“The question of gender is a question of language.” Barbara Johnson’s perceptive formulation of the relationship between gender and language succinctly characterizes the approach of a group of feminists who draw upon the discourses of postmodernism. Yet what distinguishes them from their feminist predecessors and postmodern counterparts is the proposal of écriture féminine—feminine writing—as a path towards the most fundamental liberation of all: freedom from oppressive thought. This paper, therefore, centers on the idea of feminine writing in “The Laugh of the Medusa”, written by Hélène Cixous in 1976, and explores its experimental literalization, Láadan in Native Tongue, and its actual realization, nüshu in China. The project, I hope, can eventually shed some light on our understanding of the opaque postmodern feminist theories of female language.

In recent years, modern technology has facilitated the collection of large-scale data from medical records, health insurance databases, and other platforms. Due to the complex structure, the analysis of such data is very challenging. The dissertation focuses on the nonparametric machine learning techniques in subgroup analysis and deep neural networks regression.

The first part of the dissertation studies the heterogeneity in the disease progression, which is essential to the development of precision medicine that aims to tailor treatments to subgroups of patients with similar characteristics. Without a priori knowledge of grouping information, our goal is to identify subgroups of individuals who share a common disorder progress over time, i.e. longitudinal trajectory. We develop a subject-specific nonparametric regression model, where the heterogeneous trajectories are modeled through the subject-specific unknown functions and can be approximated by B-splines. We then apply the fusion penalized method that can automatically divide the individuals into different subgroups based on the B-spline coefficients as well as estimating the coefficients simultaneously. We also illustrate the performance of this method through simulation studies and a biomedical data application.

The second part of the dissertation considers a sparse deep ReLU network (SDRN) estimator obtained from empirical risk minimization with a Lipschitz loss function in the presence of a large number of features. Instead of utilizing full grids, the unknown target function is approximated by a deep ReLU network with sparse grids. Our framework can be applied to a variety of regression and classification problems. The unknown target function to estimate is assumed to be in a Sobolev space with mixed derivatives. Functions in this space only need to satisfy a smoothness condition rather than having a compositional structure. We develop non-asymptotic excess riskbounds for our SDRN estimator. We further derive that the SDRN estimator can achieve the same minimax rate of estimation (up to logarithmic factors) as one-dimensional nonparametric regression when the dimension of the features is fixed, and the estimator has a suboptimal rate when the dimension grows with the sample size. We show that the depth and the total number of nodes and weights of the ReLU network need to grow as the sample size increases to ensure a good performance, and also investigate how fast they should increase with the sample size. These results provide an important theoretical guidance and basis for empirical studies by deep neural networks.

The problem of the strange has exerted a powerful fascination on different literary traditions. In China, zhiguai (translated as “accounts of the strange”) was produced in great number, ranging from administrative reports of drought and misrule to accounts of apparently supernatural events. What makes it even more intriguing is the involvement of Confucian literati; scholars who normally did not deign to discuss the extraordinary were actively engaged in compiling these accounts. Literary criticism on zhiguai has also been a tenuous construction. Zhiguai shifts among different bibliographical categories, and was not recognized as a genre until the Ming Dynasty (1368-1644). Even today there has never been scholarly consensus on its definition. Zhiguai, therefore, is strange in its content, compilation and criticism. What are these accounts? How shall we read them? By what criteria should we judge what is strange and what is not? My dissertation offers a theory of the strange by defining zhiguai as a genre. Tracing its development in classical Chinese literature, I analyze how zhiguai challenges categorical dichotomies – history vs. fiction, natural vs. supernatural, and belief vs. disbelief – and occupies a liminal status in between. The result is a reassessment of what is normal, natural and real vis-à-vis what is anomalous, supernatural and fantastic. Devising a new ontological framework – this-world and other-world(s), I argue that it is the interaction between the two – the esoteric and/or exotic and our quotidian empirical experience – that defines the genre. The theoretical part of the dissertation is complemented with two case studies – Shenxian zhuan (Traditions of Divine Transcendents), a 4th-century zhiguai collection, and various examples in contemporary Chinese cultural production from television programs to internet gossip. Through a diachronic study as such can I uncover how the strange is woven into everyday life, and how this age-old Chinese literary genre that appears to be marginalized in its own time and nearly extinct in our modern world is still thriving today.