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
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(): 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 # 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]])) # use a kernel width of sigma=2, which is 8 in SHOGUN's parametrization # which is k(x,y)=exp(-||x-y||^2 / tau), in constrast to the standard # k(x,y)=exp(-||x-y||^2 / (2*sigma^2)), so tau=2*sigma^2 kernel=GaussianKernel(10,8) hsic=HSIC(kernel,kernel,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)
