Abstract: In previous work we introduced principal surfaces as hyperridges of probability distributions in a differential geometrical sense. Specifically, given an n-dimensional probability ...

We consider efficient construction of nonlinear solution paths for general l₁-regularization. Unlike the existing methods that incrementally build the solution path through a combination of local ...

The problem of local linear approximation to a curved boundary using gridded data is closely connected to both curve estimation methods in statistics and rational approximation in number theory. The ...