def err_computing(nlp,nn,ni,D_ftr,sgma0,lamda0):
### the error for ridge regression
err_pres = np.zeros(nlp)
### the error for the rff
err_rffs = np.zeros(nlp)
### the error difference for the two regression
err_pre_rffs = np.zeros(nlp)
for num in range(nlp):
### generating data
xs,ys,xt,yt =dat_gen(nn,ni)
### run xvalidation
kernel = GaussianKernel(sgma0)
lamda_pre, width_pre = kernel.xvalidate(xs,ys,method="ridge_regress")
kernel.rff_generate(D_ftr)
lamda_rff,width_rff = kernel.xvalidate(xs,ys,method="ridge_regress_rff")
### perform ridge regression
y_pre, err_pre0 = err_pre(xs,ys,xt,yt,width_pre,lamda_pre)
err_pres[num] = err_pre0
### perform random fourier features
y_rff, err_rff0 = err_rff(xs,ys,xt,yt,width_rff,lamda_rff,D_ftr)
err_rffs[num] = err_rff0
### comparing the difference between two predictions
err_pre_rffs[num] = np.linalg.norm(y_pre-y_rff)**2/ni
### the mean square error for ridge regression
mse_pre = np.mean(err_pres)
### the mean square error for rff
mse_rff = np.mean(err_rffs)
### the mean square error for the difference between ridge and rff
mse_pre_rff = np.mean(err_pre_rffs)
results = np.array([mse_pre,mse_rff,mse_pre_rff])
return results
def ridge_error(nlp, nn, ni, sgma=1.0):
mse_pres = np.zeros(nlp)
for ii in np.arange(nlp):
x_tr, y_tr, x_tt, y_tt = dat_gen(nn, ni)
kernel = GaussianKernel(float(sgma))
lamda_pre, width_pre = kernel.xvalidate(x_tr,
y_tr,
method="ridge_regress")
mse_pres[ii] = err_pre(x_tr, y_tr, x_tt, y_tt, width_pre, lamda_pre)
mse_pre = np.mean(mse_pres)
return mse_pre
def rff_error(nlp, nn, ni, D, sgma=1.0):
mse_rffs = np.zeros(nlp)
for ii in np.arange(nlp):
x_tr, y_tr, x_tt, y_tt = dat_gen(nn, ni)
kernel = GaussianKernel(float(sgma))
kernel.rff_generate(D)
lamda_rff, width_rff = kernel.xvalidate(x_tr,
y_tr,
method="ridge_regress_rff")
mse_rffs[ii] = err_rff(x_tr, y_tr, x_tt, y_tt, width_rff, lamda_rff, D)
mse_rff = np.mean(mse_rffs)
return mse_rff