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Note on the geodesic Monte Carlo
Geodesic Monte Carlo (gMC) comprises a powerful class of algorithms for ...
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Hamiltonian Monte-Carlo for Orthogonal Matrices
We consider the problem of sampling from posterior distributions for Bay...
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Discussion of "Riemann manifold Langevin and Hamiltonian Monte Carlo methods" by M. Girolami and B. Calderhead
This technical report is the union of two contributions to the discussio...
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Simulating sticky particles: A Monte Carlo method to sample a Stratification
Many problems in materials science and biology involve particles interac...
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Dynamically rescaled Hamiltonian Monte Carlo for Bayesian Hierarchical Models
Dynamically rescaled Hamiltonian Monte Carlo (DRHMC) is introduced as a ...
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H-CNNs: Convolutional Neural Networks for Riemannian Homogeneous Spaces
Convolutional neural networks are ubiquitous in Machine Learning applica...
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The LAPW method with eigendecomposition based on the Hari–Zimmermann generalized hyperbolic SVD
In this paper we propose an accurate, highly parallel algorithm for the ...
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Hamiltonian Monte Carlo on Symmetric and Homogeneous Spaces via Symplectic Reduction
The Hamiltonian Monte Carlo method generates samples by introducing a mechanical system that explores the target density. For distributions on manifolds it is not always simple to perform the mechanics as a result of the lack of global coordinates, the constraints of the manifold, and the requirement to compute the geodesic flow. In this paper we explain how to construct the Hamiltonian system on naturally reductive homogeneous spaces using symplectic reduction, which lifts the HMC scheme to a matrix Lie group with global coordinates and constant metric. This provides a general framework that is applicable to many manifolds that arise in applications, such as hyperspheres, hyperbolic spaces, symmetric positive-definite matrices, Grassmannian, and Stiefel manifolds.
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