def evaluation_multiclassovrevaluation_modular(traindat, label_traindat,
testdat, label_testdat):
from shogun.Features import MulticlassLabels
from shogun.Evaluation import MulticlassOVREvaluation, ROCEvaluation
from modshogun import MulticlassLibLinear, RealFeatures, ContingencyTableEvaluation, ACCURACY
from shogun.Mathematics import Math
Math.init_random(1)
ground_truth_labels = MulticlassLabels(label_traindat)
svm = MulticlassLibLinear(1.0, RealFeatures(traindat),
MulticlassLabels(label_traindat))
svm.train()
predicted_labels = svm.apply()
binary_evaluator = ROCEvaluation()
evaluator = MulticlassOVREvaluation(binary_evaluator)
mean_roc = evaluator.evaluate(predicted_labels, ground_truth_labels)
#print mean_roc
binary_evaluator = ContingencyTableEvaluation(ACCURACY)
evaluator = MulticlassOVREvaluation(binary_evaluator)
mean_accuracy = evaluator.evaluate(predicted_labels, ground_truth_labels)
#print mean_accuracy
return mean_roc, mean_accuracy
def evaluation_multiclassovrevaluation_modular (traindat, label_traindat): from shogun.Features import MulticlassLabels from shogun.Evaluation import MulticlassOVREvaluation,ROCEvaluation from modshogun import MulticlassLibLinear,RealFeatures,ContingencyTableEvaluation,ACCURACY from shogun.Mathematics import Math Math.init_random(1) ground_truth_labels = MulticlassLabels(label_traindat) svm = MulticlassLibLinear(1.0,RealFeatures(traindat),MulticlassLabels(label_traindat)) svm.parallel.set_num_threads(1) svm.train() predicted_labels = svm.apply() binary_evaluator = ROCEvaluation() evaluator = MulticlassOVREvaluation(binary_evaluator) mean_roc = evaluator.evaluate(predicted_labels,ground_truth_labels) #print mean_roc binary_evaluator = ContingencyTableEvaluation(ACCURACY) evaluator = MulticlassOVREvaluation(binary_evaluator) mean_accuracy = evaluator.evaluate(predicted_labels,ground_truth_labels) #print mean_accuracy return mean_roc, mean_accuracy, predicted_labels, svm
def evaluation_clustering (features=fea, ground_truth=gnd_raw, ncenters=10):
from shogun.Evaluation import ClusteringAccuracy, ClusteringMutualInformation
from shogun.Features import MulticlassLabels
from shogun.Mathematics import Math
# reproducable results
Math.init_random(1)
centroids = run_clustering(features, ncenters)
gnd_hat = assign_labels(features, centroids, ncenters)
gnd = MulticlassLabels(ground_truth)
AccuracyEval = ClusteringAccuracy()
AccuracyEval.best_map(gnd_hat, gnd)
accuracy = AccuracyEval.evaluate(gnd_hat, gnd)
#print(('Clustering accuracy = %.4f' % accuracy))
MIEval = ClusteringMutualInformation()
mutual_info = MIEval.evaluate(gnd_hat, gnd)
#print(('Clustering mutual information = %.4f' % mutual_info))
# TODO mutual information does not work with serialization
#return gnd, gnd_hat, accuracy, MIEval, mutual_info
return gnd, gnd_hat, accuracy
def evaluation_clustering(features=fea, ground_truth=gnd_raw, ncenters=10):
from shogun.Evaluation import ClusteringAccuracy, ClusteringMutualInformation
from shogun.Features import MulticlassLabels
from shogun.Mathematics import Math
# reproducable results
Math.init_random(1)
centroids = run_clustering(features, ncenters)
gnd_hat = assign_labels(features, centroids, ncenters)
gnd = MulticlassLabels(ground_truth)
AccuracyEval = ClusteringAccuracy()
AccuracyEval.best_map(gnd_hat, gnd)
accuracy = AccuracyEval.evaluate(gnd_hat, gnd)
#print(('Clustering accuracy = %.4f' % accuracy))
MIEval = ClusteringMutualInformation()
mutual_info = MIEval.evaluate(gnd_hat, gnd)
#print(('Clustering mutual information = %.4f' % mutual_info))
# TODO mutual information does not work with serialization
#return gnd, gnd_hat, accuracy, MIEval, mutual_info
