136 citations · 207 across the 24 of their papers we have counts for
26 papers
Notes on generative modeling: flow matching, diffusion, optimal transport and Schr{ö}dinger bridge
Titouan Vayer
These notes recapitulate the high level mathematical principles behind different techniques for generative modeling. I show the connections between optimal transport and standard t…
On sparsity, extremal structure, and monotonicity properties of Wasserstein and Gromov-Wasserstein optimal transport plans
Titouan Vayer
This note gives a self-contained overview of some important properties of the Gromov-Wasserstein (GW) distance, compared with the standard linear optimal transport (OT) framework.…
Path-conditioned training: a principled way to rescale ReLU neural networks
Arthur Lebeurrier, Titouan Vayer, Rémi Gribonval
Despite recent algorithmic advances, we still lack principled ways to leverage the well-documented rescaling symmetries in ReLU neural network parameters. While two properly rescal…
Bridging Arbitrary and Tree Metrics via Differentiable Gromov Hyperbolicity
Pierre Houedry, Nicolas Courty, Florestan Martin-Baillon +2
Trees and the associated shortest-path tree metrics provide a powerful framework for representing hierarchical and combinatorial structures in data. Given an arbitrary metric space…
A note on the relations between mixture models, maximum-likelihood and entropic optimal transport
Titouan Vayer, Etienne Lasalle
This note aims to demonstrate that performing maximum-likelihood estimation for a mixture model is equivalent to minimizing over the parameters an optimal transport problem with en…
PASCO (PArallel Structured COarsening): an overlay to speed up graph clustering algorithms
Etienne Lasalle, Rémi Vaudaine, Titouan Vayer +4
Clustering the nodes of a graph is a cornerstone of graph analysis and has been extensively studied. However, some popular methods are not suitable for very large graphs: e.g., spe…
Schur's Positive-Definite Network: Deep Learning in the SPD cone with structure
Can Pouliquen, Mathurin Massias, Titouan Vayer
Estimating matrices in the symmetric positive-definite (SPD) cone is of interest for many applications ranging from computer vision to graph learning. While there exist various con…
Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein
Hugues Van Assel, Cédric Vincent-Cuaz, Nicolas Courty +3
Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. Traditionally, this involves using dimensionality reduction (DR)…
Compressive Recovery of Sparse Precision Matrices
Titouan Vayer, Etienne Lasalle, Rémi Gribonval +1
We consider the problem of learning a graph modeling the statistical relations of the variables from a dataset with samples . Standard approa…
Interpolating between Clustering and Dimensionality Reduction with Gromov-Wasserstein
Hugues Van Assel, Cédric Vincent-Cuaz, Titouan Vayer +2
We present a versatile adaptation of existing dimensionality reduction (DR) objectives, enabling the simultaneous reduction of both sample and feature sizes. Correspondances betwee…
Optimal Transport with Adaptive Regularisation
Hugues Van Assel, Titouan Vayer, Remi Flamary +1
Regularising the primal formulation of optimal transport (OT) with a strictly convex term leads to enhanced numerical complexity and a denser transport plan. Many formulations impo…
Implicit Differentiation for Hyperparameter Tuning the Weighted Graphical Lasso
Can Pouliquen, Paulo Gonçalves, Mathurin Massias +1
We provide a framework and algorithm for tuning the hyperparameters of the Graphical Lasso via a bilevel optimization problem solved with a first-order method. In particular, we de…
SNEkhorn: Dimension Reduction with Symmetric Entropic Affinities
Hugues Van Assel, Titouan Vayer, Rémi Flamary +1
Many approaches in machine learning rely on a weighted graph to encode the similarities between samples in a dataset. Entropic affinities (EAs), which are notably used in the popul…
Entropic Wasserstein Component Analysis
Antoine Collas, Titouan Vayer, Rémi Flamary +1
Dimension reduction (DR) methods provide systematic approaches for analyzing high-dimensional data. A key requirement for DR is to incorporate global dependencies among original an…
Learning Graphical Factor Models with Riemannian Optimization
Alexandre Hippert-Ferrer, Florent Bouchard, Ammar Mian +2
Graphical models and factor analysis are well-established tools in multivariate statistics. While these models can be both linked to structures exhibited by covariance and precisio…
Template based Graph Neural Network with Optimal Transport Distances
Cédric Vincent-Cuaz, Rémi Flamary, Marco Corneli +2
Current Graph Neural Networks (GNN) architectures generally rely on two important components: node features embedding through message passing, and aggregation with a specialized fo…
Controlling Wasserstein Distances by Kernel Norms with Application to Compressive Statistical Learning
Titouan Vayer, Rémi Gribonval
Comparing probability distributions is at the crux of many machine learning algorithms. Maximum Mean Discrepancies (MMD) and Wasserstein distances are two classes of distances betw…
Semi-relaxed Gromov-Wasserstein divergence with applications on graphs
Cédric Vincent-Cuaz, Rémi Flamary, Marco Corneli +2
Comparing structured objects such as graphs is a fundamental operation involved in many learning tasks. To this end, the Gromov-Wasserstein (GW) distance, based on Optimal Transpor…
Fast Multiscale Diffusion on Graphs
Sibylle Marcotte, Amélie Barbe, Rémi Gribonval +4
Diffusing a graph signal at multiple scales requires computing the action of the exponential of several multiples of the Laplacian matrix. We tighten a bound on the approximation e…
Online Graph Dictionary Learning
Cédric Vincent-Cuaz, Titouan Vayer, Rémi Flamary +2
Dictionary learning is a key tool for representation learning, that explains the data as linear combination of few basic elements. Yet, this analysis is not amenable in the context…
A contribution to Optimal Transport on incomparable spaces
Titouan Vayer
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of po…
Time Series Alignment with Global Invariances
Titouan Vayer, Romain Tavenard, Laetitia Chapel +3
Multivariate time series are ubiquitous objects in signal processing. Measuring a distance or similarity between two such objects is of prime interest in a variety of applications,…
CO-Optimal Transport
Ievgen Redko, Titouan Vayer, Rémi Flamary +1
Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation…
Sliced Gromov-Wasserstein
Titouan Vayer, Rémi Flamary, Romain Tavenard +2
Recently used in various machine learning contexts, the Gromov-Wasserstein distance (GW) allows for comparing distributions whose supports do not necessarily lie in the same metric…