Related papers: Scalable Approximate Algorithms for Optimal Transp…
Optimal transport (OT) is a widely used technique for distribution alignment, with applications throughout the machine learning, graphics, and vision communities. Without any additional structural assumptions on trans-port, however, OT can…
Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…
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…
Ordinary least squares (OLS) is the default method for fitting linear models, but is not applicable for problems with dimensionality larger than the sample size. For these problems, we advocate the use of a generalized version of OLS…
This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to…
We provide a computational complexity analysis for the Sinkhorn algorithm that solves the entropic regularized Unbalanced Optimal Transport (UOT) problem between two measures of possibly different masses with at most $n$ components. We show…
Computational optimal transport (OT) has recently emerged as a powerful framework with applications in various fields. In this paper we focus on a relaxation of the original OT problem, the entropic OT problem, which allows to implement…
Reduced order models (ROMs) are widely used in scientific computing to tackle high-dimensional systems. However, traditional ROM methods may only partially capture the intrinsic geometric characteristics of the data. These characteristics…
Despite the success of deep learning-based algorithms, it is widely known that neural networks may fail to be robust. A popular paradigm to enforce robustness is adversarial training (AT), however, this introduces many computational and…
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…
Optimal Transport (OT) distances such as Wasserstein have been used in several areas such as GANs and domain adaptation. OT, however, is very sensitive to outliers (samples with large noise) in the data since in its objective function,…
Learning from point sets is an essential component in many computer vision and machine learning applications. Native, unordered, and permutation invariant set structure space is challenging to model, particularly for point set…
Partial identification often arises when the joint distribution of the data is known only up to its marginals. We consider the corresponding partially identified GMM model and develop a methodology for identification, estimation, and…
We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…
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…
Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the…
Persistence diagrams (PDs) are now routinely used to summarize the underlying topology of complex data. Despite several appealing properties, incorporating PDs in learning pipelines can be challenging because their natural geometry is not…
This paper describes a novel paradigm that formalizes automatic piano transcription (APT) as an optimal transport (OT) problem, not as a frame-level multi-label binary classification problem. Our method learns to minimize the cost of…
The matching principles behind optimal transport (OT) play an increasingly important role in machine learning, a trend which can be observed when OT is used to disambiguate datasets in applications (e.g. single-cell genomics) or used to…
Optimal Transport (OT) has recently emerged as a central tool in data sciences to compare in a geometrically faithful way point clouds and more generally probability distributions. The wide adoption of OT into existing data analysis and…