Our approach uses the Kac-Rice formula (as described in Adler & Taylor 2007) applied to the problem of maximizing a Gaussian process. The resulting test statistic has a known distribution in finite samples, assuming Gaussian errors. We examine this test statistic in the case of the lasso, ...
Group LassoBridge regressionGroup bridge regressionSplice detection•We prove that group-wise ℓp-regularization has algorithmic stability and thus generalizes.•We derive ADMM and FISTA algorithms for solving group-wise ℓp-regularization.•We show that for p=5/4, 4/3, 3/2 and 2 the ...
Regularized LR includes ridge regression (RR) by applying L2-norm, lasso regression (LAR) by applying L1-norm, lasso regression by applying L2-norm, and elastic net (EN) by applying L1-norm and L2-norm simultaneously, according to the shrinkage penalty function applied to the cost function. ...