This paper is concerned with the problems of interaction screening and nonlinear classification in a high-dimensional setting. We propose a two-step procedure, IIS-SQDA, where in the first step an innovated interaction screening (IIS) approach based on transforming the original p-dimensional feature vector is proposed, and in the second step a sparse quadratic discriminant analysis (SQDA) is proposed for further selecting important interactions and main effects and simultaneously conducting classification. Our IIS approach screens important interactions by examining only p features instead of all two-way interactions of order O(p 2 ). Our theory shows that the proposed method enjoys sure screening property in interaction selection in the high-dimensional setting of p growing exponentially with the sample size. In the selection and classification step, we establish a sparse inequality on the estimated coefficient vector for QDA and prove that the classification error of our procedure can be upperbounded by the oracle classification error plus some smaller order term. Extensive simulation studies and real data analysis show that our proposal compares favorably with existing methods in interaction selection and high-dimensional classification.

Edited by Julian SchroederKeywords: Triacylglycerol DGAT1 ABI4 ABI5 Synergistic effect a b s t r a c t Triacylglycerol (TAG) accumulation is essential for seed maturation in plants. Diacylglycerol acyltransferase 1 (DGAT1) is the rate-limiting enzyme in TAG biosynthesis. In this study, we show that TAG accumulation in Arabidopsis seedlings is correlated with environmental stress, and both ABI4 and ABI5 play important roles in regulating DGAT1 expression. Tobacco transient assays revealed the synergistic effect of ABI4 with ABI5 in regulating DGAT1 expression. Taken together, our findings indicate ABI5 is an important accessory factor with ABI4 in the activation of DGAT1 in Arabidopsis seedlings under stress.

Accurate prognosis of patients with cancer is important for the stratification of patients, the optimization of treatment strategies, and the design of clinical trials. Both clinical features and molecular data can be used for this purpose, for instance, to predict the survival of patients censored at specific time points. Multi-omics data, including genome-wide gene expression, methylation, protein expression, copy number alteration, and somatic mutation data, are becoming increasingly common in cancer studies. To harness the rich information in multi-omics data, we developed GDP (Group lass regularized Deep learning for cancer Prognosis), a computational tool for survival prediction using both clinical and multi-omics data. GDP integrated a deep learning framework and Cox proportional hazard model (CPH) together, and applied group lasso regularization to incorporate gene-level group prior knowledge into the model training process. We evaluated its performance in both simulated and real data from The Cancer Genome Atlas (TCGA) project. In simulated data, our results supported the importance of group prior information in the regularization of the model. Compared to the standard lasso regularization, we showed that group lasso achieved higher prediction accuracy when the group prior knowledge was provided. We also found that GDP performed better than CPH for complex survival data. Furthermore, analysis on real data demonstrated that GDP performed favorably against other methods in several cancers with large-scale omics data sets, such as glioblastoma multiforme, kidney renal clear cell carcinoma, and bladder urothelial carcinoma. In summary, we demonstrated that GDP is a powerful tool for prognosis of patients with cancer, especially when large-scale molecular features are available.

Feature interactions can contribute to a large proportion of variation in many prediction models. In the era of big data, the coexistence of high dimensionality in both responses and covariates poses unprecedented challenges in identifying important interactions. In this paper, we suggest a two-stage interaction identification method, called the interaction pursuit via distance correlation (IPDC), in the setting of high-dimensional multi-response interaction models that exploits feature screening applied to transformed variables with distance correlation followed by feature selection. Such a procedure is computationally efficient, generally applicable beyond the heredity assumption, and effective even when the number of responses diverges with the sample size. Under mild regularity conditions, we show that this method enjoys nice theoretical properties including the sure screening property, support union recovery, and oracle inequalities in prediction and estimation for both interactions and main effects. The advantages of our method are supported by several simulation studies and real data analysis.

Our findings have implications for developing a multilevel leadership approach to implementation in health care. Leadership development should build on different competencies based on managers' level but align managers' priorities on the same implementation goals.This is an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License 4.0 (CCBY-NC-ND), where it is permissible to download and share the work provided it is properly cited. The work cannot be changed in any way or used commercially without permission from the journal.