The z-gromov-wasserstein distance
The Gromov-Wasserstein (GW) distance is a powerful tool for comparing metric measure
spaces which has found broad applications in data science and machine learning. Driven by …
spaces which has found broad applications in data science and machine learning. Driven by …
On Probabilistic Embeddings in Optimal Dimension Reduction
R Murray, A Pickarski - arXiv preprint arXiv:2408.02433, 2024 - arxiv.org
Dimension reduction algorithms are a crucial part of many data science pipelines, including
data exploration, feature creation and selection, and denoising. Despite their wide …
data exploration, feature creation and selection, and denoising. Despite their wide …
Geometry and Stability of Supervised Learning Problems
We introduce a notion of distance between supervised learning problems, which we call the
Risk distance. This optimal-transport-inspired distance facilitates stability results; one can …
Risk distance. This optimal-transport-inspired distance facilitates stability results; one can …
Variational Graph Contrastive Learning
S Xie, JH Giraldo - arXiv preprint arXiv:2411.07150, 2024 - arxiv.org
Graph representation learning (GRL) is a fundamental task in machine learning, aiming to
encode high-dimensional graph-structured data into low-dimensional vectors. Self …
encode high-dimensional graph-structured data into low-dimensional vectors. Self …
Generalized Dimension Reduction Using Semi-Relaxed Gromov-Wasserstein Distance
RA Clark, T Needham, T Weighill - arXiv preprint arXiv:2405.15959, 2024 - arxiv.org
Dimension reduction techniques typically seek an embedding of a high-dimensional point
cloud into a low-dimensional Euclidean space which optimally preserves the geometry of …
cloud into a low-dimensional Euclidean space which optimally preserves the geometry of …
The NP-hardness of the Gromov-Wasserstein distance
N Kravtsova - arXiv preprint arXiv:2408.06525, 2024 - arxiv.org
This note addresses the property frequently mentioned in the literature that the Gromov-
Wasserstein (GW) distance is NP-hard. We provide the details on the non-convex nature of …
Wasserstein (GW) distance is NP-hard. We provide the details on the non-convex nature of …
[图书][B] Large Dimensional Data Analysis using Orthogonally Decomposable Tensors: Statistical Optimality and Computational Tractability
A Auddy - 2023 - search.proquest.com
Modern data analysis requires the study of tensors, or multi-way arrays. A p-th order tensor
𝓣 is an element of ℝ d×···× d, and has dp entries. We consider the case where the dimension …
𝓣 is an element of ℝ d×···× d, and has dp entries. We consider the case where the dimension …