MI-AG 0.9.5.9

Use mutual information and accelerated gradient method to filter out and optimize nonconvex sparse learning problems on large genetic data based on bed/bim/fam. Multiprocessing is now available.

MI_AG

This packages uses mutual information and accelerated gradient method to screen for SNPs and optimize the nonconvex sparse learning problem on large genetic data based on bed/bim/fam files. The corresponding paper by Yang et al. is coming soon...

The available functions are:

• continuous_filter caculates the mutual information between a continuous outcome and a bialletic SNP using FFT. Missing data is acceptable and will be removed. The arguments are:

  • bed_file, bim_file, fam_file are the location of the plink1 files;
  • outcome, outcome_iid are the outcome values and the iids for the outcome. For genetic data, it is usual that the order of SNP iid and the outcome iid don't match. While SNP iid can be obtained from the plink1 files, outcome iid here is to be declared separately. outcome_iid should be a list of strings or a one-dimensional numpy string array.
  • a_min, a_max are the minimum and maximum of the continous outcome used to evaluate the support; N=500 is the default values for grid size for FFT.

• binary_filter works similarly, execpt that a_min, a_max, N are not available obviously.

• continuous_filter_parallel and binary_filter_parallel are the multiprocessing version of the above two functions, with core_num can be used to declare the number of cores to be used for multiprocessing.

• 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.

• SNP_UAG_LM_SCAD_MCP and SNP_UAG_logistic_SCAD_MCP work similar to UAG_LM_SCAD_MCP and UAG_logistic_SCAD_MCP; and SNP_solution_path_LM and SNP_solution_path_logistic work similar to solution_path_LM, solution_path_logistic -- except that it takes plink1 files so it will be more memory-efficient. Since PCA adjustment is usually used to adjust for population structure, PCA can be given for pca as a 2-d array -- each column should be one principal component. The pca version is SNP_UAG_LM_SCAD_MCP_PCA and SNP_UAG_logistic_SCAD_MCP_PCA.