KL-divergence Based Deep Learning for Discrete Time Model

Neural Network (Deep Learning) is a modern model in Artificial Intelligence and it has been exploited in Survival Analysis. Although several improvements have been shown by previous works, training an excellent deep learning model requires a huge amount of data, which may not hold in practice. To address this challenge, we develop a Kullback-Leibler-based (KL) deep learning procedure to integrate external survival prediction models with newly collected time-to-event data. Time-dependent KL discrimination information is utilized to measure the discrepancy between the external and internal data. This is the first work considering using prior information to deal with short data problem in Survival Analysis for deep learning. Simulation and real data results show that the proposed model achieves better performance and higher robustness compared with previous works.

Covariance-Insured Screening

Modern bio-technologies have produced a vast amount of high-throughput data with the number of predictors far greater than the sample size. In order to identify more novel biomarkers and understand biological mechanisms, it is vital to detect signals weakly associated with outcomes among ultrahigh-dimensional predictors. However, existing screening methods, which typically ignore correlation information, are likely to miss these weak signals. By incorporating the inter-feature dependence, we propose a covariance-insured screening methodology to identify predictors that are jointly informative but only marginally weakly associated with outcomes. The validity of the method is examined via extensive simulations and real data studies for selecting potential genetic factors related to the onset of cancer.

Classification with Ultrahigh-Dimensional Features

Although much progress has been made in classification with high-dimensional features \citep{Fan_Fan:2008, JGuo:2010, CaiSun:2014, PRXu:2014}, classification with ultrahigh-dimensional features, wherein the features much outnumber the sample size, defies most existing work. This paper introduces a novel and computationally feasible multivariate screening and classification method for ultrahigh-dimensional data. Leveraging inter-feature correlations, the proposed method enables detection of marginally weak and sparse signals and recovery of the true informative feature set, and achieves asymptotic optimal misclassification rates. We also show that the proposed procedure provides more powerful discovery boundaries compared to those in \citet{CaiSun:2014} and \citet{JJin:2009}. The performance of the proposed procedure is evaluated using simulation studies and demonstrated via classification of patients with different post-transplantation renal functional types.