95 citations · 155 across the 23 of their papers we have counts for
25 papers
Determinantal expressions of certain integrals on symmetric spaces
Salem Said, Cyrus Mostajeran
The integral of a function defined on a symmetric space may be expressed in the form of a determinant (or Pfaffian), when is -invariant and, in a certain…
Geometric Learning of Hidden Markov Models via a Method of Moments Algorithm
Berlin Chen, Cyrus Mostajeran, Salem Said
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. In partic…
Riemannian statistics meets random matrix theory: towards learning from high-dimensional covariance matrices
Salem Said, Simon Heuveline, Cyrus Mostajeran
Riemannian Gaussian distributions were initially introduced as basic building blocks for learning models which aim to capture the intrinsic structure of statistical populations of…
Gaussian distributions on Riemannian symmetric spaces, random matrices, and planar Feynman diagrams
Simon Heuveline, Salem Said, Cyrus Mostajeran
Gaussian distributions can be generalized from Euclidean space to a wide class of Riemannian manifolds. Gaussian distributions on manifolds are harder to make use of in application…
On Riemannian Stochastic Approximation Schemes with Fixed Step-Size
Alain Durmus, Pablo Jiménez, Éric Moulines +1
This paper studies fixed step-size stochastic approximation (SA) schemes, including stochastic gradient schemes, in a Riemannian framework. It is motivated by several applications,…
Online learning of Riemannian hidden Markov models in homogeneous Hadamard spaces
Quinten Tupker, Salem Said, Cyrus Mostajeran
Hidden Markov models with observations in a Euclidean space play an important role in signal and image processing. Previous work extending to models where observations lie in Riema…