Papers

Distributional Sliced Embedding Discrepancy for Incomparable Distributions

M. Z. Alaya, M. Bérar, G. Gasso, A. Rakotomamonjy

arXiv, 2021

Gromov-Wasserstein (GW) distance is a key tool for manifold learning and cross- domain learning, allowing the comparison of distributions that do not live in the same metric space. Because of its high computational complexity, several approximate GW distances have been proposed based on entropy regularization or on slicing, and one-dimensional GW computation. Read more

POT: Python Optimal Transport

R. Flamary, N. Courty, A. Gramfort, M. Z. Alaya, A. Boisbunon, S. Chambon, L. Chapel, A. Corenflos, K. Fatras, N. Fournier, L. Gautheron, N.T.H. Gayraud, H. Janati, A. Rakotomamonjy, I. Redko, A. Rolet, A. Schutz, V. Seguy, D. J. Sutherland, R. Tavenard, A. Tong, T. Vayer

Journal of Machine Learning Research, 2021

Optimal transport has recently been reintroduced to the machine learning community thanks in part to novel efficient optimization procedures allowing for medium to large scale applications. We propose a Python toolbox that implements several key optimal transport ideas for the machine learning community. Read more

Optimal Transport for Conditional Domain Matching and Label Shift

A. Rakotomamonjy, R. Flamary, G. Gasso, M. Z. Alaya, M. Berar, N. Courty

arXiv, 2021

We address the problem of unsupervised domain adaptation under the setting of generalized target shift (joint class-conditional and label shifts). For this framework, we theoretically show that, for good generalization, it is necessary to learn a latent representation in which both marginals and class-conditional distributions are aligned across domains. Read more

Binacox: Automatic Cut-Points Detection in High-Dimensional Cox Model, with Applications to Genetic Data

S. Bussy, M. Z. Alaya, A. Guilloux, A.-S. Jannot

in revision to Biometrics, 2021

We introduce the binacox, a prognostic method to deal with the problem of detecting multiple cut-points per features in a multivariate setting where a large number of continuous features are available. The method is based on the Cox model and combines one-hot encoding with the binarsity penalty, which uses total-variation regularization together with an extra linear constraint, and enables feature selection. Read more

Theoretical Guarantees for Bridging Metric Measure Embedding and Optimal Transport

M. Z. Alaya, M. Bérar, G. Gasso, A. Rakotomamonjy

in revision to Neurocomputing, 2021, 2020

We propose a novel approach for comparing distributions whose supports do not necessarily lie on the same metric space. Unlike Gromov-Wasserstein (GW) distance which compares pairwise distances of elements from each distribution, we consider a method allowing to embed the metric measure spaces in a common Euclidean space and compute an optimal transport (OT) on the embedded distributions. This leads to what we call a sub-embedding robust Wasserstein (SERW). Read more

Partial Gromov-Wasserstein with Applications on Positive-Unlabeled Learning

L. Chapel, M. Z. Alaya, G. Gasso

Proceedings Conference NeurIPS, 2020

Classical optimal transport problem seeks a transportation map that preserves the total mass between two probability distributions, requiring their masses to be equal. This may be too restrictive in some applications such as color or shape matching, since the distributions may have arbitrary masses and/or only a fraction of the total mass has to be transported. Read more

Open Set Domain Adaptation using Optimal Transport

M. Kechaou, R. Hérault, M. Z. Alaya, G. Gasso

Proceedings Conference ECML-PKDD, 2020

We present a 2-step optimal transport approach that per-forms a mapping from a source distribution to a target distribution. Here, the target has the particularity to present new classes not present in the source domain. The first step of the approach aims at rejecting the samples issued from these new classes using an optimal transport plan. The second step solves the target (class ratio) shift still as an optimal transport problem. Read more

Screening Sinkhorn Algorithm for Regularized Optimal Transport

M. Z. Alaya, M. Bérar, G. Gasso, A. Rakotomamonjy

Proceedings Conference NeurIPS, 2019

We introduce in this paper a novel strategy for efficiently approximating the Sinkhorn distance between two discrete measures. After identifying neglectable components of the dual solution of the regularized Sinkhorn problem, we propose to screen those components by directly setting them at that value before entering the Sinkhorn problem. This allows us to solve a smaller Sinkhorn problem while ensuring approximation with provable guarantees. Read more

Collective Matrix Completion

M. Z. Alaya, O. Klopp

Journal of Machine Learning Research, 2019

Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system. However, in practical situations, data is often obtained from multiple sources which results in a collection of matrices rather than a single one. In this work, we consider the problem of collective matrix completion with multiple and heterogeneous matrices, which can be count, binary, continuous, etc. Read more

Binarsity: a Penalization for One-Hot Encoded Features in Linear Supervised Learning

M. Z. Alaya, S. Bussy, S. Gaïffas, A. Guilloux

Journal of Machine Learning Research, 2019

This paper deals with the problem of large-scale linear supervised learning in settings where a large number of continuous features are available. We propose to combine the well-known trick of one-hot encoding of continuous features with a new penalization called binarsity. In each group of binary features coming from the one-hot encoding of a single raw continuous feature, this penalization uses totalvariation regularization together with an extra linear constraint. Read more

High-Dimensional Time-Varying Aalen and Cox Models

M. Z. Alaya, T. Allart, A. Guilloux, S. Lemler

Preprint, 2017, 2017

We consider the problem of estimating the intensity of a counting process in high-dimensional time-varying Aalen and Cox models. We introduce a covariate-specific weighted total-variation penalization, using data-driven weights that correctly scale the penalization along the observation interval. Read more

Learning the Intensity of Time Events with Change-Points

M. Z. Alaya, S. Gaïffas, A. Guilloux

IEEE Transactions on Information Theory, 2015

We consider the problem of learning the inhomogeneous intensity of a counting process, under a sparse segmentation assumption. We introduce a weighted total-variation penalization, using data-driven weights that correctly scale the penalization along the observation interval. We prove that this leads to a sharp tuning of the convex relaxation of the segmentation prior, by stating oracle inequalities with fast rates of convergence, and consistency for change-points detection. Read more