[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 …

The minimal canonical form of a tensor network

A Acuaviva, V Makam, H Nieuwboer… - 2023 IEEE 64th …, 2023 - ieeexplore.ieee.org
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 …

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 …

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 …

Maximum likelihood estimation for tensor normal models via castling transforms

H Derksen, V Makam, M Walter - Forum of Mathematics, Sigma, 2022 - cambridge.org
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 …

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 …

Complexity of Robust Orbit Problems for Torus Actions and the abc-conjecture

P Bürgisser, ML Doğan, V Makam, M Walter… - arxiv preprint arxiv …, 2024 - arxiv.org
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 …

A Bridge between Invariant Theory and Maximum Likelihood Estimation

C Améndola, K Kohn, P Reichenbach, A Seigal - SIAM Review, 2024 - SIAM
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 …

Open Problem: Polynomial linearly-convergent method for g-convex optimization?

C Criscitiello, D Martínez-Rubio… - The Thirty Sixth …, 2023 - proceedings.mlr.press
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 …

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 …