return gnd, gnd_hat, accuracy
def statistics_kmm (n,d): from shogun.Features import RealFeatures from shogun.Features import DataGenerator from shogun.Kernel import GaussianKernel, MSG_DEBUG from shogun.Statistics import KernelMeanMatching from shogun.Mathematics import Math # init seed for reproducability Math.init_random(1) random.seed(1); data = random.randn(d,n) # create shogun feature representation features=RealFeatures(data) # 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) kernel.init(features,features) kmm = KernelMeanMatching(kernel,array([0,1,2,3,7,8,9],dtype=int32),array([4,5,6],dtype=int32)) w = kmm.compute_weights() #print w return w
def modelselection_grid_search_kernel (num_subsets, num_vectors, dim_vectors):
# init seed for reproducability
Math.init_random(1)
random.seed(1);
# create some (non-sense) data
matrix=random.rand(dim_vectors, num_vectors)
# create num_feautres 2-dimensional vectors
features=RealFeatures()
features.set_feature_matrix(matrix)
# create labels, two classes
labels=BinaryLabels(num_vectors)
for i in range(num_vectors):
labels.set_label(i, 1 if i%2==0 else -1)
# create svm
classifier=LibSVM()
# splitting strategy
splitting_strategy=StratifiedCrossValidationSplitting(labels, num_subsets)
# accuracy evaluation
evaluation_criterion=ContingencyTableEvaluation(ACCURACY)
# cross validation class for evaluation in model selection
cross=CrossValidation(classifier, features, labels, splitting_strategy, evaluation_criterion)
cross.set_num_runs(1)
# print all parameter available for modelselection
# Dont worry if yours is not included, simply write to the mailing list
#classifier.print_modsel_params()
# model parameter selection
param_tree=create_param_tree()
#param_tree.print_tree()
grid_search=GridSearchModelSelection(param_tree, cross)
print_state=False
best_combination=grid_search.select_model(print_state)
#print("best parameter(s):")
#best_combination.print_tree()
best_combination.apply_to_machine(classifier)
# larger number of runs to have tighter confidence intervals
cross.set_num_runs(10)
cross.set_conf_int_alpha(0.01)
result=cross.evaluate()
casted=CrossValidationResult.obtain_from_generic(result);
#print "result mean:", casted.mean
return classifier,result,casted.mean
def evaluation_clustering_simple(n_data=100, sqrt_num_blobs=4, distance=5):
from shogun.Evaluation import ClusteringAccuracy, ClusteringMutualInformation
from shogun.Features import MulticlassLabels, GaussianBlobsDataGenerator
from shogun.Mathematics import Math
# reproducable results
Math.init_random(1)
# produce sone Gaussian blobs to cluster
ncenters = sqrt_num_blobs**2
stretch = 1
angle = 1
gen = GaussianBlobsDataGenerator(sqrt_num_blobs, distance, stretch, angle)
features = gen.get_streamed_features(n_data)
X = features.get_feature_matrix()
# compute approximate "ground truth" labels via taking the closest blob mean
coords = array(range(0, sqrt_num_blobs * distance, distance))
idx_0 = [abs(coords - x).argmin() for x in X[0]]
idx_1 = [abs(coords - x).argmin() for x in X[1]]
ground_truth = array(
[idx_0[i] * sqrt_num_blobs + idx_1[i] for i in range(n_data)],
dtype="float64")
#for label in unique(ground_truth):
# indices=ground_truth==label
# plot(X[0][indices], X[1][indices], 'o')
#show()
centroids = run_clustering(features, ncenters)
gnd_hat = assign_labels(features, centroids, ncenters)
gnd = MulticlassLabels(ground_truth)
AccuracyEval = ClusteringAccuracy()
AccuracyEval.best_map(gnd_hat, gnd)
accuracy = AccuracyEval.evaluate(gnd_hat, gnd)
# in this case we know that the clustering has to be very good
#print(('Clustering accuracy = %.4f' % accuracy))
