Researchers propose using a $q$Gaussian distribution derived from Tsallis entropy maximization as an alternative to Gaussian models in statistical sparse learning. This approach is more robust and efficient when dealing with correlated data, which is common in biostatistics. The authors also introduce a novel framework for composite optimization problems, adapting numerical methods to find equilibria in flows. They apply this framework to the Hager-Zhang conjugate gradient algorithm, resulting in a numerically stable and efficient algorithm for sparse statistical learning. --- Why it matters: This research matters because it provides a more robust alternative to Gaussian models, which often struggle with outliers and correlated data. The proposed $q$Gaussian distribution and novel optimization framework can improve the accuracy of statistical sparse learning in fields like biostatistics. Source: https://arxiv.org/abs/2608.17244