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Found 11 papers, 0 papers with code
Invariant kernels on Riemannian symmetric spaces: a harmonic-analytic approach
This work aims to prove that the classical Gaussian kernel, when defined on a non-Euclidean symmetric space, is never positive-definite for any choice of parameter.
Geometric Learning with Positively Decomposable Kernels
Classical kernel methods are based on positive-definite kernels, which map data spaces into reproducing kernel Hilbert spaces (RKHS).
Geometric Learning of Hidden Markov Models via a Method of Moments Algorithm
We present a novel algorithm for learning the parameters of hidden Markov models (HMMs) in a geometric setting where the observations take values in Riemannian manifolds.
Riemannian statistics meets random matrix theory: towards learning from high-dimensional covariance matrices
Its main contribution is to prove that Riemannian Gaussian distributions of real, complex, or quaternion covariance matrices are equivalent to orthogonal, unitary, or symplectic log-normal matrix ensembles.
On Riemannian Stochastic Approximation Schemes with Fixed Step-Size
This result gives rise to a family of stationary distributions indexed by the step-size, which is further shown to converge to a Dirac measure, concentrated at the solution of the problem at hand, as the step-size goes to 0.
Online learning of Riemannian hidden Markov models in homogeneous Hadamard spaces
Hidden Markov models with observations in a Euclidean space play an important role in signal and image processing.
Statistical models and probabilistic methods on Riemannian manifolds
This entry contains the core material of my habilitation thesis, soon to be officially submitted.
Statistics Theory Statistics Theory
Hidden Markov chains and fields with observations in Riemannian manifolds
Hidden Markov chain, or Markov field, models, with observations in a Euclidean space, play a major role across signal and image processing.
Statistics Theory Statistics Theory
Riemannian information gradient methods for the parameter estimation of ECD: Some applications in image processing
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.
Convergence Analysis of Riemannian Stochastic Approximation Schemes
This paper analyzes the convergence for a large class of Riemannian stochastic approximation (SA) schemes, which aim at tackling stochastic optimization problems.
Riemannian geometry for Compound Gaussian distributions: application to recursive change detection
A new Riemannian geometry for the Compound Gaussian distribution is proposed.
