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最大间隔线性分类器的泛化误差：过参数化下的良性过拟合与高维渐近AI 解读

Modern machine learning classifiers often exhibit vanishing classification error on the training set. They achieve this by learning nonlinear representations of the inputs that map the data into linearly separable classes. Motivated by these phenomena, we revisit high-dimensional maximum margin classification for linearly separable data. We consider a stylized setting in which data (yi,xi), i≤n are i.i.d. with xi∼N(0,Σ) a p-dimensional Gaussian feature vector, and yi∈{+1,−1}…

半非参数随机波动率模型下的杠杆效应之谜AI 解读

This article extends the solution proposed by Aït-Sahalia, Fan, and Li for the leverage effect puzzle, which refers to a fact that empirical correlation between daily asset returns and the changes of daily volatility estimated from high frequency data is nearly zero. Complementing the analysis in Aït-Sahalia, Fan, and Li via the Heston model, we work with a generic semi-nonparametric stochastic volatility model via an operator-based expansion method. Under such a general…

复发事件与失效时间的联合尺度变换模型AI 解读

Recurrent event data arise frequently in various fields such as biomedical sciences, public health, engineering, and social sciences. In many instances, the observation of the recurrent event process can be stopped by the occurrence of a correlated failure event, such as treatment failure and death. In this article, we propose a joint scale-change model for the recurrent event process and the failure time, where a shared frailty variable is used to model the association…

分层抽样下聚类失效时间的半参数加速失效时间建模AI 解读

Clustered failure times often arise from studies with stratified sampling designs where it is desired to reduce both cost and sampling error. Semiparametric accelerated failure time (AFT) models have not been used as frequently as Cox relative risk models in such settings due to lack of efficient and reliable computing routines for inferences. The challenge roots in the nonsmoothness of the rank-based estimating functions, and for clustered data, the asymptotic properties of…

多变量生存过程的函数型关联模型AI 解读

We consider multivariate temporal processes that are continuously observed within overlapping time windows. The intended application is in censored multistate and multivariate survival settings, where point processes are continuously observed. These data differ from other functional data, like longitudinal data, which are discretely observed at irregular times. Existing functional approaches to survival processes use intensity models, which require smoothing and depend…

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