Related papers: Energy-guided Entropic Neural Optimal Transport
Recently, Optimal Transport has been proposed as a probabilistic framework in Machine Learning for comparing and manipulating probability distributions. This is rooted in its rich history and theory, and has offered new solutions to…
Recently, linear regression models incorporating an optimal transport (OT) loss have been explored for applications such as supervised unmixing of spectra, music transcription, and mass spectrometry. However, these task-specific approaches…
We present a functional calculus treatment of Entropic Optimal Transport (EOT) between Gaussian measures on separable Hilbert spaces, providing a unified framework that handles infinite-dimensional degeneracy. By leveraging the notion of…
This paper addresses the limitations of standard uncertainty models, e.g., robust (norm-bounded) and stochastic (one fixed distribution, e.g., Gaussian), and proposes to model uncertainty via Optimal Transport (OT) ambiguity sets. These…
Maximum likelihood estimation is widely used in training Energy-based models (EBMs). Training requires samples from an unnormalized distribution, which is usually intractable, and in practice, these are obtained by MCMC algorithms such as…
Deep energy-based models (EBMs) are very flexible in distribution parametrization but computationally challenging because of the intractable partition function. They are typically trained via maximum likelihood, using contrastive divergence…
The relevance of optimal transport methods to machine learning has long been hindered by two salient limitations. First, the $O(n^3)$ computational cost of standard sample-based solvers (when used on batches of $n$ samples) is prohibitive.…
Flow Matching (FM) generative models offer efficient simulation-free training and deterministic sampling, but their practical deployment is challenged by high-precision parameter requirements. We adapt optimal transport (OT)-based…
Optimal transport (OT) theory underlies many emerging machine learning (ML) methods nowadays solving a wide range of tasks such as generative modeling, transfer learning and information retrieval. These latter works, however, usually build…
Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…
In this work, we develop an optimal transport (OT) based framework to select informative prototypical examples that best represent a given target dataset. Summarizing a given target dataset via representative examples is an important…
Efficient energy management is essential for reliable and sustainable microgrid operation amid increasing renewable integration. In this paper, an imitation learning-based framework to approximate mixed-integer Economic Model Predictive…
Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important…
We propose Energy-based generator matching (EGM), a modality-agnostic approach to train generative models from energy functions in the absence of data. Extending the recently proposed generator matching, EGM enables training of arbitrary…
Network alignment, which aims to find node correspondence across different networks, is the cornerstone of various downstream multi-network and Web mining tasks. Most of the embedding-based methods indirectly model cross-network node…
We investigate the problem of efficiently computing optimal transport (OT) distances, which is equivalent to the node-capacitated minimum cost maximum flow problem in a bipartite graph. We compare runtimes in computing OT distances on data…
Large Language Models (LLMs) struggle with reliable mathematical reasoning, and current verification methods are often computationally expensive. This paper introduces the Energy Outcome Reward Model (EORM), a highly efficient, lightweight…
Eco-driving (ED) can be used for fuel savings in existing vehicles, requiring only a few hardware modifications. For this technology to be successful in a dynamic environment, ED requires an online real-time implementable policy. In this…
Energy-based models (EBMs) exhibit a variety of desirable properties in predictive tasks, such as generality, simplicity and compositionality. However, training EBMs on high-dimensional datasets remains unstable and expensive. In this…
Latent space Energy-Based Models (EBMs), also known as energy-based priors, have drawn growing interests in the field of generative modeling due to its flexibility in the formulation and strong modeling power of the latent space. However,…