Source code for naginterfaces.​library.​examples.​correg.​ridge_opt_ex

#!/usr/bin/env python
"``naginterface.library.correg.ridge_opt`` Python Example."

# NAG Copyright 2017-2019.

# pylint: disable=invalid-name

from naginterfaces.library import correg

[docs]def main(): """ Example for :func:`naginterfaces.library.correg.ridge_opt`. Ridge regression, optimizing a ridge regression parameter. >>> main() naginterfaces.library.correg.ridge_opt Python Example Results. Ridge regression optimizing GCV prediction error for a body fat model. Value of ridge parameter: 0.0712 Sum of squares of residuals: 1.0917e+02 Degrees of freedom: 16 Number of effective parameters: 2.9059 Parameter estimates 1 20.1950 2 9.7934 3 9.9576 4 -2.0125 Number of iterations: 6 Ridge parameter minimises GCV Estimated prediction errors: GCV = 7.4718 UEV = 6.3862 FPE = 7.3141 BIC = 8.2380 LOO CV = 7.5495 Residuals 1 -1.9894 2 3.5469 3 -3.0392 4 -3.0309 5 -0.1899 6 -0.3146 7 0.9775 8 4.0157 9 2.5332 10 -2.3560 11 0.5446 12 2.3989 13 -4.0876 14 3.2778 15 0.2894 16 0.7330 17 -0.7116 18 -0.6092 19 -2.9995 20 1.0110 Variance inflation factors 1 0.2928 2 0.4162 3 0.8089 """ print('naginterfaces.library.correg.ridge_opt Python Example Results.') print( 'Ridge regression optimizing GCV prediction error ' 'for a body fat model.' ) # The independent variables: x = [ [19.5, 43.1, 29.1], [24.7, 49.8, 28.2], [30.7, 51.9, 37.0], [29.8, 54.3, 31.1], [19.1, 42.2, 30.9], [25.6, 53.9, 23.7], [31.4, 58.5, 27.6], [27.9, 52.1, 30.6], [22.1, 49.9, 23.2], [25.5, 53.5, 24.8], [31.1, 56.6, 30.0], [30.4, 56.7, 28.3], [18.7, 46.5, 23.0], [19.7, 44.2, 28.6], [14.6, 42.7, 21.3], [29.5, 54.4, 30.1], [27.7, 55.3, 25.7], [30.2, 58.6, 24.6], [22.7, 48.2, 27.1], [25.2, 51.0, 27.5], ] # The inclusions: isx = [1]*len(x[0]) # The dependent variable: y = [ 11.9, 22.8, 18.7, 20.1, 12.9, 21.7, 27.1, 25.4, 21.3, 19.3, 25.4, 27.2, 11.7, 17.8, 12.8, 23.9, 22.6, 25.4, 14.8, 21.1, ] # The optimization starting point: h = 0.5 # The prediction-error mode (GCV): opt = 1 # The iteration limit: niter = 25 # The termination tolerance: tol = 1.e-4 # Calculate parameter estimates for the standardized data: orig = 2 # Calculate leave-one-out cross-validation estimate: optloo = 2 regn = correg.ridge_opt( x, isx, y, h, opt, niter, tol, orig, optloo, ) print('Value of ridge parameter: {:10.4f}'.format(regn.h)) print('Sum of squares of residuals: {:11.4e}'.format(regn.rss)) print('Degrees of freedom: {:d}'.format(regn.df)) print('Number of effective parameters: {:10.4f}'.format(regn.nep)) print('Parameter estimates') for i, b_i in enumerate(regn.b): print('{:d} {:11.4f}'.format(i+1, b_i)) print('Number of iterations: {:d}'.format(regn.niter)) print('Ridge parameter minimises GCV') print('Estimated prediction errors:') print('GCV = {:10.4f}'.format(regn.perr[0])) print('UEV = {:10.4f}'.format(regn.perr[1])) print('FPE = {:10.4f}'.format(regn.perr[2])) print('BIC = {:10.4f}'.format(regn.perr[3])) print('LOO CV = {:10.4f}'.format(regn.perr[4])) print('Residuals') for i, r_i in enumerate(regn.res): print('{:d} {:11.4f}'.format(i+1, r_i)) print('Variance inflation factors') for i, v_i in enumerate(regn.vif): print('{:d} {:11.4f}'.format(i+1, v_i))
if __name__ == '__main__': import doctest import sys sys.exit( doctest.testmod( None, verbose=True, report=False, optionflags=doctest.REPORT_NDIFF, ).failed )