Related papers: Coreset selection for the Sinkhorn divergence and …

By means of two simple convexity arguments we are able to develop a general method for proving consistency and asymptotic normality of estimators that are defined by minimisation of convex criterion functions. This method is then applied to…

Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the…

We consider the numerical solution of the discrete multi-marginal optimal transport (MOT) by means of the Sinkhorn algorithm. In general, the Sinkhorn algorithm suffers from the curse of dimensionality with respect to the number of…

We propose a fast and scalable algorithm to project a given density on a set of structured measures defined over a compact 2D domain. The measures can be discrete or supported on curves for instance. The proposed principle and algorithm are…

In this article, we discuss the optimal allocation problem in an experiment when a regression model is used for statistical analysis. Monotonic convergence for a general class of multiplicative algorithms for $D$-optimality has been…

In this work, we propose a novel end-to-end sinkhorn autoencoder with noise generator for efficient data collection simulation. Simulating processes that aim at collecting experimental data is crucial for multiple real-life applications,…

We establish a Karhunen-Lo`eve expansion for generic centered, second order stochastic processes, which does not rely on topological assumptions. We further investigate in which norms the expansion converges and derive exact average rates…

This work introduces novel computational methods for entropic optimal transport (OT) problems under martingale-type conditions. The considered problems include the discrete martingale optimal transport (MOT) problem. Moreover, as the…

Imitation learning algorithms have been interpreted as variants of divergence minimization problems. The ability to compare occupancy measures between experts and learners is crucial in their effectiveness in learning from demonstrations.…

Coordinate descent methods employ random partial updates of decision variables in order to solve huge-scale convex optimization problems. In this work, we introduce new adaptive rules for the random selection of their updates. By adaptive,…

\emph{Optimal Transport} (OT) has emerged as an important computational tool in machine learning and computer vision, providing a geometrical framework for studying probability measures. OT unfortunately suffers from the curse of…

We design coresets for Ordered k-Median, a generalization of classical clustering problems such as k-Median and k-Center, that offers a more flexible data analysis, like easily combining multiple objectives (e.g., to increase fairness or…

Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…

Diffusion maps is a manifold learning algorithm widely used for dimensionality reduction. Using a sample from a distribution, it approximates the eigenvalues and eigenfunctions of associated Laplace-Beltrami operators. Theoretical bounds on…

In sparse coding, we attempt to extract features of input vectors, assuming that the data is inherently structured as a sparse superposition of basic building blocks. Similarly, neural networks perform a given task by learning features of…

We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…

The squared Wasserstein distance is a natural quantity to compare probability distributions in a non-parametric setting. This quantity is usually estimated with the plug-in estimator, defined via a discrete optimal transport problem which…

Linear thresholding models postulate that the conditional distribution of a response variable in terms of covariates differs on the two sides of a (typically unknown) hyperplane in the covariate space. A key goal in such models is to learn…

The choice of loss function in classification involves a fundamental trade-off: smooth losses (like Cross-Entropy) enable fast optimization rates but yield slow square-root consistency bounds, while piecewise-linear losses (like Hinge)…

Coreset selection compresses large datasets into compact, representative subsets, reducing the energy and computational burden of training deep neural networks. Existing methods are either: (i) DNN-based, which are tied to model-specific…