Many problems require the selection of a subset variables from full set optimization variables. The computational complexity an exhaustive search over all possible subsets is, however, prohibitively expensive, necessitating more efficient but potentially suboptimal strategies. We focus on sparse variable for generalized Rayleigh quotient and eigenvalue problems. Such often arise in signal proce...

Variable selection is central to high-dimensional data analysis, and various algorithms have been developed. Ideally, a variable algorithm shall be flexible, scalable, with theoretical guarantee, yet most existing cannot attain these properties at the same time. In this article, three-step developed, involving kernel-based estimation of regression function its gradient functions as well hard th...

A new class of Markov chain Monte Carlo (MCMC) algorithms, based on simulating piecewise deterministic processes (PDMPs), has recently shown great promise: they are nonreversible, can mix better than standard MCMC and use subsampling ideas to speed up computation in big data scenarios. However, current PDMP samplers only sample from posterior densities that differentiable almost everywhere, whi...