smoothedLasso: Smoothed LASSO Regression via Nesterov Smoothing

We provide full functionality to compute smoothed LASSO regression estimates. For this, the LASSO objective function is first smoothed using Nesterov smoothing (see Y. Nesterov (2005) <doi:10.1007/s10107-004-0552-5>), resulting in a modified LASSO objective function with explicit gradients everywhere. The smoothed objective function and its gradient are used to minimize it via BFGS, and the obtained minimizer is returned. Using Nesterov smoothing, the smoothed LASSO objective function can be made arbitrarily close to the original (unsmoothed) one. In particular, the Nesterov approach has the advantage that it comes with explicit accuracy bounds, both on the L1/L2 difference of the unsmoothed to the smoothed LASSO objective function as well as on their respective minimizers. A progressive smoothing approach is provided which iteratively smoothes the LASSO, resulting in more stable regression estimates.

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