def statistics_mmd_kernel_selection_single(m,distance,stretch,num_blobs,angle,selection_method):
from modshogun import RealFeatures
from modshogun import GaussianBlobsDataGenerator
from modshogun import GaussianKernel, CombinedKernel
from modshogun import LinearTimeMMD
from modshogun import MMDKernelSelectionMedian
from modshogun import MMDKernelSelectionMax
from modshogun import MMDKernelSelectionOpt
from modshogun import PERMUTATION, MMD1_GAUSSIAN
from modshogun import EuclideanDistance
from modshogun import Statistics, Math
# init seed for reproducability
Math.init_random(1)
# note that the linear time statistic is designed for much larger datasets
# results for this low number will be bad (unstable, type I error wrong)
m=1000
distance=10
stretch=5
num_blobs=3
angle=pi/4
# streaming data generator
gen_p=GaussianBlobsDataGenerator(num_blobs, distance, 1, 0)
gen_q=GaussianBlobsDataGenerator(num_blobs, distance, stretch, angle)
# stream some data and plot
num_plot=1000
features=gen_p.get_streamed_features(num_plot)
features=features.create_merged_copy(gen_q.get_streamed_features(num_plot))
data=features.get_feature_matrix()
#figure()
#subplot(2,2,1)
#grid(True)
#plot(data[0][0:num_plot], data[1][0:num_plot], 'r.', label='$x$')
#title('$X\sim p$')
#subplot(2,2,2)
#grid(True)
#plot(data[0][num_plot+1:2*num_plot], data[1][num_plot+1:2*num_plot], 'b.', label='$x$', alpha=0.5)
#title('$Y\sim q$')
# create combined kernel with Gaussian kernels inside (shoguns Gaussian kernel is
# different to the standard form, see documentation)
sigmas=[2**x for x in range(-3,10)]
widths=[x*x*2 for x in sigmas]
combined=CombinedKernel()
for i in range(len(sigmas)):
combined.append_kernel(GaussianKernel(10, widths[i]))
# mmd instance using streaming features, blocksize of 10000
block_size=1000
mmd=LinearTimeMMD(combined, gen_p, gen_q, m, block_size)
# kernel selection instance (this can easily replaced by the other methods for selecting
# single kernels
if selection_method=="opt":
selection=MMDKernelSelectionOpt(mmd)
elif selection_method=="max":
selection=MMDKernelSelectionMax(mmd)
elif selection_method=="median":
selection=MMDKernelSelectionMedian(mmd)
# print measures (just for information)
# in case Opt: ratios of MMD and standard deviation
# in case Max: MMDs for each kernel
# Does not work for median method
if selection_method!="median":
ratios=selection.compute_measures()
#print "Measures:", ratios
#subplot(2,2,3)
#plot(ratios)
#title('Measures')
# perform kernel selection
kernel=selection.select_kernel()
kernel=GaussianKernel.obtain_from_generic(kernel)
#print "selected kernel width:", kernel.get_width()
# compute tpye I and II error (use many more trials). Type I error is only
# estimated to check MMD1_GAUSSIAN method for estimating the null
# distribution. Note that testing has to happen on difference data than
# kernel selecting, but the linear time mmd does this implicitly
mmd.set_kernel(kernel)
mmd.set_null_approximation_method(MMD1_GAUSSIAN)
# number of trials should be larger to compute tight confidence bounds
num_trials=5;
alpha=0.05 # test power
typeIerrors=[0 for x in range(num_trials)]
typeIIerrors=[0 for x in range(num_trials)]
for i in range(num_trials):
# this effectively means that p=q - rejecting is tpye I error
mmd.set_simulate_h0(True)
typeIerrors[i]=mmd.perform_test()>alpha
mmd.set_simulate_h0(False)
typeIIerrors[i]=mmd.perform_test()>alpha
#print "type I error:", mean(typeIerrors), ", type II error:", mean(typeIIerrors)
return kernel,typeIerrors,typeIIerrors
