nonconvexAG 1.0.0

Implementation of accelerated gradient algorithm with strong rules for (high-dimensional) nonconvex sparse learning problems. Restarting, memory-mapping, and multiprocessing are now available.

nonconvexAG

This is an implementation of restarting accelerated gradient algorithm with strong rules for (high-dimensional) nonconvex sparse learning problems. The corresponding paper can be found at arXiv.

The available functions are:

• UAG_LM_SCAD_MCP, UAG_logistic_SCAD_MCP: these functions find a local minizer for the SCAD/MCP penalized linear models/logistic models. The arguments are: * design_matrix: the design matrix input, should be a two-dimensional numpy array; * outcome: the outcome, should be one dimensional numpy array, continuous for linear model, binary for logistic model; * beta_0: starting value; optional, if not declared, it will be calculated based on the Gauss-Markov theory estimators of $\beta$; * tol: tolerance parameter; the tolerance parameter is set to be the uniform norm of two iterations; * maxit: maximum number of iteratios allowed; * _lambda: _lambda value; * penalty: could be "SCAD" or "MCP"; * a=3.7, gamma=2: a for SCAD and gamma for MCP; it is recommended for a to be set as $3.7$; * L_convex: the L-smoothness constant for the convex component, if not declared, it will be calculated by itself * add_intercept_column: boolean, should the fucntion add an intercept column?

• solution_path_LM, solution_path_logistic: calculate the solution path for linear/logistic models; the only difference from above is that lambda_ is now a one-dimensional numpy array for the values of $\lambda$ to be used.

• UAG_LM_SCAD_MCP_strongrule, UAG_logistic_SCAD_MCP_strongrule work just like UAG_LM_SCAD_MCP, UAG_logistic_SCAD_MCP -- except they use strong rule to filter out many covariates before carrying out the optimization step. Same for solution_path_LM_strongrule and solution_path_logistic_strongrule. Strong rule increases the computational speed dramatically.

• The package also offers implementation of certain features using memory mapping. memmap_lambda_max_LM and memmap_lambda_max_logistic calculate the least values for \lambda to vanish all penalized coefficients. memmap_UAG_LM_SCAD_MCP, memmap_UAG_logisitc_SCAD_MCP, and memmap_solution_path_LM, memmap_solution_path_LM work similar to the non-memorymapping version of the function. For memory mapping versions of the functions, the design_matrix or X parameter should declare the path of the memorymapped file, and _dtype='float32' declares the data type, _order declares the order of the memorymapped files ("F" for Fortran or "C" for C++). Multiprocess with memory mapping is also available as memmap_lambda_max_LM_parallel, memmap_lambda_max_logistic_parallel, memmap_UAG_LM_SCAD_MCP_parallel, memmap_UAG_logistic_SCAD_MCP_parallel, memmap_solution_path_LM_parallel, memmap_solution_path_logistic_parallel -- for these functions, an extra argument core_num can be used to declare the cores to be used -- if not decalred, it will use all the cores.