text: 268,24,1322211983161094145,29000998,Debashis Ghosh,"For the statisticians in the audience, wanted to quickly discuss a new paper: <LINK> This deals with a field called sufficient dimension reduction.   It started in the 1980s and 1990s and had this seemingly restrictive condition called the linearity condition. Lots of methods were developed in the 1990s and early 2000s for sufficient dimension reduction (SDR). They required the linearity condition.  More recently, people have moved into nonlinear SDR methods, primarily using kernels, which are popular in support vector machines. Our paper shows that the linearity condition induces kernels just like those in the nonlinear SDR literature. This involves using 100-year old math results (my favorite kind). This is joint work with my co-author Youngjoo Cho (not on Twitter), who is at the University of Texas, El Paso.",https://arxiv.org/abs/2010.15009,"There has been a lot of interest in sufficient dimension reduction (SDR) methodologies as well as nonlinear extensions in the statistics literature. In this note, we use classical results regarding metric spaces and positive definite functions to link linear SDR procedures to their nonlinear counterparts. ",Bridging linearity-based and kernel-based sufficient dimension reduction,5,"['For the statisticians in the audience, wanted to quickly discuss a new paper: <LINK>', 'This deals with a field called sufficient dimension reduction.     It started in the 1980s and 1990s and had this seemingly restrictive condition called the linearity condition.', 'Lots of methods were developed in the 1990s and early 2000s for sufficient dimension reduction (SDR).  They required the linearity condition.    More recently, people have moved into nonlinear SDR methods, primarily using kernels, which are popular in support vector machines.', 'Our paper shows that the linearity condition induces kernels just like those in the nonlinear SDR literature.  This involves using 100-year old math results (my favorite kind).', 'This is joint work with my co-author Youngjoo Cho (not on Twitter), who is at the University of Texas, El Paso.']",20,10,822