assert (accuracy > 0.8)
MIEval = ClusteringMutualInformation()
mutual_info = MIEval.evaluate(gnd_hat, gnd)
#print(('Clustering mutual information = %.4f' % mutual_info))
# TODO add multiclass labels and MI once the serialization works
#return gnd, accuracy, mutual_info
return accuracy
def evaluation_clustering_simple (n_data=100, sqrt_num_blobs=4, distance=5):
from shogun.Evaluation import ClusteringAccuracy, ClusteringMutualInformation
from shogun.Features import MulticlassLabels, GaussianBlobsDataGenerator
from shogun.Mathematics import Math
# reproducable results
Math.init_random(1)
# produce sone Gaussian blobs to cluster
ncenters=sqrt_num_blobs**2
stretch=1
angle=1
gen=GaussianBlobsDataGenerator(sqrt_num_blobs, distance, stretch, angle)
features=gen.get_streamed_features(n_data)
X=features.get_feature_matrix()
# compute approximate "ground truth" labels via taking the closest blob mean
coords=array(range(0,sqrt_num_blobs*distance,distance))
idx_0=[abs(coords -x).argmin() for x in X[0]]
idx_1=[abs(coords -x).argmin() for x in X[1]]
ground_truth=array([idx_0[i]*sqrt_num_blobs + idx_1[i] for i in range(n_data)], dtype="float64")
#for label in unique(ground_truth):
# indices=ground_truth==label
# plot(X[0][indices], X[1][indices], 'o')
#show()
centroids = run_clustering(features, ncenters)
gnd_hat = assign_labels(features, centroids, ncenters)
gnd = MulticlassLabels(ground_truth)
AccuracyEval = ClusteringAccuracy()
AccuracyEval.best_map(gnd_hat, gnd)
accuracy = AccuracyEval.evaluate(gnd_hat, gnd)
# in this case we know that the clustering has to be very good
#print(('Clustering accuracy = %.4f' % accuracy))
assert(accuracy>0.8)
MIEval = ClusteringMutualInformation()
mutual_info = MIEval.evaluate(gnd_hat, gnd)
#print(('Clustering mutual information = %.4f' % mutual_info))
# TODO add multiclass labels and MI once the serialization works
#return gnd, accuracy, mutual_info
return accuracy
def statistics_quadratic_time_mmd (m,dim,difference): from shogun.Features import RealFeatures from shogun.Features import MeanShiftDataGenerator from shogun.Kernel import GaussianKernel, CustomKernel from shogun.Statistics import QuadraticTimeMMD from shogun.Statistics import BOOTSTRAP, MMD2_SPECTRUM, MMD2_GAMMA, BIASED, UNBIASED from shogun.Mathematics import Statistics, IntVector, RealVector, Math # init seed for reproducability Math.init_random(1) # number of examples kept low in order to make things fast # streaming data generator for mean shift distributions gen_p=MeanShiftDataGenerator(0, dim); gen_q=MeanShiftDataGenerator(difference, dim); # stream some data from generator feat_p=gen_p.get_streamed_features(m); feat_q=gen_q.get_streamed_features(m); # set kernel a-priori. usually one would do some kernel selection. See # other examples for this. width=10; kernel=GaussianKernel(10, width); # create quadratic time mmd instance. Note that this constructor # copies p and q and does not reference them mmd=QuadraticTimeMMD(kernel, feat_p, feat_q); # perform test: compute p-value and test if null-hypothesis is rejected for # a test level of 0.05 alpha=0.05; # using bootstrapping (slow, not the most reliable way. Consider pre- # computing the kernel when using it, see below). # Also, in practice, use at least 250 iterations mmd.set_null_approximation_method(BOOTSTRAP); mmd.set_bootstrap_iterations(3); p_value_boot=mmd.perform_test(); # reject if p-value is smaller than test level #print "bootstrap: p!