Related papers: Computing high-dimensional optimal transport by fl…
Adapted optimal transport (AOT) problems are optimal transport problems for distributions of a time series where couplings are constrained to have a temporal causal structure. In this paper, we develop computational tools for solving AOT…
Optimal transport (OT) compares probability distributions by computing a meaningful alignment between their samples. CO-optimal transport (COOT) takes this comparison further by inferring an alignment between features as well. While this…
Deep generative models aim to learn the underlying distribution of data and generate new ones. Despite the diversity of generative models and their high-quality generation performance in practice, most of them lack rigorous theoretical…
With the advent of large datasets, offline reinforcement learning (RL) is a promising framework for learning good decision-making policies without the need to interact with the real environment. However, offline RL requires the dataset to…
In this paper, we present a new formulation of unbalanced optimal transport called Dual Regularized Optimal Transport (DROT). We argue that regularizing the dual formulation of optimal transport results in a version of unbalanced optimal…
Cross-domain alignment between two sets of entities (e.g., objects in an image, words in a sentence) is fundamental to both computer vision and natural language processing. Existing methods mainly focus on designing advanced attention…
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…
Optimal transport aligns samples across distributions by minimizing the transportation cost between them, e.g., the geometric distances. Yet, it ignores coherence structure in the data such as clusters, does not handle outliers well, and…
The study focuses on estimating and predicting time-varying origin to destination (OD) trip tables for a dynamic traffic assignment (DTA) model. A bi-level optimisation problem is formulated and solved to estimate OD flows from pre-existent…
Optimal transport is a framework that facilitates the most efficient allocation of a limited amount of resources. However, the most efficient allocation scheme does not necessarily preserve the most fairness. In this paper, we establish a…
Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study…
Uncertainty often plays an important role in dynamic flow problems. In this paper, we consider both, a stationary and a dynamic flow model with uncertain boundary data on networks. We introduce two different ways how to compute the…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
Solving the non-convex optimal power flow (OPF) problem for large-scale power distribution systems is computationally expensive. An alternative is to solve the relaxed convex problem or linear approximated problem, but these methods lead to…
We present a novel hierarchical framework for optimal transport (OT) using string diagrams, namely string diagrams of optimal transports. This framework reduces complex hierarchical OT problems to standard OT problems, allowing efficient…
Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In…
Variational Auto-Encoders enforce their learned intermediate latent-space data distribution to be a simple distribution, such as an isotropic Gaussian. However, this causes the posterior collapse problem and loses manifold structure which…
Speculative sampling reduces the latency of autoregressive decoding for target model LLMs without sacrificing inference quality, by using a cheap draft model to suggest a candidate token and a verification criterion to accept or resample…
In recent years, with the advancements in information and communication technology, different emerging on-demand shared mobility services have been introduced as innovative solutions in the low-density areas, including on-demand transit…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…