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[KNIHA][B] An introduction to optimization on smooth manifolds
N Boumal - 2023 - books.google.com
Optimization on Riemannian manifolds-the result of smooth geometry and optimization
merging into one elegant modern framework-spans many areas of science and engineering …
merging into one elegant modern framework-spans many areas of science and engineering …
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
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 …
Negative curvature obstructs acceleration for strongly geodesically convex optimization, even with exact first-order oracles
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 …
Interior-point methods on manifolds: theory and applications
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 …
Complexity of Robust Orbit Problems for Torus Actions and the abc-conjecture
When a group acts on a set, it naturally partitions it into orbits, giving rise to orbit problems.
These are natural algorithmic problems, as symmetries are central in numerous questions …
These are natural algorithmic problems, as symmetries are central in numerous questions …
A Bridge between Invariant Theory and Maximum Likelihood Estimation
We uncover connections between maximum likelihood estimation in statistics and norm
minimization over a group orbit in invariant theory. We present a dictionary that relates …
minimization over a group orbit in invariant theory. We present a dictionary that relates …
Open Problem: Polynomial linearly-convergent method for g-convex optimization?
Abstract Let $ f\colon\mathcal {M}\to\mathbb {R} $ be a Lipschitz and geodesically convex
function defined on a $ d $-dimensional Riemannian manifold $\mathcal {M} $. Does there …
function defined on a $ d $-dimensional Riemannian manifold $\mathcal {M} $. Does there …
iPCA and stability of star quivers
C Franks, V Makam - arxiv preprint arxiv:2302.09658, 2023 - arxiv.org
Integrated principal components analysis, or iPCA, is an unsupervised learning technique
for grouped vector data recently defined by Tang and Allen. Like PCA, iPCA computes new …
for grouped vector data recently defined by Tang and Allen. Like PCA, iPCA computes new …