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Many applied settings in empirical economics involve simultaneous estimation of a large number of parameters. In particular, applied economists are often interested in estimating the effects of many-valued treatments (like teacher effects…

A novel methodology is developed for the solution of the data-driven Monge optimal transport barycenter problem, where the pushforward condition is formulated in terms of the statistical independence between two sets of random variables:…

Autoencoders have been widely used for dimensional reduction and feature extraction. Various types of autoencoders have been proposed by introducing regularization terms. Most of these regularizations improve representation learning by…

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…

Training energy-based models (EBMs) with noise-contrastive estimation (NCE) is theoretically feasible but practically challenging. Effective learning requires the noise distribution to be approximately similar to the target distribution,…

We present an iterative inverse reinforcement learning algorithm to infer optimal cost functions in continuous spaces. Based on a popular maximum entropy criteria, our approach iteratively finds a weight improvement step and proposes a…

In optimal transport (OT), a Monge map is known as a mapping that transports a source distribution to a target distribution in the most cost-efficient way. Recently, multiple neural estimators for Monge maps have been developed and applied…

We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dN is a geodesic Borel distance which makes (X,dN) a possibly branching geodesic space. We show that under some assumptions on the…

Mixture-of-Expert (MoE) based large language models (LLMs), such as the recent Mixtral and DeepSeek-MoE, have shown great promise in scaling model size without suffering from the quadratic growth of training cost of dense transformers. Like…

The classical Monge-Kantorovich (MK) problem as originally posed is concerned with how best to move a pile of soil or rubble to an excavation or fill with the least amount of work relative to some cost function. When the cost is given by…

One of the central objects in the theory of optimal transport is the Brenier map: the unique monotone transformation which pushes forward an absolutely continuous probability law onto any other given law. A line of recent work has analyzed…

In this paper, an optimization-based framework for generating estimation-aware trajectories is presented. In this setup, measurement (output) uncertainties are state-dependent and set-valued. Enveloping ellipsoids are employed to…

Optimal transport maps and plans between two absolutely continuous measures $\mu$ and $\nu$ can be approximated by solving semi-discrete or fully-discrete optimal transport problems. These two problems ensue from approximating $\mu$ or both…

We introduce a new non-linear optimal transport formulation for a pair of probability measures on $\mathbb{R}^d$ sharing a common barycentre, in which admissible transference plans satisfy two martingale-type constraints. This bi-martingale…

A fundamental problem in wireless networks is the \emph{minimum spanning tree} (MST) problem: given a set $V$ of wireless nodes, compute a spanning tree $T$, so that the total cost of $T$ is minimized. In recent years, there has been a lot…

Mixture-of-Experts (MoE) models typically fix the number of activated experts $k$ at both training and inference. However, real-world deployments often face heterogeneous hardware, fluctuating workloads, and diverse quality-latency…

Many applications require the collection of data on different variables or measurements over many system performance metrics. We term those broadly as measures or variables. Often data collection along each measure incurs a cost, thus it is…

We consider the problem of autonomous navigation using limited information from a remote sensor network. Because the remote sensors are power and bandwidth limited, we use event-triggered (ET) estimation to manage communication costs. We…

Muscles consume metabolic energy (ATP) to produce force. A mathematical model for energy expenditure can be useful in estimating real-time costs of movements or to predict energy optimal movements. Metabolic cost models developed so far…

An interval transportation problem represents a model for a transportation problem in which the values of supply, demand, and transportation costs are affected by uncertainty and can vary independently within given interval ranges. One of…