def statistics_hsic(n, difference, angle):
from modshogun import RealFeatures
from modshogun import DataGenerator
from modshogun import GaussianKernel
from modshogun import HSIC
from modshogun import PERMUTATION, HSIC_GAMMA
from modshogun import EuclideanDistance
from modshogun import Statistics, Math
# for reproducable results (the numpy one might not be reproducible across
# different OS/Python-distributions
Math.init_random(1)
np.random.seed(1)
# note that the HSIC has to store kernel matrices
# which upper bounds the sample size
# use data generator class to produce example data
data = DataGenerator.generate_sym_mix_gauss(n, difference, angle)
#plot(data[0], data[1], 'x');show()
# create shogun feature representation
features_x = RealFeatures(np.array([data[0]]))
features_y = RealFeatures(np.array([data[1]]))
# compute median data distance in order to use for Gaussian kernel width
# 0.5*median_distance normally (factor two in Gaussian kernel)
# However, shoguns kernel width is different to usual parametrization
# Therefore 0.5*2*median_distance^2
# Use a subset of data for that, only 200 elements. Median is stable
subset = np.random.permutation(features_x.get_num_vectors()).astype(
np.int32)
subset = subset[0:200]
features_x.add_subset(subset)
dist = EuclideanDistance(features_x, features_x)
distances = dist.get_distance_matrix()
features_x.remove_subset()
median_distance = np.median(distances)
sigma_x = median_distance**2
features_y.add_subset(subset)
dist = EuclideanDistance(features_y, features_y)
distances = dist.get_distance_matrix()
features_y.remove_subset()
median_distance = np.median(distances)
sigma_y = median_distance**2
#print "median distance for Gaussian kernel on x:", sigma_x
#print "median distance for Gaussian kernel on y:", sigma_y
kernel_x = GaussianKernel(10, sigma_x)
kernel_y = GaussianKernel(10, sigma_y)
hsic = HSIC(kernel_x, kernel_y, features_x, features_y)
# perform test: compute p-value and test if null-hypothesis is rejected for
# a test level of 0.05 using different methods to approximate
# null-distribution
statistic = hsic.compute_statistic()
#print "HSIC:", statistic
alpha = 0.05
#print "computing p-value using sampling null"
hsic.set_null_approximation_method(PERMUTATION)
# normally, at least 250 iterations should be done, but that takes long
hsic.set_num_null_samples(100)
# sampling null allows usage of unbiased or biased statistic
p_value_boot = hsic.compute_p_value(statistic)
thresh_boot = hsic.compute_threshold(alpha)
#print "p_value:", p_value_boot
#print "threshold for 0.05 alpha:", thresh_boot
#print "p_value <", alpha, ", i.e. test sais p and q are dependend:", p_value_boot<alpha
#print "computing p-value using gamma method"
hsic.set_null_approximation_method(HSIC_GAMMA)
p_value_gamma = hsic.compute_p_value(statistic)
thresh_gamma = hsic.compute_threshold(alpha)
#print "p_value:", p_value_gamma
#print "threshold for 0.05 alpha:", thresh_gamma
#print "p_value <", alpha, ", i.e. test sais p and q are dependend:", p_value_gamma<alpha
# sample from null distribution (these may be plotted or whatsoever)
# mean should be close to zero, variance stronly depends on data/kernel
# sampling null, biased statistic
#print "sampling null distribution using sample_null"
hsic.set_null_approximation_method(PERMUTATION)
hsic.set_num_null_samples(100)
null_samples = hsic.sample_null()
#print "null mean:", np.mean(null_samples)
#print "null variance:", np.var(null_samples)
#hist(null_samples, 100); show()
return p_value_boot, thresh_boot, p_value_gamma, thresh_gamma, statistic, null_samples
def statistics_hsic (n, difference, angle): from modshogun import RealFeatures from modshogun import DataGenerator from modshogun import GaussianKernel from modshogun import HSIC from modshogun import BOOTSTRAP, HSIC_GAMMA from modshogun import EuclideanDistance from modshogun import Math, Statistics, IntVector # init seed for reproducability Math.init_random(1) # note that the HSIC has to store kernel matrices # which upper bounds the sample size # use data generator class to produce example data data=DataGenerator.generate_sym_mix_gauss(n,difference,angle) #plot(data[0], data[1], 'x');show() # create shogun feature representation features_x=RealFeatures(array([data[0]])) features_y=RealFeatures(array([data[1]])) # compute median data distance in order to use for Gaussian kernel width # 0.5*median_distance normally (factor two in Gaussian kernel) # However, shoguns kernel width is different to usual parametrization # Therefore 0.5*2*median_distance^2 # Use a subset of data for that, only 200 elements. Median is stable subset=IntVector.randperm_vec(features_x.get_num_vectors()) subset=subset[0:200] features_x.add_subset(subset) dist=EuclideanDistance(features_x, features_x) distances=dist.get_distance_matrix() features_x.remove_subset() median_distance=Statistics.matrix_median(distances, True) sigma_x=median_distance**2 features_y.add_subset(subset) dist=EuclideanDistance(features_y, features_y) distances=dist.get_distance_matrix() features_y.remove_subset() median_distance=Statistics.matrix_median(distances, True) sigma_y=median_distance**2 #print "median distance for Gaussian kernel on x:", sigma_x #print "median distance for Gaussian kernel on y:", sigma_y kernel_x=GaussianKernel(10,sigma_x) kernel_y=GaussianKernel(10,sigma_y) hsic=HSIC(kernel_x,kernel_y,features_x,features_y) # perform test: compute p-value and test if null-hypothesis is rejected for # a test level of 0.05 using different methods to approximate # null-distribution statistic=hsic.compute_statistic() #print "HSIC:", statistic alpha=0.05 #print "computing p-value using bootstrapping" hsic.set_null_approximation_method(BOOTSTRAP) # normally, at least 250 iterations should be done, but that takes long hsic.set_bootstrap_iterations(100) # bootstrapping allows usage of unbiased or biased statistic p_value_boot=hsic.compute_p_value(statistic) thresh_boot=hsic.compute_threshold(alpha) #print "p_value:", p_value_boot #print "threshold for 0.05 alpha:", thresh_boot #print "p_value <", alpha, ", i.e. test sais p and q are dependend:", p_value_boot<alpha #print "computing p-value using gamma method" hsic.set_null_approximation_method(HSIC_GAMMA) p_value_gamma=hsic.compute_p_value(statistic) thresh_gamma=hsic.compute_threshold(alpha) #print "p_value:", p_value_gamma #print "threshold for 0.05 alpha:", thresh_gamma #print "p_value <", alpha, ", i.e. test sais p and q are dependend::", p_value_gamma<alpha # sample from null distribution (these may be plotted or whatsoever) # mean should be close to zero, variance stronly depends on data/kernel # bootstrapping, biased statistic #print "sampling null distribution using bootstrapping" hsic.set_null_approximation_method(BOOTSTRAP) hsic.set_bootstrap_iterations(100) null_samples=hsic.bootstrap_null() #print "null mean:", mean(null_samples) #print "null variance:", var(null_samples) #hist(null_samples, 100); show() return p_value_boot, thresh_boot, p_value_gamma, thresh_gamma, statistic, null_samples
