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Abstract: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 $\mathsf{autotune}$, 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 $\mathsf{autotune}$ is faster, and provides better generalization and model selection than established alternatives in low signal-to-noise regimes. In the process, $\mathsf{autotune}$ 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 $\mathsf{autotune}$ on a real-world financial data set. An R package based on C++ is also made publicly available on Github.

Submission history

From: Tathagata Sadhukhan [view email]
[v1] Thu, 11 Dec 2025 22:00:12 UTC (2,749 KB)
[v2] Mon, 15 Dec 2025 18:16:42 UTC (2,776 KB)
[v3] Fri, 28 Aug 2026 17:41:34 UTC (2,962 KB)