=q: ", p_value_boot<alpha # using spectrum method. Use at least 250 samples from null. # This is consistent but sometimes breaks, always monitor type I error. # See tutorial for number of eigenvalues to use . # Only works with BIASED statistic mmd.set_statistic_type(BIASED); mmd.set_null_approximation_method(MMD2_SPECTRUM); mmd.set_num_eigenvalues_spectrum(3); mmd.set_num_samples_sepctrum(250); p_value_spectrum=mmd.perform_test(); # reject if p-value is smaller than test level #print "spectrum: p!=q: ", p_value_spectrum<alpha # using gamma method. This is a quick hack, which works most of the time # but is NOT guaranteed to. See tutorial for details. # Only works with BIASED statistic mmd.set_statistic_type(BIASED); mmd.set_null_approximation_method(MMD2_GAMMA); p_value_gamma=mmd.perform_test(); # reject if p-value is smaller than test level #print "gamma: p!=q: ", p_value_gamma<alpha # compute tpye I and II error (use many more trials in practice). # Type I error is not necessary if one uses bootstrapping. We do it here # anyway, but note that this is an efficient way of computing it. # Also note that testing has to happen on # difference data than kernel selection, but the linear time mmd does this # implicitly and we used a fixed kernel here. mmd.set_null_approximation_method(BOOTSTRAP); mmd.set_bootstrap_iterations(5); num_trials=5; type_I_errors=RealVector(num_trials); type_II_errors=RealVector(num_trials); inds=int32(array([x for x in range(2*m)])) # numpy p_and_q=mmd.get_p_and_q(); # use a precomputed kernel to be faster kernel.init(p_and_q, p_and_q); precomputed=CustomKernel(kernel); mmd.set_kernel(precomputed); for i in range(num_trials): # this effectively means that p=q - rejecting is tpye I error inds=random.permutation(inds) # numpy permutation precomputed.add_row_subset(inds); precomputed.add_col_subset(inds); type_I_errors[i]=mmd.perform_test()>alpha; precomputed.remove_row_subset(); precomputed.remove_col_subset(); # on normal data, this gives type II error type_II_errors[i]=mmd.perform_test()>alpha; return type_I_errors.get(),type_I_errors.get(),p_value_boot,p_value_spectrum,p_value_gamma,
def statistics_mmd_kernel_selection_single(m,distance,stretch,num_blobs,angle,selection_method):
from shogun.Features import RealFeatures
from shogun.Features import GaussianBlobsDataGenerator
from shogun.Kernel import GaussianKernel, CombinedKernel
from shogun.Statistics import LinearTimeMMD
from shogun.Statistics import MMDKernelSelectionMedian
from shogun.Statistics import MMDKernelSelectionMax
from shogun.Statistics import MMDKernelSelectionOpt
from shogun.Statistics import BOOTSTRAP, MMD1_GAUSSIAN
from shogun.Distance import EuclideanDistance
from shogun.Mathematics import Statistics, Math
# init seed for reproducability
Math.init_random(1)
# note that the linear time statistic is designed for much larger datasets
# results for this low number will be bad (unstable, type I error wrong)
m=1000
distance=10
stretch=5
num_blobs=3
angle=pi/4
# streaming data generator
gen_p=GaussianBlobsDataGenerator(num_blobs, distance, 1, 0)
gen_q=GaussianBlobsDataGenerator(num_blobs, distance, stretch, angle)
# stream some data and plot
num_plot=1000
features=gen_p.get_streamed_features(num_plot)
features=features.create_merged_copy(gen_q.get_streamed_features(num_plot))
data=features.get_feature_matrix()
#figure()
#subplot(2,2,1)
#grid(True)
#plot(data[0][0:num_plot], data[1][0:num_plot], 'r.', label='$x$')
#title('$X\sim p$')
#subplot(2,2,2)
#grid(True)
#plot(data[0][num_plot+1:2*num_plot], data[1][num_plot+1:2*num_plot], 'b.', label='$x$', alpha=0.5)
#title('$Y\sim q$')
# create combined kernel with Gaussian kernels inside (shoguns Gaussian kernel is
# different to the standard form, see documentation)
sigmas=[2**x for x in range(-3,10)]
