Based on the theories of sliced inverse regression (SIR) and reproducing kernel Hilbert space (RKHS), a new approach RDSIR (RKHS-based Double SIR) to nonlinear dimension reduction for survival data is proposed. An isometric isomorphism constructed based RKHS property, then function in can be represented by inner product two elements that reside isomorphic feature space. Due censorship data, dou...

Variable selection, also known as feature selection in machine learning, plays an important role in modeling high dimensional data and is key to data-driven scientific discoveries. We consider here the problem of detecting influential variables under the general index model, in which the response is dependent of predictors through an unknown function of one or more linear combinations of them. ...

In high-dimensional data analysis, sufficient dimension reduction (SDR) methods are effective in reducing the predictor dimension, while retaining full regression information and imposing no parametric models. However, it is common in high-dimensional data that a subset of predictors may have missing observations. Existing SDR methods resort to the complete-case analysis by removing all the sub...

MOTIVATION Identification of transcription factor binding motifs (TFBMs) is a crucial first step towards the understanding of regulatory circuitries controlling the expression of genes. In this paper, we propose a novel procedure called regularized sliced inverse regression (RSIR) for identifying TFBMs. RSIR follows a recent trend to combine information contained in both gene expression measure...

In Li and Yin (2008, Biometrics 64, 124-131), a ridge SIR estimator is introduced as the solution of a minimization problem and computed thanks to an alternating least-squares algorithm. This methodology reveals good performance in practice. In this note, we focus on the theoretical properties of the estimator. It is shown that the minimization problem is degenerated in the sense that only two ...

Variable selection methods play important roles in modeling high dimensional data and are keys to data-driven scientific discoveries. In this paper, we consider the problem of variable selection with interaction detection under the sliced inverse index modeling framework, in which the response is influenced by predictors through an unknown function of both linear combinations of predictors and ...