Geometric Jensen-Shannon Divergence Between Gaussian Measures On Hilbert Space

• URL: http://arxiv.org/abs/2506.10494v1
• Date: Thu, 12 Jun 2025 08:53:16 GMT
• Title: Geometric Jensen-Shannon Divergence Between Gaussian Measures On Hilbert Space
• Authors: Minh Ha Quang, Frank Nielsen,
• Abstract summary: This work studies the Geometric Jensen-Shannon divergence, based on the notion of geometric mean of probability measures, in the setting of Gaussian measures on an infinite-dimensional Hilbert space.<n>We present a closed form expression for this divergence that directly generalizes the finite-dimensional version.
• Score: 5.985204759362746
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This work studies the Geometric Jensen-Shannon divergence, based on the notion of geometric mean of probability measures, in the setting of Gaussian measures on an infinite-dimensional Hilbert space. On the set of all Gaussian measures equivalent to a fixed one, we present a closed form expression for this divergence that directly generalizes the finite-dimensional version. Using the notion of Log-Determinant divergences between positive definite unitized trace class operators, we then define a Regularized Geometric Jensen-Shannon divergence that is valid for any pair of Gaussian measures and that recovers the exact Geometric Jensen-Shannon divergence between two equivalent Gaussian measures when the regularization parameter tends to zero.

Related papers

• Two tales for a geometric Jensen--Shannon divergence [7.070726553564701]
  The geometric Jensen--Shannon divergence (G-JSD) gained popularity in machine learning and information sciences.<n>We introduce an alternative definition of the geometric Jensen--Shannon divergence tailored to positive densities.<n>This novel divergence is termed the extended G-JSD as it extends to more general positive measures.
  arXiv  Detail & Related papers  (2025-08-07T06:34:39Z)
• From Two Sample Testing to Singular Gaussian Discrimination [0.0]
  Discerning two singular Gaussians is simpler from an information-theoretic perspective than non-parametric two-sample testing.<n>This appears to be a new instance of the blessing of dimensionality that can be harnessed for the design of efficient inference tools in great generality.
  arXiv  Detail & Related papers  (2025-05-07T17:56:19Z)
• Bayesian Circular Regression with von Mises Quasi-Processes [57.88921637944379]
  In this work we explore a family of expressive and interpretable distributions over circle-valued random functions.<n>For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Gibbs sampling.<n>We present experiments applying this model to the prediction of wind directions and the percentage of the running gait cycle as a function of joint angles.
  arXiv  Detail & Related papers  (2024-06-19T01:57:21Z)
• Intrinsic Bayesian Cramér-Rao Bound with an Application to Covariance Matrix Estimation [49.67011673289242]
  This paper presents a new performance bound for estimation problems where the parameter to estimate lies in a smooth manifold. It induces a geometry for the parameter manifold, as well as an intrinsic notion of the estimation error measure.
  arXiv  Detail & Related papers  (2023-11-08T15:17:13Z)
• 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)
• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• Hyperbolic VAE via Latent Gaussian Distributions [7.258394470200572]
  We propose a Gaussian manifold variational auto-encoder (GM-VAE) whose latent space consists of a set of Gaussian distributions. In experiments, we demonstrate the efficacy of GM-VAE on two different tasks: density estimation of image datasets and environment modeling in model-based reinforcement learning.
  arXiv  Detail & Related papers  (2022-09-30T04:09:06Z)
• Kullback-Leibler and Renyi divergences in reproducing kernel Hilbert space and Gaussian process settings [0.0]
  We present formulations for regularized Kullback-Leibler and R'enyi divergences via the Alpha Log-Determinant (Log-Det) divergences. For characteristic kernels, the first setting leads to divergences between arbitrary Borel probability measures on a complete, separable metric space. We show that the Alpha Log-Det divergences are continuous in the Hilbert-Schmidt norm, which enables us to apply laws of large numbers for Hilbert space-valued random variables.
  arXiv  Detail & Related papers  (2022-07-18T06:40:46Z)
• A Unifying and Canonical Description of Measure-Preserving Diffusions [60.59592461429012]
  A complete recipe of measure-preserving diffusions in Euclidean space was recently derived unifying several MCMC algorithms into a single framework. We develop a geometric theory that improves and generalises this construction to any manifold.
  arXiv  Detail & Related papers  (2021-05-06T17:36:55Z)
• Convergence and finite sample approximations of entropic regularized Wasserstein distances in Gaussian and RKHS settings [0.0]
  We study the convergence and finite sample approximations of entropic regularized Wasserstein distances in the Hilbert space setting. For Gaussian measures on an infinite-dimensional Hilbert space, convergence in the 2-Sinkhorn divergence is weaker than convergence in the exact 2-Wasserstein distance.
  arXiv  Detail & Related papers  (2021-01-05T09:46:58Z)
• Rectification induced by geometry in two-dimensional quantum spin lattices [58.720142291102135]
  We address the role of geometrical asymmetry in the occurrence of spin rectification in two-dimensional quantum spin chains. We show that geometrical asymmetry, along with inhomogeneous magnetic fields, can induce spin current rectification even in the XX model.
  arXiv  Detail & Related papers  (2020-12-02T18:10:02Z)
• Entropy-Regularized $2$-Wasserstein Distance between Gaussian Measures [2.320417845168326]
  We study the Gaussian geometry under the entropy-regularized 2-Wasserstein distance. We provide a fixed-point characterization of a population barycenter when restricted to the manifold of Gaussians. As the geometries change by varying the regularization magnitude, we study the limiting cases of vanishing and infinite magnitudes.
  arXiv  Detail & Related papers  (2020-06-05T13:18:57Z)

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.