Implementation of accelerated gradient algorithm with strong rules for (high-dimensional) nonconvex sparse learning problems. Restarting, memory-mapping, and multiprocessing are now available.
Project description
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 andgamma
for MCP; it is recommended fora
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 thatlambda_
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 likeUAG_LM_SCAD_MCP
,UAG_logistic_SCAD_MCP
-- except they use strong rule to filter out many covariates before carrying out the optimization step. Same forsolution_path_LM_strongrule
andsolution_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
andmemmap_lambda_max_logistic
calculate the least values for \lambda to vanish all penalized coefficients.memmap_UAG_LM_SCAD_MCP
,memmap_UAG_logisitc_SCAD_MCP
, andmemmap_solution_path_LM
,memmap_solution_path_LM
work similar to the non-memorymapping version of the function. For memory mapping versions of the functions, thedesign_matrix
orX
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 asmemmap_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 argumentcore_num
can be used to declare the cores to be used -- if not decalred, it will use all the cores.
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