Kernel Knockoffs Selection for Nonparametric Additive Models.

Thanks to its fine balance between model flexibility and interpretability, the nonparametric additive model has been widely used, and variable selection for this type of model has been frequently studied. However, none of the existing solutions can control the false discovery rate (FDR) unless the sample size tends to infinity. The knockoff framework is a recent proposal that can address this issue, but few knockoff solutions are directly applicable to nonparametric models. In this article, we propose a novel kernel knockoffs selection procedure for the nonparametric additive model. We integrate three key components: the knockoffs, the subsampling for stability, and the random feature mapping for nonparametric function approximation. We show that the proposed method is guaranteed to control the FDR for any sample size, and achieves a power that approaches one as the sample size tends to infinity. We demonstrate the efficacy of our method through intensive simulations and comparisons with the alternative solutions. our proposal thus makes useful contributions to the methodology of nonparametric variable selection, FDR-based inference, as well as knockoffs.

Orthogonalized Kernel Debiased Machine Learning for Multimodal Data Analysis.

Multimodal imaging has transformed neuroscience research. While it presents unprecedented opportunities, it also imposes serious challenges. Particularly, it is difficult to combine the merits of the interpretability attributed to a simple association model with the flexibility achieved by a highly adaptive nonlinear model. In this article, we propose an orthogonalized kernel debiased machine learning approach, which is built upon the Neyman orthogonality and a form of decomposition orthogonality, for multimodal data analysis. We target the setting that naturally arises in almost all multimodal studies, where there is a primary modality of interest, plus additional auxiliary modalities. We establish the root-N-consistency and asymptotic normality of the estimated primary parameter, the semi-parametric estimation efficiency, and the asymptotic validity of the confidence band of the predicted primary modality effect. Our proposal enjoys, to a good extent, both model interpretability and model flexibility. It is also considerably different from the existing statistical methods for multimodal data integration, as well as the orthogonality-based methods for high-dimensional inferences. We demonstrate the efficacy of our method through both simulations and an application to a multimodal neuroimaging study of Alzheimer's disease.

A synthesis of pathways linking diet, metabolic risk and cardiovascular disease: a framework to guide further research and approaches to evidence-based practice.

Cardiovascular disease (CVD) is the most common non-communicable disease occurring globally. Although previous literature has provided useful insights into the important role that diet plays in CVD prevention and treatment, understanding the causal role of diets is a difficult task considering inherent and introduced weaknesses of observational (e.g. not properly addressing confounders and mediators) and experimental research designs (e.g. not appropriate or well designed). In this narrative review, we organised current evidence linking diet, as well as conventional and emerging physiological risk factors, with CVD risk, incidence and mortality in a series of diagrams. The diagrams presented can aid causal inference studies as they provide a visual representation of the types of studies underlying the associations between potential risk markers/factors for CVD. This may facilitate the selection of variables to be considered and the creation of analytical models. Evidence depicted in the diagrams was systematically collected from studies included in the British Nutrition Task Force report on diet and CVD and database searches, including Medline and Embase. Although several markers and disorders linked to conventional and emerging risk factors for CVD were identified, the causal link between many remains unknown. There is a need to address the multifactorial nature of CVD and the complex interplay between conventional and emerging risk factors with natural and built environments, while bringing the life course into the spotlight.

Kernel Ordinary Differential Equations.

Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations. We do not assume the functional forms in ODE to be known, or restrict them to be linear or additive, and we allow pairwise interactions. We perform sparse estimation to select individual functionals, and construct confidence intervals for the estimated signal trajectories. We establish the estimation optimality and selection consistency of kernel ODE under both the low-dimensional and high-dimensional settings, where the number of unknown functionals can be smaller or larger than the sample size. Our proposal builds upon the smoothing spline analysis of variance (SS-ANOVA) framework, but tackles several important problems that are not yet fully addressed, and thus extends the scope of existing SS-ANOVA as well. We demonstrate the efficacy of our method through numerous ODE examples.