Tuning Parameters in High-Dimensional Statistics
High-dimensional statistics is the basis for analyzing large and complex data sets that are generated by cutting-edge technologies in genetics, neuroscience, astronomy, and many other fields. However, Lasso, Ridge Regression, Graphical Lasso, and other standard methods in high-dimensional statistics depend on tuning parameters that are difficult to calibrate in practice. In this talk, I present two novel approaches to overcome this difficulty. My first approach is based on a novel testing scheme that is inspired by Lepskiâ€™s idea for bandwidth selection in non-parametric statistics. This approach provides tuning parameter calibration for estimation and prediction with the Lasso and other standard methods and is to date the only way to ensure high performance, fast computations, and optimal finite sample guarantees. My second approach is based on the minimization of an objective function that avoids tuning parameters altogether. This approach provides accurate variable selection in regression settings and, additionally, opens up new possibilities for the estimation of gene regulation networks, microbial ecosystems, and many other network structures.