NSF-BSF: Collaborative Research: CIF: Small: Neural Estimation of Statistical Divergences: Theoretical Foundations and Applications to Communication Systems

大量的数据和计算的最新进展极大地提高了信息处理系统的可靠性和性能。在许多应用程序中，这些系统为有关生成数据的分布的统计问题提供近似答案。基于神经网络的估计器已经成为处理大型复杂数据集的首选方法。它们的流行是由于它们在实践中的出色表现和计算效率。但对他们出色表现背后原因的了解仍然非常有限。该项目的目标是提高对神经估计工作原理的理解，并提供正式的性能保证，以帮助指导无线通信等领域的实际应用。除了技术发展之外，该项目还包括研究生指导、本科生包容、通过夏令营向高中推广、国际合作以及开发教程视频。这个项目使用统计散度来测量概率分布之间的差异，对数据问题进行建模。虽然有许多方法可以估计数据的统计差异，但神经估计器现在已经成为处理大型高维数据集的首选方法。该项目将发展神经估计的综合统计和计算理论，并将其应用于通信领域的新应用。它有两个主要目标。第一个目标是非渐近神经估计理论，该理论解释了所有已知的误差来源：函数逼近、经验估计和优化。第二个将设计一个灵活的，有效的计算，并证明准确的方法神经容量估计和数据驱动的极性编码。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

An abundance of data and recent advances in computation have dramatically increased the reliability and performance of information processing systems. In many applications, these systems provide approximate answers to statistical questions about the distributions that generate the data. Estimators based on neural networks have become the method of choice when dealing with large and complicated datasets. Their popularity is due to their excellent performance in practice and their computational efficiency. But knowledge of the reasons behind their outstanding performance remains quite limited. The goal of this project is to improve the understanding of why neural estimation works and to provide formal performance guarantees that help guide practical applications in fields such as wireless communications. In addition to technological developments, the project features graduate student mentoring, undergraduate inclusion, outreach to high school via a summer camp, international collaboration, and the development of tutorial videos.This project models questions about data using statistical divergences that measure the discrepancy between probability distributions. While there are many approaches to estimating statistical divergences from data, neural estimators have now become the method of choice when dealing with large, high-dimensional datasets. The project will develop a comprehensive statistical and computational theory of neural estimation and apply it to novel applications to communications. It has two main thrusts. The first targets a non-asymptotic neural estimation theory that accounts for all known sources of error: functional approximation, empirical estimation, and optimization. The second will devise a flexible, efficiently computable, and provably accurate methodology for neural capacity estimation and data-driven polar coding.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.