Xingguo Li, Tuo Zhao, Tong Zhang and Han Liu
Implements the pathwise calibrated sparse shooting algorithm (PICASSO) for high dimensional regularized sparse linear regression, sparse logistic regression, and sparse undirected graphical model estimation. As a pathwise coordinate optimization algorithm, PICASSO 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. Moreover, users can choose different regularizers, including L1, MCP, and SCAD regularizers. The computation is memory-optimized using the sparse matrix output.

Jason Ge, Xingguo Li, Mengdi Wang, Tong Zhang, Han Liu and Tuo Zhao
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.

Computationally efficient tools for fitting generalized linear models and square root loss 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.