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A lava attack on the recovery of sums of dense and sparse signals. (arXiv:1502.03155v2 [stat.ME] CROSS LISTED)
来源于:arXiv
Common high-dimensional methods for prediction rely on having either a sparse
signal model, a model in which most parameters are zero and there are a small
number of non-zero parameters that are large in magnitude, or a dense signal
model, a model with no large parameters and very many small non-zero
parameters. We consider a generalization of these two basic models, termed here
a "sparse+dense" model, in which the signal is given by the sum of a sparse
signal and a dense signal. Such a structure poses problems for traditional
sparse estimators, such as the lasso, and for traditional dense estimation
methods, such as ridge estimation. We propose a new penalization-based method,
called lava, which is computationally efficient. With suitable choices of
penalty parameters, the proposed method strictly dominates both lasso and
ridge. We derive analytic expressions for the finite-sample risk function of
the lava estimator in the Gaussian sequence model. We also provide an deviation
bound fo 查看全文>>