论文检索

复杂分组高维多响应模型的典型相关搜索特征选择AI 解读

High-dimensional multiresponse models with complex group structures in both the response variables and the covariates arise from current researches in important fields such as genetics and medicine. However, no enough research has been done on such models. One of a few researches, if not the only one, is the article by Li, Nan, and Zhu where the sparse group Lasso approach is extended to such models. In this article, we propose a novel approach named the sequential canonical…

结合扩展贝叶斯信息准则的序贯 Lasso 超高维特征选择AI 解读

In this article, we propose a method called sequential Lasso (SLasso) for feature selection in sparse high-dimensional linear models. The SLasso selects features by sequentially solving partially penalized least squares problems where the features selected in earlier steps are not penalized. The SLasso uses extended BIC (EBIC) as the stopping rule. The procedure stops when EBIC reaches a minimum. The asymptotic properties of SLasso are considered when the dimension of the…

用交互样条模型拟合多元回归函数AI 解读

SUMMARY In nonparametric multivariate regression analysis, we seek methods to reduce the dimensionality of the regression function to bypass the difficulty caused by the curse of dimensionality. The original additive models approximate a regression function by additive univariate functions, which overcome successfully the difficulty caused by the curse of dimensionality and have a clear interpretation. But since they ignore any interactions between regressors they are not…

交互样条模型及其收敛速率AI 解读

We consider interaction splines which model a multivariate regression function $f$ as a constant plus the sum of functions of one variable (main effects), plus the sum of functions of two variables (two-factor interactions), and so on. The estimation of $f$ by the penalized least squares method and the asymptotic properties of the models are studied in this article. It is shown that, under some regularity conditions on the data points, the expected squared error averaged…