widths=[x*x*2 for x in sigmas]
combined=CombinedKernel()
for i in range(len(sigmas)):
combined.append_kernel(GaussianKernel(10, widths[i]))
# mmd instance using streaming features, blocksize of 10000
block_size=1000
mmd=LinearTimeMMD(combined, gen_p, gen_q, m, block_size)
# kernel selection instance (this can easily replaced by the other methods for selecting
# single kernels
if selection_method=="opt":
selection=MMDKernelSelectionOpt(mmd)
elif selection_method=="max":
selection=MMDKernelSelectionMax(mmd)
elif selection_method=="median":
selection=MMDKernelSelectionMedian(mmd)
# print measures (just for information)
# in case Opt: ratios of MMD and standard deviation
# in case Max: MMDs for each kernel
# Does not work for median method
if selection_method!="median":
ratios=selection.compute_measures()
#print "Measures:", ratios
#subplot(2,2,3)
#plot(ratios)
#title('Measures')
# perform kernel selection
kernel=selection.select_kernel()
kernel=GaussianKernel.obtain_from_generic(kernel)
#print "selected kernel width:", kernel.get_width()
# compute tpye I and II error (use many more trials). Type I error is only
# estimated to check MMD1_GAUSSIAN method for estimating the null
# distribution. Note that testing has to happen on difference data than
# kernel selecting, but the linear time mmd does this implicitly
mmd.set_kernel(kernel)
mmd.set_null_approximation_method(MMD1_GAUSSIAN)
# number of trials should be larger to compute tight confidence bounds
num_trials=5;
alpha=0.05 # test power
typeIerrors=[0 for x in range(num_trials)]
typeIIerrors=[0 for x in range(num_trials)]
for i in range(num_trials):
# this effectively means that p=q - rejecting is tpye I error
mmd.set_simulate_h0(True)
typeIerrors[i]=mmd.perform_test()>alpha
mmd.set_simulate_h0(False)
typeIIerrors[i]=mmd.perform_test()>alpha
#print "type I error:", mean(typeIerrors), ", type II error:", mean(typeIIerrors)
return kernel,typeIerrors,typeIIerrors
def statistics_linear_time_mmd (n,dim,difference): from shogun.Features import RealFeatures from shogun.Features import MeanShiftDataGenerator 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 # init seed for reproducability Math.init_random(1) # note that the linear time statistic is designed for much larger datasets # so increase to get reasonable results # streaming data generator for mean shift distributions gen_p=MeanShiftDataGenerator(0, dim) gen_q=MeanShiftDataGenerator(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_boot=mmd.compute_p_value(statistic) #print "p_value_boot:", p_value_boot #print "p_value_boot <", alpha, ", i.e. test sais p!=q:", p_value_boot<alpha #print "computing p-value using gaussian approximation" mmd.set_null_approximation_method(MMD1_GAUSSIAN) p_value_gaussian=mmd.compute_p_value(statistic) #print "p_value_gaussian:", p_value_gaussian #print "p_value_gaussian <", alpha, ", i.e. test sais p!=q:", p_value_gaussian<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) # compute type I and type II errors for Gaussian approximation # number of trials should be larger to compute tight confidence bounds mmd.set_null_approximation_method(MMD1_GAUSSIAN) num_trials=5; alpha=0.05 # test power typeIerrors=[0 for x in range(num_trials)] typeIIerrors=[0 for x in range(num_trials)] for i in range(num_trials): # this effectively means that p=q - rejecting is tpye I error mmd.set_simulate_h0(True) typeIerrors[i]=mmd.perform_test()>alpha mmd.set_simulate_h0(False) typeIIerrors[i]=mmd.perform_test()>alpha #print "type I error:", mean(typeIerrors), ", type II error:", mean(typeIIerrors) return statistic, p_value_boot, p_value_gaussian, null_samples, typeIerrors, typeIIerrors
