def statistics_quadratic_time_mmd():
from shogun.Features import RealFeatures
from shogun.Features import MeanShiftDataGenerator
from shogun.Kernel import GaussianKernel
from shogun.Statistics import QuadraticTimeMMD
from shogun.Statistics import BOOTSTRAP, MMD2_SPECTRUM, MMD2_GAMMA, BIASED, UNBIASED
from shogun.Distance import EuclideanDistance
from shogun.Mathematics import Statistics, IntVector
# note that the quadratic time mmd has to store kernel matrices
# which upper bounds the sample size
n = 100
dim = 2
difference = 0.5
# streaming data generator for mean shift distributions
gen_p = MeanShiftDataGenerator(0, dim)
gen_q = MeanShiftDataGenerator(difference, dim)
# Stream examples and merge them in order to compute median on joint sample
# alternative is to call a different constructor of QuadraticTimeMMD
features = gen_p.get_streamed_features(n)
features = features.create_merged_copy(gen_q.get_streamed_features(n))
# use data generator class to produce example data
data = features.get_feature_matrix()
print "dimension means of X", mean(data.T[0:n].T)
print "dimension means of Y", mean(data.T[n : 2 * n + 1].T)
# 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
# Use a permutation set to temporarily merge features in merged examples
subset = IntVector.randperm_vec(features.get_num_vectors())
subset = subset[0:200]
features.add_subset(subset)
dist = EuclideanDistance(features, features)
distances = dist.get_distance_matrix()
features.remove_subset()
median_distance = Statistics.matrix_median(distances, True)
sigma = median_distance ** 2
print "median distance for Gaussian kernel:", sigma
kernel = GaussianKernel(10, sigma)
mmd = QuadraticTimeMMD(kernel, features, n)
# 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 = mmd.compute_statistic()
alpha = 0.05
print "computing p-value using bootstrapping"
mmd.set_null_approximation_method(BOOTSTRAP)
# normally, at least 250 iterations should be done, but that takes long
mmd.set_bootstrap_iterations(10)
# bootstrapping allows usage of unbiased or biased statistic
mmd.set_statistic_type(UNBIASED)
p_value = mmd.compute_p_value(statistic)
print "p_value:", p_value
print "p_value <", alpha, ", i.e. test sais p!=q:", p_value < alpha
# only can do this if SHOGUN was compiled with LAPACK so check
if "sample_null_spectrum" in dir(QuadraticTimeMMD):
print "computing p-value using spectrum method"
mmd.set_null_approximation_method(MMD2_SPECTRUM)
# normally, at least 250 iterations should be done, but that takes long
mmd.set_num_samples_sepctrum(50)
mmd.set_num_eigenvalues_spectrum(n - 10)
# spectrum method computes p-value for biased statistics only
mmd.set_statistic_type(BIASED)
p_value = mmd.compute_p_value(statistic)
print "p_value:", p_value
print "p_value <", alpha, ", i.e. test sais p!=q:", p_value < alpha
print "computing p-value using gamma method"
mmd.set_null_approximation_method(MMD2_GAMMA)
# gamma method computes p-value for biased statistics only
mmd.set_statistic_type(BIASED)
p_value = mmd.compute_p_value(statistic)
print "p_value:", p_value
print "p_value <", alpha, ", i.e. test sais p!=q:", p_value < 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"
mmd.set_null_approximation_method(BOOTSTRAP)
mmd.set_statistic_type(BIASED)
mmd.set_bootstrap_iterations(10)
null_samples = mmd.bootstrap_null()
print "null mean:", mean(null_samples)
print "null variance:", var(null_samples)
# sample from null distribution (these may be plotted or whatsoever)
# mean should be close to zero, variance stronly depends on data/kernel
# spectrum, biased statistic
print "sampling null distribution using spectrum method"
mmd.set_null_approximation_method(MMD2_SPECTRUM)
mmd.set_statistic_type(BIASED)
# 200 samples using 100 eigenvalues
null_samples = mmd.sample_null_spectrum(50, 10)
print "null mean:", mean(null_samples)
print "null variance:", var(null_samples)
def statistics_quadratic_time_mmd (): from shogun.Features import RealFeatures from shogun.Features import MeanShiftRealDataGenerator from shogun.Kernel import GaussianKernel from shogun.Statistics import QuadraticTimeMMD from shogun.Statistics import BOOTSTRAP, MMD2_SPECTRUM, MMD2_GAMMA, BIASED, UNBIASED from shogun.Distance import EuclideanDistance from shogun.Mathematics import Statistics, IntVector # note that the quadratic time mmd has to store kernel matrices # which upper bounds the sample size n=500 dim=2 difference=0.5 # streaming data generator for mean shift distributions gen_p=MeanShiftRealDataGenerator(0, dim) gen_q=MeanShiftRealDataGenerator(difference, dim) # Stream examples and merge them