Related papers: Entropic vector quantile regression: Duality and G…
Uniform random rotations (URRs) are a common preprocessing step in modern quantization approaches used for gradient compression, inference acceleration, KV-cache compression, model weight quantization, and approximate nearest-neighbor…
We propose a new framework for generative modeling based on a discrete-time stochastic control formulation of measure transport. Adapting classic results from control theory, we formulate our problem as a linear program whose dual variables…
Quantile Regression (QR) can be used to estimate aleatoric uncertainty in deep neural networks and can generate prediction intervals. Quantifying uncertainty is particularly important in critical applications such as clinical diagnosis,…
The Gromov-Wasserstein (GW) distance, rooted in optimal transport (OT) theory, quantifies dissimilarity between metric measure spaces and provides a framework for aligning heterogeneous datasets. While computational aspects of the GW…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
Vector-quantized networks (VQNs) have exhibited remarkable performance across various tasks, yet they are prone to training instability, which complicates the training process due to the necessity for techniques such as subtle…
Quadratic regularization has emerged as a potential alternative to the popular entropic regularization in computational optimal transport, offering the theoretical advantage of producing sparse couplings through its hinge density structure.…
The VQE algorithm has turned out to be quite expensive to run given the way we currently access quantum processors (i.e. over the cloud). In order to alleviate this issue, we introduce Quantum Sampling Regression (QSR), an alternative…
The quadratically regularized optimal transport problem is empirically known to have sparse solutions: its optimal coupling $\pi_{\varepsilon}$ has sparse support for small regularization parameter $\varepsilon$, in contrast to entropic…
For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal transport plan weakly converges to a centered Gaussian…
We study unsupervised generative modeling in terms of the optimal transport (OT) problem between true (but unknown) data distribution $P_X$ and the latent variable model distribution $P_G$. We show that the OT problem can be equivalently…
Given an intractable distribution $p$, the problem of variational inference (VI) is to find the best approximation from some more tractable family $Q$. Commonly, one chooses $Q$ to be a family of factorized distributions (i.e., the…
Vehicle routing problem (VRP) is an NP-hard optimization problem that has been an interest of research for decades in science and industry. The objective is to plan routes of vehicles to deliver a fixed number of customers with optimal…
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…
Quantum variational optimization has been posed as an alternative to solve optimization problems faster and at a larger scale than what classical methods allow. In this paper we study systematically the role of entanglement, the structure…
This survey has been written in occasion of the School and Workshop about Optimal Transport on Quantum Structures at Erd\"os Center in September 2022. We discuss some recent results on noncommutative entropic optimal transport problems and…
We develop a new approach to vector quantization, which guarantees an intrinsic stationarity property that also holds, in contrast to regular quantization, for non-optimal quantization grids. This goal is achieved by replacing the usual…
Optimal decentralized controller design is notoriously difficult, but recent research has identified large subclasses of such problems that may be convexified and thus are amenable to solution via efficient numerical methods. One recently…
We introduce a concept of optimal transport for vector-valued measures and its dual formulation. In this note we concentrate on the semi-discrete case and show some fundamental differences between the scalar and vector cases. A…
This paper investigates Support Vector Regression (SVR) within the framework of the Risk Quadrangle (RQ) theory. Every RQ includes four stochastic functionals -- error, regret, risk, and \emph{deviation}, bound together by a so-called…