We study the classic problem of choosing a prior distribution for a location parameter β = (β1, . . . , βp) as p grows large. First, we study the standard “global-local shrinkage” approach, based on scale mixtures of normals. Two theorems are presented which characterize certain desirable properties of shrinkage priors for sparse problems. Next, we review some recent results showing how Lévy pr...

We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on the nonparametric component and shrinkage penalty on the parametric components, which can achieve function smoothing and sparse estimation simultaneously. We e...

This article proposes an unsupervised method for learning compositional sparse code for representing natural images. Our method is built upon the original sparse coding framework where there is a dictionary of basis functions often in the form of localized, elongated and oriented wavelets, so that each image can be represented by a linear combination of a small number of basis functions automat...

This reports presents new codes for the numerical solutiuon of highly nonlin-ear systems. They realize the most recent variants of aane invariant Newton Techniques due to Deuuhard. The standard method is implemented in the code NLEQ1, whereas the code NLEQ2 contains a rank reduction device additionally. The code NLEQ1S is the sparse version of NLEQ1, i.e. the arising linear systems are solved w...

In guided wave pipeline inspection, echoes reflected from closely spaced reflectors generally overlap, meaning useful information is lost. To solve the overlapping problem, sparse deconvolution methods have been developed in the past decade. However, conventional sparse deconvolution methods have limitations in handling guided wave signals, because the input signal is directly used as the proto...

This paper introduces the factorial marked temporal point process model and presents efficient learning methods. In conventional (multi-dimensional) marked temporal point process models, event is often encoded by a single discrete variable i.e. a marker. In this paper, we describe the factorial marked point processes whereby time-stamped event is factored into multiple markers. Accordingly the ...