Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein space
MZ Diao, K Balasubramanian… - … on Machine Learning, 2023 - proceedings.mlr.press
Variational inference (VI) seeks to approximate a target distribution $\pi $ by an element of a
tractable family of distributions. Of key interest in statistics and machine learning is Gaussian …
tractable family of distributions. Of key interest in statistics and machine learning is Gaussian …
A survey of geometric optimization for deep learning: from Euclidean space to Riemannian manifold
Deep Learning (DL) has achieved remarkable success in tackling complex Artificial
Intelligence tasks. The standard training of neural networks employs backpropagation to …
Intelligence tasks. The standard training of neural networks employs backpropagation to …
[PDF][PDF] Statistical optimal transport
Statistical Optimal Transport arXiv:2407.18163v2 [math.ST] 7 Nov 2024 Page 1 Statistical
Optimal Transport Sinho Chewi Yale Jonathan Niles-Weed NYU Philippe Rigollet MIT …
Optimal Transport Sinho Chewi Yale Jonathan Niles-Weed NYU Philippe Rigollet MIT …
Riemannian conjugate gradient methods: General framework and specific algorithms with convergence analyses
H Sato - SIAM Journal on Optimization, 2022 - SIAM
Conjugate gradient methods are important first-order optimization algorithms both in
Euclidean spaces and on Riemannian manifolds. However, while various types of conjugate …
Euclidean spaces and on Riemannian manifolds. However, while various types of conjugate …
The schrödinger bridge between gaussian measures has a closed form
The static optimal transport $(\mathrm {OT}) $ problem between Gaussians seeks to recover
an optimal map, or more generally a coupling, to morph a Gaussian into another. It has been …
an optimal map, or more generally a coupling, to morph a Gaussian into another. It has been …
First-order algorithms for min-max optimization in geodesic metric spaces
From optimal transport to robust dimensionality reduction, many machine learning
applicationscan be cast into the min-max optimization problems over Riemannian manifolds …
applicationscan be cast into the min-max optimization problems over Riemannian manifolds …
Riemannian Hamiltonian methods for min-max optimization on manifolds
In this paper, we study min-max optimization problems on Riemannian manifolds. We
introduce a Riemannian Hamiltonian function, minimization of which serves as a proxy for …
introduce a Riemannian Hamiltonian function, minimization of which serves as a proxy for …
Convergence of policy gradient methods for finite-horizon exploratory linear-quadratic control problems
M Giegrich, C Reisinger, Y Zhang - SIAM Journal on Control and Optimization, 2024 - SIAM
We study the global linear convergence of policy gradient (PG) methods for finite-horizon
continuous-time exploratory linear-quadratic control (LQC) problems. The setting includes …
continuous-time exploratory linear-quadratic control (LQC) problems. The setting includes …
Simplifying momentum-based positive-definite submanifold optimization with applications to deep learning
Riemannian submanifold optimization with momentum is computationally challenging
because, to ensure that the iterates remain on the submanifold, we often need to solve …
because, to ensure that the iterates remain on the submanifold, we often need to solve …
Differentially private Riemannian optimization
In this paper, we study the differentially private empirical risk minimization problem where
the parameter is constrained to a Riemannian manifold. We introduce a framework for …
the parameter is constrained to a Riemannian manifold. We introduce a framework for …