Related papers: Globally solving the Gromov-Wasserstein problem fo…
Computational difficulty of quadratic matching and the Gromov-Wasserstein distance has led to various approximation and relaxation schemes. One of such methods, relying on the notion of distance profiles, has been widely used in practice,…
Supervised graph prediction addresses regression problems where the outputs are structured graphs. Although several approaches exist for graph-valued prediction, principled uncertainty quantification remains limited. We propose a conformal…
We analyze an algorithm to numerically solve the mean-field optimal control problems by approximating the optimal feedback controls using neural networks with problem specific architectures. We approximate the model by an $N$-particle…
We propose a novel fused Gromov-Wasserstein alignment method to jointly learn the Hawkes processes in different event spaces, and align their event types. Given two Hawkes processes, we use fused Gromov-Wasserstein discrepancy to measure…
The Grassmannian of affine subspaces is a natural generalization of both the Euclidean space, points being zero-dimensional affine subspaces, and the usual Grassmannian, linear subspaces being special cases of affine subspaces. We show…
In this study, we explore the challenge of efficiently representing scenes with a constrained number of Gaussians. Our analysis shifts from traditional graphics and 2D computer vision to the perspective of point clouds, highlighting the…
In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel. Recently, other distances…
The closest pair of points problem or closest pair problem (CPP) is an important problem in computational geometry where we have to find a pair of points from a set of points in metric space with the smallest distance between them. This…
UV-parameterized Gaussian Splatting (UVGS) maps an unstructured set of 3D Gaussians to a regular UV tensor, enabling compact storage and explicit control of representation capacity. Existing UVGS, however, uses a deterministic spherical…
We consider the general dimensionality reduction problem of locating in a high-dimensional data cloud, a $k$-dimensional non-Gaussian subspace of interesting features. We use a projection pursuit approach -- we search for mutually…
The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems,…
We establish the validity of asymptotic limits for the general transportation problem between random i.i.d. points and their common distribution, with respect to the squared Euclidean distance cost, in any dimension larger than three.…
The design of optical systems capable of processing and manipulating ultra-short pulses and ultra-focused beams is highly challenging with far reaching fundamental technological applications. One key obstacle routinely encountered while…
A geometrical pattern is a set of points with all pairwise distances (or, more generally, relative distances) specified. Finding matches to such patterns has applications to spatial data in seismic, astronomical, and transportation…
Most previous learning-based graph matching algorithms solve the \textit{quadratic assignment problem} (QAP) by dropping one or more of the matching constraints and adopting a relaxed assignment solver to obtain sub-optimal correspondences.…
The ability to represent and compare machine learning models is crucial in order to quantify subtle model changes, evaluate generative models, and gather insights on neural network architectures. Existing techniques for comparing data…
In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding…
Gaussian mixture models find their place as a powerful tool, mostly in the clustering problem, but with proper preparation also in feature extraction, pattern recognition, image segmentation and in general machine learning. When faced with…
Simultaneous Localization and Planning (SLAP) under process and measurement uncertainties is a challenge. It involves solving a stochastic control problem modeled as a Partially Observed Markov Decision Process (POMDP) in a general…
This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…