# 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=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
def statistics_mmd_kernel_selection_combined(m, distance, stretch, num_blobs,
angle, selection_method):
from shogun.Features import RealFeatures
from shogun.Features import GaussianBlobsDataGenerator
from shogun.Kernel import GaussianKernel, CombinedKernel
from shogun.Statistics import LinearTimeMMD
from shogun.Statistics import MMDKernelSelectionCombMaxL2
from shogun.Statistics import MMDKernelSelectionCombOpt
from shogun.Statistics import BOOTSTRAP, MMD1_GAUSSIAN
from shogun.Distance import EuclideanDistance
from shogun.Mathematics import Statistics, Math
# init seed for reproducability
Math.init_random(1)
# note that the linear time statistic is designed for much larger datasets
# results for this low number will be bad (unstable, type I error wrong)
# streaming data generator
gen_p = GaussianBlobsDataGenerator(num_blobs, distance, 1, 0)
gen_q = GaussianBlobsDataGenerator(num_blobs, distance, stretch, angle)
# stream some data and plot
num_plot = 1000
features = gen_p.get_streamed_features(num_plot)
features = features.create_merged_copy(
gen_q.get_streamed_features(num_plot))
data = features.get_feature_matrix()
#figure()
#subplot(2,2,1)
#grid(True)
#plot(data[0][0:num_plot], data[1][0:num_plot], 'r.', label='$x$')
#title('$X\sim p$')
#subplot(2,2,2)
#grid(True)
#plot(data[0][num_plot+1:2*num_plot], data[1][num_plot+1:2*num_plot], 'b.', label='$x$', alpha=0.5)
#title('$Y\sim q$')
# create combined kernel with Gaussian kernels inside (shoguns Gaussian kernel is
# different to the standard form, see documentation)
sigmas = [2**x for x in range(-3, 10)]
widths = [x * x * 2 for x in sigmas]
combined = CombinedKernel()
for i in range(len(sigmas)):
combined.append_kernel(GaussianKernel(10, widths[i]))
# mmd instance using streaming features, blocksize of 10000
block_size = 10000
mmd = LinearTimeMMD(combined, gen_p, gen_q, m, block_size)
# kernel selection instance (this can easily replaced by the other methods for selecting
# combined kernels
if selection_method == "opt":
selection = MMDKernelSelectionCombOpt(mmd)
elif selection_method == "l2":
selection = MMDKernelSelectionCombMaxL2(mmd)
# perform kernel selection (kernel is automatically set)
kernel = selection.select_kernel()
kernel = CombinedKernel.obtain_from_generic(kernel)
#print "selected kernel weights:", kernel.get_subkernel_weights()
#subplot(2,2,3)
#plot(kernel.get_subkernel_weights())
#title("Kernel weights")
# compute tpye I and II error (use many more trials). Type I error is only
# estimated to check MMD1_GAUSSIAN method for estimating the null
# distribution. Note that testing has to happen on difference data than
# kernel selecting, but the linear time mmd does this implicitly
mmd.set_null_approximation_method(MMD1_GAUSSIAN)
# number of trials should be larger to compute tight confidence bounds
num_trials = 5
alpha = 0.05 # test power
typeIerrors = [0 for x in range(num_trials)]
typeIIerrors = [0 for x in range(num_trials)]
for i in range(num_trials):
# this effectively means that p=q - rejecting is tpye I error
mmd.set_simulate_h0(True)
typeIerrors[i] = mmd.perform_test() > alpha
mmd.set_simulate_h0(False)
typeIIerrors[i] = mmd.perform_test() > alpha
#print "type I error:", mean(typeIerrors), ", type II error:", mean(typeIIerrors)
return kernel, typeIerrors, typeIIerrors
def evaluation_cross_validation_multiclass_storage (traindat=traindat, label_traindat=label_traindat):
from shogun.Evaluation import CrossValidation, CrossValidationResult
from shogun.Evaluation import CrossValidationPrintOutput
