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.Howe...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.展开更多
Simultaneously finding active predictors and controlling the false discovery rate(FDR)for high-dimensional survival data is an important but challenging statistical problem.In this paper,the authors propose a novel va...Simultaneously finding active predictors and controlling the false discovery rate(FDR)for high-dimensional survival data is an important but challenging statistical problem.In this paper,the authors propose a novel variable selection procedure with error rate control for the high-dimensional Cox model.By adopting a data-splitting strategy,the authors construct a series of symmetric statistics and then utilize the symmetry property to derive a data-driven threshold to achieve error rate control.The authors establish finite-sample and asymptotic FDR control results under some mild conditions.Simulation results as well as a real data application show that the proposed approach successfully controls FDR and is often more powerful than the competing approaches.展开更多
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...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.展开更多
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...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.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11971017 and 11971018)Shanghai Rising-Star Program(Grant No.20QA1407500)+1 种基金Multidisciplinary Cross Research Foundation of Shanghai Jiao Tong University(Grant Nos.YG2019QNA26,YG2019QNA37 and YG2021QN06)Neil Shen's SJTU Medical Research Fund of Shanghai Jiao Tong University。
文摘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.
基金supported by the National Natural Science Foundation of China under Grant Nos.12301364,12322112,12071038,11925106,12231011,11931001,12226007,12326325,and 12131006the National Key R&D Program of China under Grant Nos.2022YFA1003703 and 2022YFA1003800+3 种基金the Natural Science Foundation of Anhui Province under Grant No.2308085QA09the Fundamental Research Funds for the Central Universities under Grant No.2243200006the Scientific and Technological Innovation Project of China Academy of Chinese Medical Sciences under Grant No.CI2023C063YLLthe University Grant Council of Hong Kong。
文摘Simultaneously finding active predictors and controlling the false discovery rate(FDR)for high-dimensional survival data is an important but challenging statistical problem.In this paper,the authors propose a novel variable selection procedure with error rate control for the high-dimensional Cox model.By adopting a data-splitting strategy,the authors construct a series of symmetric statistics and then utilize the symmetry property to derive a data-driven threshold to achieve error rate control.The authors establish finite-sample and asymptotic FDR control results under some mild conditions.Simulation results as well as a real data application show that the proposed approach successfully controls FDR and is often more powerful than the competing approaches.
基金supported by National Natural Science Foundation of China(Grant No.11701034)supported by National Science Foundation of USA(Grant No.DMS1820702)。
文摘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.
基金National Natural Science Foundation of China,Grant/Award Numbers:12205012,71731002Beijing Normal University via the Youth Talent Strategic Program,Grant/Award Number:28705-310432106Atlas Project of bio-archae by Swarma Research。
文摘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.
