相关论文: Comparing Multivariate Distributions: A Novel Appr…

In many real-world settings--e.g., single-cell RNA sequencing, mobility sensing, and environmental monitoring--data are observed only as temporally aggregated snapshots collected over finite time windows, often with noisy or uncertain…

We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…

Characteristic-function based goodness-of-fit tests are suggested for multivariate observations. The test statistics, which are straightforward to compute, are defined as two-sample criteria measuring discrepancy between multivariate ranks…

Transporting findings from a study population to a target population is central to evidence-based decision-making in real-world settings. Most existing methods require individual-level data from both populations to account for covariate…

We investigate the transport properties of the Holstein model using the numerically exact quantum typicality (QT) approach. Roughly speaking, QT exploits the fact that even a single, randomly chosen pure state can effectively represent the…

We propose a framework for conditional vector quantile regression (CVQR) that combines neural optimal transport with amortized optimization, and apply it to multivariate conformal prediction. Classical quantile regression does not extend…

The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing…

Existing quantum routing implicitly mimics classical routing principles, with finding the ``best'' path (aka pathfinding), according to a selected routing metric, as a core mechanism for establishing end-to-end entanglement. However,…

Loosely speaking, the concept of quantum typicality refers to the fact that a single pure state can imitate the full statistical ensemble. This fact has given rise to a rather simple but remarkably useful numerical approach to simulate the…

Quantum networks are important for quantum communication, enabling tasks such as quantum teleportation, quantum key distribution, quantum sensing, and quantum error correction, often utilizing graph states, a specific class of multipartite…

This paper proposes the use of the Hellinger--Kantorovich metric from unbalanced optimal transport (UOT) in a dimensionality reduction and learning (supervised and unsupervised) pipeline. The performance of UOT is compared to that of…

A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n<m, and the task is relatively…

Multiple photonic degrees of freedom can be explored to generate high-dimensional quantum states; commonly referred to as `qudits'. Qudits offer several advantages for quantum communications, including higher information capacity, noise…

It is known that quantum correlations exhibited by a maximally entangled qubit pair can be simulated with the help of shared randomness, supplemented with additional resources, such as communication, post-selection or non-local boxes. For…

Motivated by modern data forms such as images and multi-view data, the multi-attribute graphical model aims to explore the conditional independence structure among vectors. Under the Gaussian assumption, the conditional independence between…

We introduce a new stochastic algorithm for solving entropic optimal transport (EOT) between two absolutely continuous probability measures $\mu$ and $\nu$. Our work is motivated by the specific setting of Monge-Kantorovich quantiles where…

This paper explores the process of optimal quantization for several types of discrete probability distributions. Quantization is a technique used to approximate a complex distribution with a smaller set of representative points, which is…

We propose a novel amortized optimization method for predicting optimal transport (OT) plans across multiple pairs of measures by leveraging Kantorovich potentials derived from sliced OT. We introduce two amortization strategies:…

We introduce the proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a…

Embedding high-dimensional data into a low-dimensional space is an indispensable component of data analysis. In numerous applications, it is necessary to align and jointly embed multiple datasets from different studies or experimental…