Related papers: Supervised Training of Conditional Monge Maps
When deploying a trained machine learning model in the real world, it is inevitable to receive inputs from out-of-distribution (OOD) sources. For instance, in continual learning settings, it is common to encounter OOD samples due to the…
To deploy machine learning models in the real world, researchers have proposed many OOD detection algorithms to help models identify unknown samples during the inference phase and prevent them from making untrustworthy predictions. Unlike…
Conformal prediction (CP) constructs uncertainty sets for model outputs with finite-sample coverage guarantees. A candidate output is included in the prediction set if its non-conformity score is not considered extreme relative to the…
The problem of domain adaptation on an unlabeled target dataset using knowledge from multiple labelled source datasets is becoming increasingly important. A key challenge is to design an approach that overcomes the covariate and target…
Quantifying differences between flow fields is a key challenge in fluid mechanics, particularly when evaluating the effectiveness of flow control. Traditional vector metrics, such as the Euclidean distance, provide straightforward pointwise…
The optimal transportation problem, first suggested by Gaspard Monge in the 18th century and later revived in the 1940s by Leonid Kantorovich, deals with the question of transporting a certain measure to another, using transport maps or…
We introduce COPT, a novel distance metric between graphs defined via an optimization routine, computing a coordinated pair of optimal transport maps simultaneously. This gives an unsupervised way to learn general-purpose graph…
Learning from set-structured data is a fundamental problem that has recently attracted increasing attention, where a series of summary networks are introduced to deal with the set input. In fact, many meta-learning problems can be treated…
Sliced Optimal Transport (SOT) is a rapidly developing branch of optimal transport (OT) that exploits the tractability of one-dimensional OT problems. By combining tools from OT, integral geometry, and computational statistics, SOT enables…
This paper addresses an Optimal Transport (OT)-based efficient multi-robot exploration problem, considering the energy constraints of a multi-robot system. The efficiency in this problem implies how a team of robots (agents) covers a given…
Many problems ask a question that can be formulated as a causal question: "what would have happened if...?" For example, "would the person have had surgery if he or she had been Black?" To address this kind of questions, calculating an…
An Optimal Transport (OT)-based decentralized collaborative multi-robot exploration strategy is proposed in this paper. This method is to achieve an efficient exploration with a predefined priority in the given domain. In this context, the…
Computing optimal transport (OT) between measures in high dimensions is doomed by the curse of dimensionality. A popular approach to avoid this curse is to project input measures on lower-dimensional subspaces (1D lines in the case of…
Some optimization or equilibrium problems involving somehow the concept of optimal transport are presented in these notes, mainly devoted to applications to economic and game theory settings. A variant model of transport, taking into…
Imbalance in covariate distributions leads to biased estimates of causal effects. Weighting methods attempt to correct this imbalance but rely on specifying models for the treatment assignment mechanism, which is unknown in observational…
Conformal Prediction (CP) is a principled framework for quantifying uncertainty in blackbox learning models, by constructing prediction sets with finite-sample coverage guarantees. Traditional approaches rely on scalar nonconformity scores,…
Unbalanced optimal transport (UOT) extends classical optimal transport to measures with different total masses, but statistical guarantees for Monge-type estimation remain limited. We study unbalanced transport with quadratic cost and…
We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…
Solving optimal transport (OT) on random minibatches is a common surrogate for exact OT in large-scale learning. In flow matching (FM), this surrogate is used to obtain OT-like couplings that can straighten probability paths and reduce…
We study the fundamental computational problem of approximating optimal transport (OT) equations using neural differential equations (Neural ODEs). More specifically, we develop a novel framework for approximating unbalanced optimal…