Asymptotic Generalization Bound of Fisher's Linear Discriminant Analysis

Fisher's linear discriminant analysis (FLDA) is an important dimension reduction method in statistical pattern recognition. It has been shown that FLDA is asymptotically Bayes optimal under the homoscedastic Gaussian assumption. However, this classical result has the following two major limitations: 1) it holds only for a fixed dimensionality $D$, and thus does not apply when $D$ and the training sample size $N$ are proportionally large; 2) it does not provide a quantitative description on how the generalization ability of FLDA is affected by $D$ and $N$. In this paper, we present an asymptotic generalization analysis of FLDA based on random matrix theory, in a setting where both $D$ and $N$ increase and $D/N\longrightarrow\gamma\in[0,1)$. The obtained lower bound of the generalization discrimination power overcomes both limitations of the classical result, i.e., it is applicable when $D$ and $N$ are proportionally large and provides a quantitative description of the generalization ability of FLDA in terms of the ratio $\gamma=D/N$ and the population discrimination power. Besides, the discrimination power bound also leads to an upper bound on the generalization error of binary-classification with FLDA

Doc2EDAG: An End-to-End Document-level Framework for Chinese Financial Event Extraction

Most existing event extraction (EE) methods merely extract event arguments within the sentence scope. However, such sentence-level EE methods struggle to handle soaring amounts of documents from emerging applications, such as finance, legislation, health, etc., where event arguments always scatter across different sentences, and even multiple such event mentions frequently co-exist in the same document. To address these challenges, we propose a novel end-to-end model, Doc2EDAG, which can generate an entity-based directed acyclic graph to fulfill the document-level EE (DEE) effectively. Moreover, we reformalize a DEE task with the no-trigger-words design to ease the document-level event labeling. To demonstrate the effectiveness of Doc2EDAG, we build a large-scale real-world dataset consisting of Chinese financial announcements with the challenges mentioned above. Extensive experiments with comprehensive analyses illustrate the superiority of Doc2EDAG over state-of-the-art methods. Data and codes can be found at https://github.com/dolphin-zs/Doc2EDAG.Comment: Accepted by EMNLP 201

Physical Activity Patterns Among Physical Education Major Students in Selected Institutions of China and the United States

The benefits associated with regular physical activity have been well documented in recent years. Numerous studies have investigated physical activity patterns among children, adolescents, and adults, yet little work to date has examined the patterns of habitual physical activity participation among pre-service physical education (PE) majors. Furthermore, inasmuch as physical activity affords health benefits irrespective of one\u27s nationality or culture, comparisons among the peoples of nations around the world becomes of greater interest. This study was designed to examine the leisure-time physical activity patterns of physical education major students in selected institutions from the People\u27s Republic of China (PRC) and the United States (U.S.). Data were collected from 184 PE major students enrolled in Beijing University of Physical Education (n = 98) and the University of Northern Iowa (n = 86) during April 1998 using a self-report questionnaire. The questionnaire was an adaptation of the Modifiable Activity Questionnaire designed to assess physical activity participation patterns and behaviors. With the exception of a few questions that were modified to reflect cultural differences, the questionnaires were identical. Results indicated that physical education major students in both the United States and China are more active than the general adult population. Approximately 62% of PRC students and 80% of U.S. students reported participation in leisure-time physical activities three or more of the previous seven days. U.S. students are generally more active than PRC students during their leisure-time, but less active during physical education activity classes. Students\u27 preference of leisure-time physical activities as well as exercise behaviors often reflects cultural and ethnic differences between the two countries. Jogging and basketball were identified as the two most frequently participated in leisure-time physical activities for both PRC and U.S. students. For PRC students, the next most prevalent activities were swimming, soccer, ping-pong, and volleyball; while U.S. students reported weight training, bicycling, softball/baseball, and dancing. Results from the past-year physical activity participation of both groups indicated a notable seasonal variation in participation rates among the most common activities. There is considerable variance in the reasons for physical activity participation among physical education major students in the United States and China. For U.S. students, reasons related to self-feelings of physical activity participation were rated the most important. For PRC students, to improve fitness and develop sport skills were ranked higher than the reasons related to individual feelings. Although there were a few notable differences between the PRC and U.S. students, for the most part, the relative importance of the reasons given for discontinuing their physical activity participation was similar

Future prospects of mass-degenerate Higgs bosons in the CPCP-conserving two-Higgs-doublet model

The scenario of two mass-degenerate Higgs bosons within the general two-Higgs-doublet model (2HDM) is revisited. We focus on the global picture when two $CP$-even Higgs bosons of $h$ and $H$ are nearly mass-degenerate. A global fit to the signal strength of the 125 GeV Higgs measured at the LHC is performed. Based on the best-fit result of the 2HDM mixing angles $(\alpha,\beta)$, theoretical constraints, charged and $CP$-odd Higgs boson direct search constraints and the electroweak precision constraints are imposed to the 2HDM parameter space. We present the signal predictions of the $(4b\,, 2b\,2\gamma)$ channels for the benchmark models at the LHC 14 TeV runs. We also study the direct Higgs boson pair productions at the LHC, and the Z-associated Higgs boson pair production search at the ILC 500 GeV runs, as well as the indirect probes at the CEPC 250 GeV run. We find that the mass-degenerate Higgs boson scenario in the Type-II 2HDM can be fully probed by these future experimental searches.Comment: 31 pages, 9 figures, 5 tables, matches with the PRD published versio