from shogun.Evaluation import CrossValidationMKLStorage, CrossValidationMulticlassStorage
from shogun.Evaluation import MulticlassAccuracy, F1Measure
from shogun.Evaluation import StratifiedCrossValidationSplitting
from shogun.Features import MulticlassLabels
from shogun.Features import RealFeatures, CombinedFeatures
from shogun.Kernel import GaussianKernel, CombinedKernel
from shogun.Classifier import MKLMulticlass
from shogun.Mathematics import Statistics, MSG_DEBUG, Math
Math.init_random(1)
# training data, combined features all on same data
features=RealFeatures(traindat)
comb_features=CombinedFeatures()
comb_features.append_feature_obj(features)
comb_features.append_feature_obj(features)
comb_features.append_feature_obj(features)
labels=MulticlassLabels(label_traindat)
# kernel, different Gaussians combined
kernel=CombinedKernel()
kernel.append_kernel(GaussianKernel(10, 0.1))
kernel.append_kernel(GaussianKernel(10, 1))
kernel.append_kernel(GaussianKernel(10, 2))
# create mkl using libsvm, due to a mem-bug, interleaved is not possible
svm=MKLMulticlass(1.0,kernel,labels);
svm.set_kernel(kernel);
# splitting strategy for 5 fold cross-validation (for classification its better
# to use "StratifiedCrossValidation", but the standard
# "StratifiedCrossValidationSplitting" is also available
splitting_strategy=StratifiedCrossValidationSplitting(labels, 3)
# evaluation method
evaluation_criterium=MulticlassAccuracy()
# cross-validation instance
cross_validation=CrossValidation(svm, comb_features, labels,
splitting_strategy, evaluation_criterium)
cross_validation.set_autolock(False)
# append cross vlaidation output classes
#cross_validation.add_cross_validation_output(CrossValidationPrintOutput())
#mkl_storage=CrossValidationMKLStorage()
#cross_validation.add_cross_validation_output(mkl_storage)
multiclass_storage=CrossValidationMulticlassStorage()
multiclass_storage.append_binary_evaluation(F1Measure())
cross_validation.add_cross_validation_output(multiclass_storage)
cross_validation.set_num_runs(3)
# perform cross-validation
result=cross_validation.evaluate()
roc_0_0_0 = multiclass_storage.get_fold_ROC(0,0,0)
#print roc_0_0_0
auc_0_0_0 = multiclass_storage.get_fold_evaluation_result(0,0,0,0)
#print auc_0_0_0
return roc_0_0_0, auc_0_0_0
def evaluation_cross_validation_multiclass_storage(
traindat=traindat, label_traindat=label_traindat):
from shogun.Evaluation import CrossValidation, CrossValidationResult
from shogun.Evaluation import CrossValidationPrintOutput
from shogun.Evaluation import CrossValidationMKLStorage, CrossValidationMulticlassStorage
from shogun.Evaluation import MulticlassAccuracy, F1Measure
from shogun.Evaluation import StratifiedCrossValidationSplitting
from shogun.Features import MulticlassLabels
from shogun.Features import RealFeatures, CombinedFeatures
from shogun.Kernel import GaussianKernel, CombinedKernel
from shogun.Classifier import MKLMulticlass
from shogun.Mathematics import Statistics, MSG_DEBUG, Math
Math.init_random(1)
# training data, combined features all on same data
features = RealFeatures(traindat)
comb_features = CombinedFeatures()
comb_features.append_feature_obj(features)
comb_features.append_feature_obj(features)
comb_features.append_feature_obj(features)
labels = MulticlassLabels(label_traindat)
# kernel, different Gaussians combined
kernel = CombinedKernel()
kernel.append_kernel(GaussianKernel(10, 0.1))
kernel.append_kernel(GaussianKernel(10, 1))
kernel.append_kernel(GaussianKernel(10, 2))
# create mkl using libsvm, due to a mem-bug, interleaved is not possible
svm = MKLMulticlass(1.0, kernel, labels)
