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

• URL: http://arxiv.org/abs/2005.10087v1
• Date: Wed, 20 May 2020 14:51:09 GMT
• Title: Riemannian geometry for Compound Gaussian distributions: application to recursive change detection
• Authors: Florent Bouchard, Ammar Mian, Jialun Zhou, Salem Said, Guillaume Ginolhac, and Yannick Berthoumieu
• Abstract summary: 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. As shown on simulated data, it allows to reach optimal performance while being computationally more efficient.
• Score: 11.90288071168733
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• The Fisher-Rao geometry of CES distributions [50.50897590847961]
  The Fisher-Rao information geometry allows for leveraging tools from differential geometry. We will present some practical uses of these geometric tools in the framework of elliptical distributions.
  arXiv  Detail & Related papers  (2023-10-02T09:23:32Z)
• Zeroth-order Riemannian Averaging Stochastic Approximation Algorithms [19.99781875916751]
  We show that textttZo-RASA achieves optimal sample complexities for generating $epsilon$-approximation first-order stationary solutions. We improve the algorithm's practicality by using geometrics and vector transport, instead of exponential mappings and parallel transports.
  arXiv  Detail & Related papers  (2023-09-25T20:13:36Z)
• Curvature-Independent Last-Iterate Convergence for Games on Riemannian Manifolds [77.4346324549323]
  We show that a step size agnostic to the curvature of the manifold achieves a curvature-independent and linear last-iterate convergence rate. To the best of our knowledge, the possibility of curvature-independent rates and/or last-iterate convergence has not been considered before.
  arXiv  Detail & Related papers  (2023-06-29T01:20:44Z)
• Riemannian Optimization for Variance Estimation in Linear Mixed Models [0.0]
  We take a completely novel view on parameter estimation in linear mixed models by exploiting the intrinsic geometry of the parameter space. Our approach yields a higher quality of the variance parameter estimates compared to existing approaches.
  arXiv  Detail & Related papers  (2022-12-18T13:08:45Z)
• Manifold Gaussian Variational Bayes on the Precision Matrix [70.44024861252554]
  We propose an optimization algorithm for Variational Inference (VI) in complex models. We develop an efficient algorithm for Gaussian Variational Inference whose updates satisfy the positive definite constraint on the variational covariance matrix. Due to its black-box nature, MGVBP stands as a ready-to-use solution for VI in complex models.
  arXiv  Detail & Related papers  (2022-10-26T10:12:31Z)
• First-Order Algorithms for Min-Max Optimization in Geodesic Metric Spaces [93.35384756718868]
  min-max algorithms have been analyzed in the Euclidean setting. We prove that the extraiteient (RCEG) method corrected lastrate convergence at a linear rate.
  arXiv  Detail & Related papers  (2022-06-04T18:53:44Z)
• Inferring Manifolds From Noisy Data Using Gaussian Processes [17.166283428199634]
  Most existing manifold learning algorithms replace the original data with lower dimensional coordinates. This article proposes a new methodology for addressing these problems, allowing the estimated manifold between fitted data points.
  arXiv  Detail & Related papers  (2021-10-14T15:50:38Z)
• On Riemannian Approach for Constrained Optimization Model in Extreme Classification Problems [2.7436792484073638]
  A constrained optimization problem is formulated as an optimization problem on matrix manifold. The proposed approach is tested on several real world large scale multi-label datasets.
  arXiv  Detail & Related papers  (2021-09-30T11:28:35Z)
• Geometric variational inference [0.0]
  Variational Inference (VI) or Markov-Chain Monte-Carlo (MCMC) techniques are used to go beyond point estimates. This work proposes geometric Variational Inference (geoVI), a method based on Riemannian geometry and the Fisher information metric. The distribution, expressed in the coordinate system induced by the transformation, takes a particularly simple form that allows for an accurate variational approximation.
  arXiv  Detail & Related papers  (2021-05-21T17:18:50Z)
• Automatic differentiation for Riemannian optimization on low-rank matrix and tensor-train manifolds [71.94111815357064]
  In scientific computing and machine learning applications, matrices and more general multidimensional arrays (tensors) can often be approximated with the help of low-rank decompositions. One of the popular tools for finding the low-rank approximations is to use the Riemannian optimization.
  arXiv  Detail & Related papers  (2021-03-27T19:56:00Z)
• Bayesian Quadrature on Riemannian Data Manifolds [79.71142807798284]
  A principled way to model nonlinear geometric structure inherent in data is provided. However, these operations are typically computationally demanding. In particular, we focus on Bayesian quadrature (BQ) to numerically compute integrals over normal laws. We show that by leveraging both prior knowledge and an active exploration scheme, BQ significantly reduces the number of required evaluations.
  arXiv  Detail & Related papers  (2021-02-12T17:38:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.