def statistics_quadratic_time_mmd(m, dim, difference):
from modshogun import RealFeatures
from modshogun import MeanShiftDataGenerator
from modshogun import GaussianKernel, CustomKernel
from modshogun import QuadraticTimeMMD
from modshogun import BOOTSTRAP, MMD2_SPECTRUM, MMD2_GAMMA, BIASED, UNBIASED
from modshogun import Statistics, IntVector, RealVector, Math
# init seed for reproducability
Math.init_random(1)
random.seed(17)
# number of examples kept low in order to make things fast
# streaming data generator for mean shift distributions
gen_p = MeanShiftDataGenerator(0, dim)
#gen_p.parallel.set_num_threads(1)
gen_q = MeanShiftDataGenerator(difference, dim)
# stream some data from generator
feat_p = gen_p.get_streamed_features(m)
feat_q = gen_q.get_streamed_features(m)
# set kernel a-priori. usually one would do some kernel selection. See
# other examples for this.
width = 10
kernel = GaussianKernel(10, width)
# create quadratic time mmd instance. Note that this constructor
# copies p and q and does not reference them
mmd = QuadraticTimeMMD(kernel, feat_p, feat_q)
# perform test: compute p-value and test if null-hypothesis is rejected for
# a test level of 0.05
alpha = 0.05
# using bootstrapping (slow, not the most reliable way. Consider pre-
# computing the kernel when using it, see below).
# Also, in practice, use at least 250 iterations
mmd.set_null_approximation_method(BOOTSTRAP)
mmd.set_bootstrap_iterations(3)
p_value_boot = mmd.perform_test()
# reject if p-value is smaller than test level
#print "bootstrap: p!=q: ", p_value_boot<alpha
# using spectrum method. Use at least 250 samples from null.
# This is consistent but sometimes breaks, always monitor type I error.
# See tutorial for number of eigenvalues to use .
# Only works with BIASED statistic
mmd.set_statistic_type(BIASED)
mmd.set_null_approximation_method(MMD2_SPECTRUM)
mmd.set_num_eigenvalues_spectrum(3)
mmd.set_num_samples_sepctrum(250)
p_value_spectrum = mmd.perform_test()
# reject if p-value is smaller than test level
#print "spectrum: p!=q: ", p_value_spectrum<alpha
# using gamma method. This is a quick hack, which works most of the time
# but is NOT guaranteed to. See tutorial for details.
# Only works with BIASED statistic
mmd.set_statistic_type(BIASED)
mmd.set_null_approximation_method(MMD2_GAMMA)
p_value_gamma = mmd.perform_test()
