Related papers: Supervised Training of Conditional Monge Maps
Recent advances in large-scale optimal transport have greatly extended its application scenarios in machine learning. However, existing methods either not explicitly learn the transport map or do not support general cost function. In this…
Transport systems on networks are crucial in various applications, but face a significant risk of being adversely affected by unforeseen circumstances such as disasters. The application of entropy-regularized optimal transport (OT) on graph…
The time-fractional optimal transport (OT) and mean-field planning (MFP) models are developed to describe the anomalous transport of the agents in a heterogeneous environment such that their densities are transported from the initial…
Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework…
Universal Domain Adaptation (UniDA) aims to transfer knowledge from a source domain to a target domain without any constraints on label sets. Since both domains may hold private classes, identifying target common samples for domain…
Mini-batch optimal transport (m-OT) has been widely used recently to deal with the memory issue of OT in large-scale applications. Despite their practicality, m-OT suffers from misspecified mappings, namely, mappings that are optimal on the…
In many safety-critical settings, probabilistic ML systems have to make predictions subject to algebraic constraints, e.g., predicting the most likely trajectory that does not cross obstacles. These real-world constraints are rarely convex,…
Optimal Mass Transport (OMT) is a well studied problem with a variety of applications in a diverse set of fields ranging from Physics to Computer Vision and in particular Statistics and Data Science. Since the original formulation of Monge…
Causal estimands can vary significantly depending on the relationship between outcomes in treatment and control groups, potentially leading to wide partial identification (PI) intervals that impede decision making. Incorporating covariates…
In this note, we derive upper-bounds on the statistical estimation rates of unbalanced optimal transport (UOT) maps for the quadratic cost. Our work relies on the stability of the semi-dual formulation of optimal transport (OT) extended to…
In this paper, we tackle the transductive semi-supervised learning problem that aims to obtain label predictions for the given unlabeled data points according to Vapnik's principle. Our proposed approach is based on optimal transport, a…
In this paper, we propose a novel approach for agent motion prediction in cluttered environments. One of the main challenges in predicting agent motion is accounting for location and context-specific information. Our main contribution is…
In the dynamic and uncertain environments where reinforcement learning (RL) operates, risk management becomes a crucial factor in ensuring reliable decision-making. Traditional RL approaches, while effective in reward optimization, often…
In this article we revisit the weak optimal transport (WOT) problem, introduced by Gozlan, Roberto, Samson and Tetali (2017). We work on the real line, with barycentric cost functions, and as our first result give the following…
The predict-then-optimize framework arises in a wide variety of applications where the unknown cost coefficients of an optimization problem are first predicted based on contextual features and then used to solve the problem. In this work,…
Optimal transport (OT) serves as a natural framework for comparing probability measures, with applications in statistics, machine learning, and applied mathematics. Alas, statistical estimation and exact computation of the OT distances…
We consider the Monge problem of optimal transport between a compactly supported source measure and a target probability measure with unbounded support. We consider the convergence of optimal maps and potential functions when the target…
Multi-source Domain Adaptation (MDA) seeks to adapt models trained on data from multiple labeled source domains to perform effectively on an unlabeled target domain data, assuming access to sources data. To address the challenges of model…
In this paper, we consider Strassen's version of optimal transport (OT) problem, which concerns minimizing the excess-cost probability (i.e., the probability that the cost is larger than a given value) over all couplings of two given…
With the widespread application of optimal transport (OT), its calculation becomes essential, and various algorithms have emerged. However, the existing methods either have low efficiency or cannot represent discontinuous maps. A novel…