Towards a theory of non-commutative optimization: Geodesic 1st and 2nd order methods for moment maps and polytopes
This paper initiates a systematic development of a theory of non-commutative optimization, a
setting which greatly extends ordinary (Euclidean) convex optimization. It aims to unify and …
setting which greatly extends ordinary (Euclidean) convex optimization. It aims to unify and …
[图书][B] Metric algebraic geometry
P Breiding, K Kohn, B Sturmfels - 2024 - library.oapen.org
Metric algebraic geometry combines concepts from algebraic geometry and differential
geometry. Building on classical foundations, it offers practical tools for the 21st century …
geometry. Building on classical foundations, it offers practical tools for the 21st century …
Maximum likelihood estimation for matrix normal models via quiver representations
We study the log-likelihood function and maximum likelihood estimate (MLE) for the matrix
normal model for both real and complex models. We describe the exact number of samples …
normal model for both real and complex models. We describe the exact number of samples …
The minimal canonical form of a tensor network
Tensor networks have a gauge degree of freedom on the virtual degrees of freedom that are
contracted. A canonical form is a choice of fixing this degree of freedom. For matrix product …
contracted. A canonical form is a choice of fixing this degree of freedom. For matrix product …
Negative curvature obstructs acceleration for strongly geodesically convex optimization, even with exact first-order oracles
C Criscitiello, N Boumal - Conference on Learning Theory, 2022 - proceedings.mlr.press
Hamilton and Moitra (2021) showed that, in certain regimes, it is not possible to accelerate
Riemannian gradient descent in the hyperbolic plane if we restrict ourselves to algorithms …
Riemannian gradient descent in the hyperbolic plane if we restrict ourselves to algorithms …
Maximum likelihood estimation for tensor normal models via castling transforms
In this paper, we study sample size thresholds for maximum likelihood estimation for tensor
normal models. Given the model parameters and the number of samples, we determine …
normal models. Given the model parameters and the number of samples, we determine …
No-go theorem for acceleration in the hyperbolic plane
L Hamilton, A Moitra - arXiv preprint arXiv:2101.05657, 2021 - arxiv.org
In recent years there has been significant effort to adapt the key tools and ideas in convex
optimization to the Riemannian setting. One key challenge has remained: Is there a …
optimization to the Riemannian setting. One key challenge has remained: Is there a …
Interior-point methods on manifolds: theory and applications
H Hirai, H Nieuwboer, M Walter - 2023 IEEE 64th Annual …, 2023 - ieeexplore.ieee.org
Interior-point methods offer a highly versatile framework for convex optimization that is
effective in theory and practice. A key notion in their theory is that of a self-concordant …
effective in theory and practice. A key notion in their theory is that of a self-concordant …
Negative curvature obstructs acceleration for strongly geodesically convex optimization, even with exact first-order oracles
C Criscitiello, N Boumal - arXiv preprint arXiv:2111.13263, 2021 - arxiv.org
Hamilton and Moitra (2021) showed that, in certain regimes, it is not possible to accelerate
Riemannian gradient descent in the hyperbolic plane if we restrict ourselves to algorithms …
Riemannian gradient descent in the hyperbolic plane if we restrict ourselves to algorithms …
Near optimal sample complexity for matrix and tensor normal models via geodesic convexity
C Franks, R Oliveira, A Ramachandran… - arXiv preprint arXiv …, 2021 - arxiv.org
The matrix normal model, the family of Gaussian matrix-variate distributions whose
covariance matrix is the Kronecker product of two lower dimensional factors, is frequently …
covariance matrix is the Kronecker product of two lower dimensional factors, is frequently …