# reject if p-value is smaller than test level
#print "gamma: p!=q: ", p_value_gamma<alpha
# compute tpye I and II error (use many more trials in practice).
# Type I error is not necessary if one uses bootstrapping. We do it here
# anyway, but note that this is an efficient way of computing it.
# Also note that testing has to happen on
# difference data than kernel selection, but the linear time mmd does this
# implicitly and we used a fixed kernel here.
mmd.set_null_approximation_method(BOOTSTRAP)
mmd.set_bootstrap_iterations(5)
num_trials = 5
type_I_errors = RealVector(num_trials)
type_II_errors = RealVector(num_trials)
inds = int32(array([x for x in range(2 * m)])) # numpy
p_and_q = mmd.get_p_and_q()
# use a precomputed kernel to be faster
kernel.init(p_and_q, p_and_q)
precomputed = CustomKernel(kernel)
mmd.set_kernel(precomputed)
for i in range(num_trials):
# this effectively means that p=q - rejecting is tpye I error
inds = random.permutation(inds) # numpy permutation
precomputed.add_row_subset(inds)
precomputed.add_col_subset(inds)
type_I_errors[i] = mmd.perform_test() > alpha
precomputed.remove_row_subset()
precomputed.remove_col_subset()
# on normal data, this gives type II error
type_II_errors[i] = mmd.perform_test() > alpha
return type_I_errors.get(), type_I_errors.get(
), p_value_boot, p_value_spectrum, p_value_gamma,
def statistics_quadratic_time_mmd (m,dim,difference): from modshogun import RealFeatures from modshogun import MeanShiftDataGenerator from modshogun import GaussianKernel, CustomKernel from modshogun import QuadraticTimeMMD from modshogun import PERMUTATION, MMD2_SPECTRUM, MMD2_GAMMA, BIASED, BIASED_DEPRECATED from modshogun import Statistics, IntVector, RealVector, Math # init seed for reproducability Math.init_random(1) random.seed(17) # number of examples kept low in order to make things fast # streaming data generator for mean shift distributions gen_p=MeanShiftDataGenerator(0, dim); #gen_p.parallel.set_num_threads(1) gen_q=MeanShiftDataGenerator(difference, dim); # stream some data from generator feat_p=gen_p.get_streamed_features(m); feat_q=gen_q.get_streamed_features(m); # set kernel a-priori. usually one would do some kernel selection. See # other examples for this. width=10; kernel=GaussianKernel(10, width); # create quadratic time mmd instance. Note that this constructor # copies p and q and does not reference them mmd=QuadraticTimeMMD(kernel, feat_p, feat_q); # perform test: compute p-value and test if null-hypothesis is rejected for # a test level of 0.05 alpha=0.05; # using permutation (slow, not the most reliable way. Consider pre- # computing the kernel when using it, see below). # Also, in practice, use at least 250 iterations mmd.set_null_approximation_method(PERMUTATION); mmd.set_num_null_samples(3); p_value_null=mmd.perform_test(); # reject if p-value is smaller than test level #print "bootstrap: p!=q: ", p_value_null<alpha # using spectrum method. Use at least 250 samples from null. # This is consistent but sometimes breaks, always monitor type I error. # See tutorial for number of eigenvalues to use . mmd.set_statistic_type(BIASED); mmd.set_null_approximation_method(MMD2_SPECTRUM); mmd.set_num_eigenvalues_spectrum(3); mmd.set_num_samples_spectrum(250); p_value_spectrum=mmd.perform_test(); # reject if p-value is smaller than test level #print "spectrum: p!=q: ", p_value_spectrum<alpha # using gamma method. This is a quick hack, which works most of the time # but is NOT guaranteed to. See tutorial for details. # Only works with BIASED_DEPRECATED statistic mmd.set_statistic_type(BIASED_DEPRECATED); mmd.set_null_approximation_method(MMD2_GAMMA); p_value_gamma=mmd.perform_test(); # reject if p-value is smaller than test level #print "gamma: p!=q: ", p_value_gamma<alpha # compute tpye I and II error (use many more trials in practice). # Type I error is not necessary if one uses permutation. We do it here # anyway, but note that this is an efficient way of computing it. # Also note that testing has to happen on # difference data than kernel selection, but the linear time mmd does this # implicitly and we used a fixed kernel here. mmd.set_statistic_type(BIASED); mmd.set_null_approximation_method(PERMUTATION); mmd.set_num_null_samples(5); num_trials=5; type_I_errors=RealVector(num_trials); type_II_errors=RealVector(num_trials); inds=int32(array([x for x in range(2*m)])) # numpy p_and_q=mmd.get_p_and_q(); # use a precomputed kernel to be faster kernel.init(p_and_q, p_and_q); precomputed=CustomKernel(kernel); mmd.set_kernel(precomputed); for i in range(num_trials): # this effectively means that p=q - rejecting is tpye I error inds=random.permutation(inds) # numpy permutation precomputed.add_row_subset(inds); precomputed.add_col_subset(inds); type_I_errors[i]=mmd.perform_test()>alpha; precomputed.remove_row_subset(); precomputed.remove_col_subset(); # on normal data, this gives type II error type_II_errors[i]=mmd.perform_test()>alpha; return type_I_errors.get(),type_I_errors.get(),p_value_null,p_value_spectrum,p_value_gamma,
