Penalized Least Squares Regression: Fast Computation via EÆ ient Approximation

Energy-EÆ ient Deterministi Routing Proto ols in Radio Networks

Smoothing spline Gaussian regression: more scalable computation via efficient approximation

Smoothing splines via the penalized least squares method provide versatile and effective nonparametric models for regression with Gaussian responses. The computation of smoothing splines is generally of the order O.n3/, n being the sample size, which severely limits its practical applicability. We study more scalable computation of smoothing spline regression via certain low dimensional approxi...

A penalty/least-squares method for optimal control problems for first-order elliptic systems

A penalty/least-squares method for optimal control problems for ®rst-order elliptic systems is considered wherein the constraint equations are enforced via penalization. The convergence, as the penalty parameter tends to zero, of the solution to the penalized optimal control problem to that of the unpenalized one is demonstrated as is the convergence of a gradient method for determining solutio...

Aggregation and Sparsity Via l1 Penalized Least Squares

This paper shows that near optimal rates of aggregation and adaptation to unknown sparsity can be simultaneously achieved via `1 penalized least squares in a nonparametric regression setting. The main tool is a novel oracle inequality on the sum between the empirical squared loss of the penalized least squares estimate and a term reflecting the sparsity of the unknown regression function.

Fully 3D PET Image Reconstruction Using A Fourier Preconditioned Conjugate-Gradient Algorithm

the data sizes in fully 3D PET imaging are very iterative image reconstruction algorithms must tge in very few iterations to be useful. One nprove the convergence rate of the conjugate:nt (CG) algorithm by incorporating precondig operators that approximate the inverse of the Ln of the objective function. If the 3D cylindriET geometry were not truncated at the ends, ;he Hessian of the penalized ...