Autotune: fast, accurate, and automatic tuning parameter selection for Lasso

Least absolute shrinkage and selection operator (Lasso), a popular method for high-dimensional regression, is now used widely for estimating high-dimensional time series models such as the vector autoregression (VAR). Selecting its tuning parameter efficiently and accurately remains a challenge, despite the abundance of available methods for doing so. We propose autotune, a strategy for Lasso to automatically tune itself by optimizing a penalized Gaussian log-likelihood alternately over regression coefficients and noise standard deviation. Using extensive simulation experiments on regression and VAR models, we show that autotune is faster, and provides better generalization and model selection than established alternatives in low signal-to-noise regimes. In the process, autotune provides a new estimator of noise standard deviation that can be used for high-dimensional inference, and a new visual diagnostic procedure for checking the sparsity assumption on regression coefficients. Finally, we demonstrate the utility of autotune on a real-world financial data set. An R package based on C++ is also made publicly available on Github.