimates is proved, by employing a novel linearisation technique. Third, it is proved that, when the Fisher information metric is used to guide the algorithm, these recursive estimates achieve an optimal asymptotic rate of convergence, in the sense that they become asymptotically efficient. These results, while relatively familiar in the Euclidean context, are here formulated and proved for the first time, in the Riemannian context. In addition, they are illustrated with a numerical application to the recursive estimation of elliptically contoured distributions.

math.ST↗