Related papers: Compressed online Sinkhorn
The recent emergence of new algorithms for permuting models into functionally equivalent regions of the solution space has shed some light on the complexity of error surfaces, and some promising properties like mode connectivity. However,…
This letter investigates dynamical optimal transport of underactuated linear systems over an infinite time horizon. In our previous work, we proposed to integrate model predictive control and the celebrated Sinkhorn algorithm to perform…
We develop a new reduction that converts any online convex optimization algorithm suffering $O(\sqrt{T})$ regret into an $\epsilon$-differentially private stochastic convex optimization algorithm with the optimal convergence rate $\tilde…
This contribution features an accelerated computation of the Sinkhorn's algorithm, which approximates the Wasserstein transportation distance, by employing nonequispaced fast Fourier transforms (NFFT). The algorithm proposed allows…
Optimal transport (OT) finds a least cost transport plan between two probability distributions using a cost matrix defined on pairs of points. Unlike standard OT, which infers unstructured pointwise mappings, low-rank optimal transport…
Optimal transport (OT) plays an essential role in various areas like machine learning and deep learning. However, computing discrete optimal transport plan for large scale problems with adequate accuracy and efficiency is still highly…
Optimal Transport (OT) theory has seen an increasing amount of attention from the computer science community due to its potency and relevance in modeling and machine learning. It introduces means that serve as powerful ways to compare…
The Sinkhorn--Knopp (SK) algorithm is a cornerstone method for matrix scaling and entropically regularized optimal transport (EOT). Despite its empirical efficiency, existing theoretical guarantees to achieve a target marginal accuracy…
In this note, we generalize the classical optimal partial transport (OPT) problem by modifying the mass destruction/creation term to function-based terms, introducing what we term ``generalized optimal partial transport'' problems. We then…
Optimal transport (OT) has become exceedingly popular in machine learning, data science, and computer vision. The core assumption in the OT problem is the equal total amount of mass in source and target measures, which limits its…
This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely-used iterative Bregman projections algorithm (or Sinkhorn--Knopp…
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…
Numerically solving multi-marginal optimal transport (MMOT) problems is computationally prohibitive, even for moderate-scale instances involving $l\ge4$ marginals with support sizes of $N\ge1000$. The cost in MMOT is represented as a tensor…
Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To…
This paper considers online convex optimization (OCO) with stochastic constraints, which generalizes Zinkevich's OCO over a known simple fixed set by introducing multiple stochastic functional constraints that are i.i.d. generated at each…
The Orthogonal Matching Pursuit (OMP) for compressed sensing iterates over a scheme of support augmentation and signal estimation. We present two novel matching pursuit algorithms with intrinsic regularization of the signal estimation step…
Sequential Compressive Sensing, which may be widely used in sensing devices, is a popular topic of recent research. This paper proposes an online recovery algorithm for sparse approximation of sequential compressive sensing. Several…
This paper considers online convex optimization over a complicated constraint set, which typically consists of multiple functional constraints and a set constraint. The conventional online projection algorithm (Zinkevich, 2003) can be…
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…
Motion planning is still an open problem for many disciplines, e.g., robotics, autonomous driving, due to their need for high computational resources that hinder real-time, efficient decision-making. A class of methods striving to provide…