Python RealFeatures.add_subset方法代码示例

# 需要导入模块: from shogun.Features import RealFeatures [as 别名]
# 或者: from shogun.Features.RealFeatures import add_subset [as 别名]
# use data generator class to produce example data
data=DataGenerator.generate_mean_data(m,dim,difference)

# create shogun feature representation
features=RealFeatures(data)

# 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
# Using all distances here would blow up memory
subset=Math.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)

# use biased statistic
mmd=LinearTimeMMD(kernel,features, m)

# sample alternative distribution
alt_samples=zeros(num_null_samples)
for i in range(len(alt_samples)):
	data=DataGenerator.generate_mean_data(m,dim,difference)

# 需要导入模块: from shogun.Features import RealFeatures [as 别名]
# 或者: from shogun.Features.RealFeatures import add_subset [as 别名]
def statistics_linear_time_mmd ():
	from shogun.Features import RealFeatures
	from shogun.Features import DataGenerator
	from shogun.Kernel import GaussianKernel
	from shogun.Statistics import LinearTimeMMD
	from shogun.Statistics import BOOTSTRAP, MMD1_GAUSSIAN
	from shogun.Distance import EuclideanDistance
	from shogun.Mathematics import Statistics, Math

	# note that the linear time statistic is designed for much larger datasets
	n=10000
	dim=2
	difference=0.5

	# use data generator class to produce example data
	# in pratice, this generate data function could be replaced by a method
	# that obtains data from a stream
	data=DataGenerator.generate_mean_data(n,dim,difference)
	
	print "dimension means of X", mean(data.T[0:n].T)
	print "dimension means of Y", mean(data.T[n:2*n+1].T)

	# create shogun feature representation
	features=RealFeatures(data)

	# 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
	# Using all distances here would blow up memory
	subset=Math.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=LinearTimeMMD(kernel,features, n)

	# perform test: compute p-value and test if null-hypothesis is rejected for
	# a test level of 0.05
	statistic=mmd.compute_statistic()
	print "test statistic:", statistic
	
	# do the same thing using two different way to approximate null-dstribution
	# bootstrapping and gaussian approximation (ony for really large samples)
	alpha=0.05

	print "computing p-value using bootstrapping"
	mmd.set_null_approximation_method(BOOTSTRAP)
	mmd.set_bootstrap_iterations(50) # normally, far more iterations are needed
	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 gaussian approximation"
	mmd.set_null_approximation_method(MMD1_GAUSSIAN)
	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
	mmd.set_null_approximation_method(BOOTSTRAP)
	mmd.set_bootstrap_iterations(10) # normally, far more iterations are needed
	null_samples=mmd.bootstrap_null()
	print "null mean:", mean(null_samples)
	print "null variance:", var(null_samples)

# 需要导入模块: from shogun.Features import RealFeatures [as 别名]
# 或者: from shogun.Features.RealFeatures import add_subset [as 别名]
def hsic_graphical():
	# parameters, change to get different results
	m=250
	difference=3
	
	# setting the angle lower makes a harder test
	angle=pi/30
	
	# number of samples taken from null and alternative distribution
	num_null_samples=500
	
	# use data generator class to produce example data
	data=DataGenerator.generate_sym_mix_gauss(m,difference,angle)
	
	# 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=int32(array([x for x in range(features_x.get_num_vectors())])) # numpy
	subset=random.permutation(subset) # numpy permutation
	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)
	
	# create hsic instance. Note that this is a convienience constructor which copies
	# feature data. features_x and features_y are not these used in hsic.
	# This is only for user-friendlyness. Usually, its ok to do this.
	# Below, the alternative distribution is sampled, which means
	# that new feature objects have to be created in each iteration (slow)
	# However, normally, the alternative distribution is not sampled
	hsic=HSIC(kernel_x,kernel_y,features_x,features_y)
	
	# sample alternative distribution
	alt_samples=zeros(num_null_samples)
	for i in range(len(alt_samples)):
		data=DataGenerator.generate_sym_mix_gauss(m,difference,angle)
		features_x.set_feature_matrix(array([data[0]]))
		features_y.set_feature_matrix(array([data[1]]))
		
		# re-create hsic instance everytime since feature objects are copied due to
		# useage of convienience constructor
		hsic=HSIC(kernel_x,kernel_y,features_x,features_y)
		alt_samples[i]=hsic.compute_statistic()
	
	# sample from null distribution
	# bootstrapping, biased statistic
	hsic.set_null_approximation_method(BOOTSTRAP)
	hsic.set_bootstrap_iterations(num_null_samples)
	null_samples_boot=hsic.bootstrap_null()
	
	# fit gamma distribution, biased statistic
	hsic.set_null_approximation_method(HSIC_GAMMA)
	gamma_params=hsic.fit_null_gamma()
	# sample gamma with parameters
	null_samples_gamma=array([gamma(gamma_params[0], gamma_params[1]) for _ in range(num_null_samples)])
	
	# plot
	figure()
	
	# plot data x and y
	subplot(2,2,1)
	gca().xaxis.set_major_locator( MaxNLocator(nbins = 4) ) # reduce number of x-ticks
	gca().yaxis.set_major_locator( MaxNLocator(nbins = 4) ) # reduce number of x-ticks
	grid(True)
	plot(data[0], data[1], 'o')
	title('Data, rotation=$\pi$/'+str(1/angle*pi)+'\nm='+str(m))
	xlabel('$x$')
	ylabel('$y$')
	
	# compute threshold for test level
	alpha=0.05
	null_samples_boot.sort()
	null_samples_gamma.sort()
	thresh_boot=null_samples_boot[floor(len(null_samples_boot)*(1-alpha))];
	thresh_gamma=null_samples_gamma[floor(len(null_samples_gamma)*(1-alpha))];
	
	type_one_error_boot=sum(null_samples_boot<thresh_boot)/float(num_null_samples)
	type_one_error_gamma=sum(null_samples_gamma<thresh_boot)/float(num_null_samples)
	
	# plot alternative distribution with threshold
	subplot(2,2,2)
#.........这里部分代码省略.........

# 需要导入模块: from shogun.Features import RealFeatures [as 别名]
# 或者: from shogun.Features.RealFeatures import add_subset [as 别名]
# use data generator class to produce example data
data=DataGenerator.generate_sym_mix_gauss(m,difference,angle)

# 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=Math.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)

# 需要导入模块: from shogun.Features import RealFeatures [as 别名]
# 或者: from shogun.Features.RealFeatures import add_subset [as 别名]
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

# 需要导入模块: from shogun.Features import RealFeatures [as 别名]
# 或者: from shogun.Features.RealFeatures import add_subset [as 别名]
def statistics_quadratic_time_mmd ():
	from shogun.Features import RealFeatures
	from shogun.Features import DataGenerator
	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, Math

	# note that the quadratic time mmd has to store kernel matrices
	# which upper bounds the sample size
	n=500
	dim=2
	difference=0.5

	# use data generator class to produce example data
	data=DataGenerator.generate_mean_data(n,dim,difference)
	
	print "dimension means of X", mean(data.T[0:n].T)
	print "dimension means of Y", mean(data.T[n:2*n+1].T)

	# create shogun feature representation
	features=RealFeatures(data)

	# 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=Math.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)