svm.set_kernel(kernel)
# splitting strategy for 5 fold cross-validation (for classification its better
# to use "StratifiedCrossValidation", but the standard
# "StratifiedCrossValidationSplitting" is also available
splitting_strategy = StratifiedCrossValidationSplitting(labels, 3)
# evaluation method
evaluation_criterium = MulticlassAccuracy()
# cross-validation instance
cross_validation = CrossValidation(svm, comb_features, labels,
splitting_strategy,
evaluation_criterium)
cross_validation.set_autolock(False)
# append cross vlaidation output classes
#cross_validation.add_cross_validation_output(CrossValidationPrintOutput())
#mkl_storage=CrossValidationMKLStorage()
#cross_validation.add_cross_validation_output(mkl_storage)
multiclass_storage = CrossValidationMulticlassStorage()
multiclass_storage.append_binary_evaluation(F1Measure())
cross_validation.add_cross_validation_output(multiclass_storage)
cross_validation.set_num_runs(3)
# perform cross-validation
result = cross_validation.evaluate()
roc_0_0_0 = multiclass_storage.get_fold_ROC(0, 0, 0)
#print roc_0_0_0
auc_0_0_0 = multiclass_storage.get_fold_evaluation_result(0, 0, 0, 0)
#print auc_0_0_0
return roc_0_0_0, auc_0_0_0
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, Math
# 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 = 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)
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_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)
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, 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 # 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=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)
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)
# number of samples taken from null and alternative distribution num_null_samples=500 # 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)
def statistics_linear_time_mmd(n, dim, difference):
from shogun.Features import RealFeatures
from shogun.Features import MeanShiftDataGenerator
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
# init seed for reproducability
Math.init_random(1)
# note that the linear time statistic is designed for much larger datasets
# so increase to get reasonable results
# streaming data generator for mean shift distributions
gen_p = MeanShiftDataGenerator(0, dim)
gen_q = MeanShiftDataGenerator(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_boot = mmd.compute_p_value(statistic)
#print "p_value_boot:", p_value_boot
#print "p_value_boot <", alpha, ", i.e. test sais p!=q:", p_value_boot<alpha
#print "computing p-value using gaussian approximation"
mmd.set_null_approximation_method(MMD1_GAUSSIAN)
p_value_gaussian = mmd.compute_p_value(statistic)
#print "p_value_gaussian:", p_value_gaussian
#print "p_value_gaussian <", alpha, ", i.e. test sais p!=q:", p_value_gaussian<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)
# compute type I and type II errors for Gaussian approximation
# number of trials should be larger to compute tight confidence bounds
mmd.set_null_approximation_method(MMD1_GAUSSIAN)
num_trials = 5
alpha = 0.05 # test power
typeIerrors = [0 for x in range(num_trials)]
typeIIerrors = [0 for x in range(num_trials)]
for i in range(num_trials):
# this effectively means that p=q - rejecting is tpye I error
mmd.set_simulate_h0(True)
typeIerrors[i] = mmd.perform_test() > alpha
mmd.set_simulate_h0(False)
typeIIerrors[i] = mmd.perform_test() > alpha
#print "type I error:", mean(typeIerrors), ", type II error:", mean(typeIIerrors)
return statistic, p_value_boot, p_value_gaussian, null_samples, typeIerrors, typeIIerrors