in order to compute median on joint sample # alternative is to call a different constructor of QuadraticTimeMMD features=gen_p.get_streamed_features(n) features=features.create_merged_copy(gen_q.get_streamed_features(n)) # use data generator class to produce example data data=features.get_feature_matrix() print "dimension means of X", mean(data.T[0:n].T) print "dimension means of Y", mean(data.T[n:2*n+1].T) # 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 # Use a permutation set to temporarily merge features in merged examples subset=IntVector.randperm_vec(features.get_num_vectors()) subset=subset[0:200] features.add_subset(subset) dist=EuclideanDistance(features, features) distances=dist.get_distance_matrix() features.remove_subset() median_distance=Statistics.matrix_median(distances, True) sigma=median_distance**2 print "median distance for Gaussian kernel:", sigma kernel=GaussianKernel(10,sigma) mmd=QuadraticTimeMMD(kernel,features, n) # 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=mmd.compute_statistic() alpha=0.05 print "computing p-value using bootstrapping" mmd.set_null_approximation_method(BOOTSTRAP) # normally, at least 250 iterations should be done, but that takes long mmd.set_bootstrap_iterations(10) # bootstrapping allows usage of unbiased or biased statistic mmd.set_statistic_type(UNBIASED) p_value=mmd.compute_p_value(statistic) print "p_value:", p_value print "p_value <", alpha, ", i.e. test sais p!=q:", p_value<alpha # only can do this if SHOGUN was compiled with LAPACK so check if "sample_null_spectrum" in dir(QuadraticTimeMMD): print "computing p-value using spectrum method" mmd.set_null_approximation_method(MMD2_SPECTRUM) # normally, at least 250 iterations should be done, but that takes long mmd.set_num_samples_sepctrum(50) mmd.set_num_eigenvalues_spectrum(n-10) # spectrum method computes p-value for biased statistics only mmd.set_statistic_type(BIASED) p_value=mmd.compute_p_value(statistic) print "p_value:", p_value print "p_value <", alpha, ", i.e. test sais p!=q:", p_value<alpha print "computing p-value using gamma method" mmd.set_null_approximation_method(MMD2_GAMMA) # gamma method computes p-value for biased statistics only mmd.set_statistic_type(BIASED) p_value=mmd.compute_p_value(statistic) print "p_value:", p_value print "p_value <", alpha, ", i.e. test sais p!=q:", p_value<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" mmd.set_null_approximation_method(BOOTSTRAP) mmd.set_statistic_type(BIASED) mmd.set_bootstrap_iterations(10) null_samples=mmd.bootstrap_null() print "null mean:", mean(null_samples) print "null variance:", var(null_samples) # sample from null distribution (these may be plotted or whatsoever) # mean should be close to zero, variance stronly depends on data/kernel # spectrum, biased statistic print "sampling null distribution using spectrum method" mmd.set_null_approximation_method(MMD2_SPECTRUM) mmd.set_statistic_type(BIASED) # 200 samples using 100 eigenvalues null_samples=mmd.sample_null_spectrum(50,10) print "null mean:", mean(null_samples) print "null variance:", var(null_samples)
def statistics_hsic (): from shogun.Features import RealFeatures from shogun.Features import DataGenerator from shogun.Kernel import GaussianKernel from shogun.Statistics import HSIC from shogun.Statistics import BOOTSTRAP, HSIC_GAMMA from shogun.Distance import EuclideanDistance from shogun.Mathematics import Statistics, IntVector # note that the HSIC has to store kernel matrices # which upper bounds the sample size n=250 difference=3 angle=pi/3 # 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=hsic.compute_p_value(statistic) thresh=hsic.compute_threshold(alpha) print "p_value:", p_value print "threshold for 0.05 alpha:", thresh print "p_value <", alpha, ", i.e. test sais p and q are dependend:", p_value<alpha print "computing p-value using gamma method" hsic.set_null_approximation_method(HSIC_GAMMA) p_value=hsic.compute_p_value(statistic) thresh=hsic.compute_threshold(alpha) print "p_value:", p_value print "threshold for 0.05 alpha:", thresh print "p_value <", alpha, ", i.e. test sais p and q are dependend::", p_value<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)
def statistics_hsic (n, difference, angle): from shogun.Features import RealFeatures from shogun.Features import DataGenerator from shogun.Kernel import GaussianKernel from shogun.Statistics import HSIC from shogun.Statistics import BOOTSTRAP, HSIC_GAMMA from shogun.Distance import EuclideanDistance from shogun.Mathematics 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
