72 citations · 127 across the 16 of their papers we have counts for
17 papers
Gauss-Newton drifting extends natural gradient descent
Théo Dumont, Théo Lacombe, François-Xavier Vialard
Drifting methods have recently been introduced as a promising new paradigm for training generative models, and have attracted a lot of attention so far. In this work, we focus on h…
Learning Monge maps with constrained drifting models
Théo Dumont, Théo Lacombe, François-Xavier Vialard
We study the estimation of optimal transport (OT) maps between an arbitrary source probability measure and a log-concave target probability measure. Our contributions are twofold.…
Persistence-based topological optimization: a survey
Mathieu Carriere, Yuichi Ike, Théo Lacombe +1
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can…
The Wasserstein gradient flow of the Sinkhorn divergence between Gaussian distributions
Mathis Hardion, Théo Lacombe
We study the Wasserstein gradient flow of the Sinkhorn divergence when both the source and the target are Gaussian distributions. We prove the existence of a flow that stays in the…
Revisiting the Sliced Wasserstein Kernel for persistence diagrams: a Figalli-Gigli approach
Marc Janthial, Théo Lacombe
The Sliced Wasserstein Kernel (SWK) for persistence diagrams was introduced in (Carri{è}re et al. 2017) as a powerful tool to implicitly embed persistence diagrams in a Hilbert spa…
Diffeomorphic interpolation for efficient persistence-based topological optimization
Mathieu Carriere, Marc Theveneau, Théo Lacombe
Topological Data Analysis (TDA) provides a pipeline to extract quantitative topological descriptors from structured objects. This enables the definition of topological loss functio…
Topological Node2vec: Enhanced Graph Embedding via Persistent Homology
Yasuaki Hiraoka, Yusuke Imoto, Killian Meehan +2
Node2vec is a graph embedding method that learns a vector representation for each node of a weighted graph while seeking to preserve relative proximity and global structure. Numeri…
MAGDiff: Covariate Data Set Shift Detection via Activation Graphs of Deep Neural Networks
Charles Arnal, Felix Hensel, Mathieu Carrière +4
Despite their successful application to a variety of tasks, neural networks remain limited, like other machine learning methods, by their sensitivity to shifts in the data: their p…
On the existence of Monge maps for the Gromov-Wasserstein problem
Théo Dumont, Théo Lacombe, François-Xavier Vialard
The Gromov--Wasserstein problem is a non-convex optimization problem over the polytope of transportation plans between two probability measures supported on two spaces, each equipp…
RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds
Thibault de Surrel, Felix Hensel, Mathieu Carrière +5
The use of topological descriptors in modern machine learning applications, such as Persistence Diagrams (PDs) arising from Topological Data Analysis (TDA), has shown great potenti…
An Homogeneous Unbalanced Regularized Optimal Transport model with applications to Optimal Transport with Boundary
Théo Lacombe
This work studies how the introduction of the entropic regularization term in unbalanced Optimal Transport (OT) models may alter their homogeneity with respect to the input measure…
A Gradient Sampling Algorithm for Stratified Maps with Applications to Topological Data Analysis
Jacob Leygonie, Mathieu Carrière, Théo Lacombe +1
We introduce a novel gradient descent algorithm extending the well-known Gradient Sampling methodology to the class of stratifiably smooth objective functions, which are defined as…
Estimation and Quantization of Expected Persistence Diagrams
Vincent Divol, Théo Lacombe
Persistence diagrams (PDs) are the most common descriptors used to encode the topology of structured data appearing in challenging learning tasks; think e.g. of graphs, time series…
Topological Uncertainty: Monitoring trained neural networks through persistence of activation graphs
Théo Lacombe, Yuichi Ike, Mathieu Carriere +3
Although neural networks are capable of reaching astonishing performances on a wide variety of contexts, properly training networks on complicated tasks requires expertise and can…
PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures
Mathieu Carrière, Frédéric Chazal, Yuichi Ike +3
Persistence diagrams, the most common descriptors of Topological Data Analysis, encode topological properties of data and have already proved pivotal in many different applications…
Understanding the Topology and the Geometry of the Space of Persistence Diagrams via Optimal Partial Transport
Vincent Divol, Théo Lacombe
Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence dia…
Large Scale computation of Means and Clusters for Persistence Diagrams using Optimal Transport
Théo Lacombe, Marco Cuturi, Steve Oudot
Persistence diagrams (PDs) are now routinely used to summarize the underlying topology of complex data. Despite several appealing properties, incorporating PDs in learning pipeline…