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_linear_time_mmd ():
	from shogun.Features import RealFeatures
	from shogun.Features import MeanShiftRealDataGenerator
	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

	# streaming data generator for mean shift distributions
	gen_p=MeanShiftRealDataGenerator(0, dim)
	gen_q=MeanShiftRealDataGenerator(difference, dim)

	# 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
	
	# Stream examples and merge them in order to compute median on joint sample
	features=gen_p.get_streamed_features(100)
	features=features.create_merged_copy(gen_q.get_streamed_features(100))
	
	# compute all pairwise distances
	dist=EuclideanDistance(features, features)
	distances=dist.get_distance_matrix()
	
	# compute median and determine kernel width (using shogun)
	median_distance=Statistics.matrix_median(distances, True)
	sigma=median_distance**2
	print "median distance for Gaussian kernel:", sigma
	kernel=GaussianKernel(10,sigma)

	# mmd instance using streaming features, blocksize of 10000
	mmd=LinearTimeMMD(kernel, gen_p, gen_q, n, 10000)

	# 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)
Example #3
0
def statistics_linear_time_mmd():
    from shogun.Features import RealFeatures
    from shogun.Features import MeanShiftRealDataGenerator
    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

    # streaming data generator for mean shift distributions
    gen_p = MeanShiftRealDataGenerator(0, dim)
    gen_q = MeanShiftRealDataGenerator(difference, dim)

    # 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

    # Stream examples and merge them in order to compute median on joint sample
    features = gen_p.get_streamed_features(100)
    features = features.create_merged_copy(gen_q.get_streamed_features(100))

    # compute all pairwise distances
    dist = EuclideanDistance(features, features)
    distances = dist.get_distance_matrix()

    # compute median and determine kernel width (using shogun)
    median_distance = Statistics.matrix_median(distances, True)
    sigma = median_distance**2
    print "median distance for Gaussian kernel:", sigma
    kernel = GaussianKernel(10, sigma)

    # mmd instance using streaming features, blocksize of 10000
    mmd = LinearTimeMMD(kernel, gen_p, gen_q, n, 10000)

    # 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)
Example #4
0
# for nice plotting that fits into our shogun tutorial
import latex_plot_inits

# parameters, change to get different results
m = 100
dim = 2

# setting the difference of the first dimension smaller makes a harder test
difference = 0.5

# number of samples taken from null and alternative distribution
num_null_samples = 500

# streaming data generator for mean shift distributions
gen_p = MeanShiftRealDataGenerator(0, dim)
gen_q = MeanShiftRealDataGenerator(difference, dim)

# 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

# Stream examples and merge them in order to compute median on joint sample
features = gen_p.get_streamed_features(100)
features = features.create_merged_copy(gen_q.get_streamed_features(100))

# compute all pairwise distances
dist = EuclideanDistance(features, features)
distances = dist.get_distance_matrix()
# for nice plotting that fits into our shogun tutorial
import latex_plot_inits

# parameters, change to get different results
m=100
dim=2

# setting the difference of the first dimension smaller makes a harder test
difference=0.5

# number of samples taken from null and alternative distribution
num_null_samples=500

# streaming data generator for mean shift distributions
gen_p=MeanShiftRealDataGenerator(0, dim)
gen_q=MeanShiftRealDataGenerator(difference, dim)

# 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

# Stream examples and merge them in order to compute median on joint sample
features=gen_p.get_streamed_features(100)
features=features.create_merged_copy(gen_q.get_streamed_features(100))

# compute all pairwise distances
dist=EuclideanDistance(features, features)
distances=dist.get_distance_matrix()