In this work, we develop a new theory and method for sufficient dimension
reduction (SDR) in single-index models, where SDR is a sub-field of supervised
dimension reduction based on conditional independence. Our work is primarily
motivated by the recent introduction of the Hellinger correlation as a
dependency measure. Utilizing this measure, we develop a method capable of
effectively detecting the dimension reduction subspace, complete with
theoretical justification. Through extensive numerical experiments, we
demonstrate that our proposed method significantly enhances and outperforms
existing SDR methods. This improvement is largely attributed to our proposed
method's deeper understanding of data dependencies and the refinement of
existing SDR techniques.

本文提出了一种新的理论和方法，用于单指数模型中的充分降维 (SDR)，SDR 是基于条件独立性的监督降维的一个子领域。利用 Hellinger 相关作为一种依赖度量，我们开发了一种能够有效检测降维子空间的方法，并给出了理论解释。通过大量的数值实验，我们证明了我们提出的方法明显优于现有的 SDR 方法。这种改进主要归因于我们提出的方法对数据依赖性的更深入理解和对现有 SDR 技术的改进。

通过 Hellinger 相关性增强充分降维

Enhancing Sufficient Dimension Reduction via Hellinger Correlation

The essence of multivariate sequential learning is all about how to extract
dependencies in data. These data sets, such as hourly medical records in
intensive care units and multi-frequency phonetic time series, often time
exhibit not only strong serial dependencies in the individual components (the
"marginal" memory) but also non-negligible memories in the cross-sectional
dependencies (the "joint" memory). Because of the multivariate complexity in
the evolution of the joint distribution that underlies the data generating
process, we take a data-driven approach and construct a novel recurrent network
architecture, termed Memory-Gated Recurrent Networks (mGRN), with gates
explicitly regulating two distinct types of memories: the marginal memory and
the joint memory. Through a combination of comprehensive simulation studies and
empirical experiments on a range of public datasets, we show that our proposed
mGRN architecture consistently outperforms state-of-the-art architectures
targeting multivariate time series.

提出了一种称为 Memory-Gated Recurrent Networks 的新颖递归网络结构，用于提取复杂的多元时间序列数据中的关联性，并通过全面的模拟和实证实验证明了其应用优越性。

记忆门循环神经网络

Memory-Gated Recurrent Networks

Existential rules, also known as data dependencies in Databases, have been
recently rediscovered as a promising family of languages for Ontology-based
Query Answering. In this paper, we prove that disjunctive embedded dependencies
exactly capture the class of recursively enumerable ontologies in
Ontology-based Conjunctive Query Answering (OCQA). Our expressive completeness
result does not rely on any built-in linear order on the database. To establish
the expressive completeness, we introduce a novel semantic definition for OCQA
ontologies. We also show that neither the class of disjunctive tuple-generating
dependencies nor the class of embedded dependencies is expressively complete
for recursively enumerable OCQA ontologies.

本文证明了分离嵌入式依赖可以精确捕捉基于本体的连词查询应答中的可递归枚举本体类，而关于 “元组生成依赖” 的复杂性类和嵌入式依赖的复杂性类都不能完全表达可递归枚举的 “基于本体的连词查询应答” 本体。