Data-driven slicing for dimension reduction in regressions:A likelihood-ratio approach

To efficiently estimate the central subspace in sufficient dimension reduction,response discretization via slicing its range is one of the most used methodologies when inverse regression-based methods are applied.However,existing slicing schemes are almost all ad hoc and not widely accepted.Thus,how to define datadriven schemes with certain optimal properties is a longstanding problem in this field.The research described here is then twofold.First,we introduce a likelihood-ratio-based framework for dimension reduction,subsuming the popularly used methods including the sliced inverse regression,the sliced average variance estimation and the likelihood acquired direction.Second,we propose a regularized log likelihood-ratio criterion to obtain a data-driven slicing scheme and derive the asymptotic properties of the estimators.A simulation study is carried out to examine the performance of the proposed method and that of existing methods.A data set concerning concrete compressive strength is also analyzed for illustration and comparison.

Stable correlation and robust feature screening

In this paper,we propose a new correlation,called stable correlation,to measure the dependence between two random vectors.The new correlation is well defined without the moment condition and is zero if and only if the two random vectors are independent.We also study its other theoretical properties.Based on the new correlation,we further propose a robust model-free feature screening procedure for ultrahigh dimensional data and establish its sure screening property and rank consistency property without imposing the subexponential or sub-Gaussian tail condition,which is commonly required in the literature of feature screening.We also examine the finite sample performance of the proposed robust feature screening procedure via Monte Carlo simulation studies and illustrate the proposed procedure by a real data example.

Theoretical perspective on synthetic man-made life:Learning from the origin of life

Creating a man-made life in the laboratory is one of life science's most intriguing yet challenging problems.Advances in synthetic biology and related theories,particularly those related to the origin of life,have laid the groundwork for further exploration and understanding in this field of artificial life or man-made life.But there remains a wealth of quantitative mathematical models and tools that have yet to be applied to this area.In this paper,we review the two main approaches often employed in the field of man-made life:the top-down approach that reduces the complexity of extant and existing living systems and the bottom-up approach that integrates welldefined components,by introducing the theoretical basis,recent advances,and their limitations.We then argue for another possible approach,namely"bottom-up from the origin of life":Starting with the establishment of autocatalytic chemical reaction networks that employ physical boundaries as the initial compartments,then designing directed evolutionary systems,with the expectation that independent compartments will eventually emerge so that the system becomes free-living.This approach is actually analogous to the process of how life originated.With this paper,we aim to stimulate the interest of synthetic biologists and experimentalists to consider a more theoretical perspective,and to promote the communication between the origin of life community and the synthetic man-made life community.