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规则格点上的稀疏加性回归AI 解读

Summary We consider estimation in a sparse additive regression model with the design points on a regular lattice. We establish the minimax convergence rates over Sobolev classes and propose a Fourier-based rate optimal estimator which is adaptive to the unknown sparsity and smoothness of the response function. The estimator is derived within a Bayesian formalism but can be naturally viewed as a penalized maximum likelihood estimator with the complexity penalties on the…

正态均值问题中贝叶斯检验与估计结合方法的最优性AI 解读

We consider a problem of recovering a high-dimensional vector μ observed in white noise, where the unknown vector μ is assumed to be sparse. The objective of the paper is to develop a Bayesian formalism which gives rise to a family of l0-type penalties. The penalties are associated with various choices of the prior distributions πn(⋅) on the number of nonzero entries of μ and, hence, are easy to interpret. The resulting Bayesian estimators lead to a general thresholding rule…

通过控制错误发现率适应未知稀疏性AI 解读

We attempt to recover an n-dimensional vector observed in white noise, where n is large and the vector is known to be sparse, but the degree of sparsity is unknown. We consider three different ways of defining sparsity of a vector: using the fraction of nonzero terms; imposing power-law decay bounds on the ordered entries; and controlling the ℓp norm for p small. We obtain a procedure which is asymptotically minimax for ℓr loss, simultaneously throughout a range of such…