Related papers: Wasserstein regularization for sparse multi-task r…

We propose a family of relaxations of the optimal transport problem which regularize the problem by introducing an additional minimization step over a small region around one of the underlying transporting measures. The type of…

We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this…

Entropic optimal transport (OT) and the Sinkhorn algorithm have made it practical for machine learning practitioners to perform the fundamental task of calculating transport distance between statistical distributions. In this work, we focus…

We study distribution-on-distribution regression problems in which a response distribution depends on multiple distributional predictors. Such settings arise naturally in applications where the outcome distribution is driven by several…

Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…

In recent years, the machine learning community has increasingly embraced the optimal transport (OT) framework for modeling distributional relationships. In this work, we introduce a sample-based neural solver for computing the Wasserstein…

Selecting input features of top relevance has become a popular method for building self-explaining models. In this work, we extend this selective rationalization approach to text matching, where the goal is to jointly select and align text…

In this paper, we propose a coupled tensor norm regularization that could enable the model output feature and the data input to lie in a low-dimensional manifold, which helps us to reduce overfitting. We show this regularization term is…

We develop a novel theoretical framework for understating OT schemes respecting a class structure. For this purpose, we propose a convex OT program with a sum-of-norms regularization term, which provably recovers the underlying class…

Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…

We propose a sparse regularization model for inversion of incomplete Fourier transforms and apply it to seismic wavefield modeling. The objective function of the proposed model employs the Moreau envelope of the $\ell_0$ norm under a tight…

Owing to their statistical properties, non-convex sparse regularizers have attracted much interest for estimating a sparse linear model from high dimensional data. Given that the solution is sparse, for accelerating convergence, a working…

A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often…

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 impose a global constraint on the transport plan, for instance…

We develop a highly scalable optimization method called "hierarchical group-thresholding" for solving a multi-task regression model with complex structured sparsity constraints on both input and output spaces. Despite the recent emergence…

We propose to align distributional data from the perspective of Wasserstein means. We raise the problem of regularizing Wasserstein means and propose several terms tailored to tackle different problems. Our formulation is based on the…

This paper considers the multi-task learning problem and in the setting where some relevant features could be shared across few related tasks. Most of the existing methods assume the extent to which the given tasks are related or share a…

This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…

This paper presents a novel loss function referred to as hybrid ordinary-Welsch (HOW) and a new sparsity-inducing regularizer associated with HOW. We theoretically show that the regularizer is quasiconvex and that the corresponding Moreau…

We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures,…