Xingguo Li — Software

Description: Computationally efficient tools for fitting generalized linear model with convex or non-convex penalty. Users can enjoy the superior statistical property of non-convex penalty such as SCAD and MCP which has significantly less estimation error and overfitting compared to convex penalty such as lasso and ridge. Computation is handled by multi-stage convex relaxation and the PathwIse CAlibrated Sparse Shooting algOrithm (PICASSO) which exploits warm start initialization, active set updating, and strong rule for coordinate preselection to boost computation, and attains a linear convergence to a unique sparse local optimum with optimal statistical properties. The computation is memory-optimized using the sparse matrix output.

Description: Provide the implementation of a family of Lasso variants including Dantzig Selector, LAD Lasso, SQRT Lasso, Lq Lasso for estimating high dimensional sparse linear model. We adopt the alternating direction method of multipliers and convert the original optimization problem into a sequential L1 penalized least square minimization problem, which can be efficiently solved by linearization algorithm. A multi-stage screening approach is adopted for further acceleration. Besides the sparse linear model estimation, we also provide the extension of these Lasso variants to sparse Gaussian graphical model estimation including TIGER and CLIME using either L1 or adaptive penalty. Missing values can be tolerated for Dantzig selector and CLIME. The computation is memory-optimized using the sparse matrix output.

Description: Provide a general framework for high-dimensional undirected graph estimation. It integrates data preprocessing, neighborhood screening, graph estimation, and model selection techniques into a pipeline. In preprocessing stage, the nonparanormal(npn) transformation is applied to help relax the normality assumption. In the graph estimation stage, the graph structure is estimated by Meinshausen-Buhlmann graph estimation or the graphical lasso, and both methods can be further accelerated by the lossy screening rule preselecting the neighborhood of each variable by correlation thresholding. We target on high-dimensional data analysis usually d >> n, and the computation is memory-optimized using the sparse matrix output. We also provide a computationally efficient approach, correlation thresholding graph estimation. Three regularization/thresholding parameter selection methods are included in this package: (1)stability approach for regularization selection (2) rotation information criterion (3) extended Bayesian information criterion which is only available for the graphical lasso.