Partial Gromov-Wasserstein with Applications on Positive-Unlabeled Learning

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

NeurIPS, 2020

Optimal Transport (OT) framework allows defining similarity between probability distributions and provides metrics such as the Wasserstein and Gromov-Wasserstein discrepancies. Classical OT problem seeks a transportation map that preserves the total mass, requiring the mass of the source and target distributions to be the same. This may be too restrictive in certain applications such as color or shape matching, since the distributions may have arbitrary masses or that only a fraction of the total mass has to be transported. Several algorithms have been devised for computing unbalanced Wasserstein metrics but when it comes with the Gromov-Wasserstein problem, no partial formulation is available yet. 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, 2020

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

Non-Aligned Distribution Distance using Metric Measure Embedding and Optimal Transport

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

arXiv, 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 that compares pairwise distance of elements from each distribution, we consider a method that embeds the metric measure spaces in a common Euclidean space and computes an optimal transport (OT) on the embedded distributions. This leads to what we call a sub-embedding robust Wasserstein (SERW). Under some conditions, SERW is a distance that considers an OT distance of the (low-distorted) embedded distributions using a common metric. Read more

Screening Sinkhorn Algorithm for Regularized Optimal Transport

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

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

in revision to Journal of Nonparametric Statitics, 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