def statistics_kmm (n,d): from modshogun import RealFeatures from modshogun import DataGenerator from modshogun import GaussianKernel, MSG_DEBUG from modshogun import KernelMeanMatching from modshogun 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 evaluation_clustering (features=fea, ground_truth=gnd_raw, ncenters=10):
from modshogun import ClusteringAccuracy, ClusteringMutualInformation
from modshogun import MulticlassLabels
from modshogun 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 generate_gmm_classification_data(request):
from modshogun import GMM, Math
num_classes = int(request.POST['num_classes'])
gmm = GMM(num_classes)
total = 40
rng = 4.0
num = total/num_classes
for i in xrange(num_classes):
gmm.set_nth_mean(np.array([Math.random(-rng, rng) for j in xrange(2)]), i)
cov_tmp = Math.normal_random(0.2, 0.1)
cov = np.array([[1.0, cov_tmp], [cov_tmp, 1.0]], dtype=float)
gmm.set_nth_cov(cov, i)
data=[]
labels=[]
for i in xrange(num_classes):
coef = np.zeros(num_classes)
coef[i] = 1.0
gmm.set_coef(coef)
data.append(np.array([gmm.sample() for j in xrange(num)]).T)
labels.append(np.array([i for j in xrange(num)]))
data = np.hstack(data)
data = data / (2.0 * rng)
xmin = np.min(data[0,:])
ymin = np.min(data[1,:])
labels = np.hstack(labels)
toy_data = []
for i in xrange(num_classes*num):
toy_data.append( { 'x': data[0, i] - xmin,
'y': data[1, i] - ymin,
'label': float(labels[i])})
return HttpResponse(json.dumps(toy_data))
def statistics_kmm(n, d):
from modshogun import RealFeatures
from modshogun import DataGenerator
from modshogun import GaussianKernel, MSG_DEBUG
from modshogun import KernelMeanMatching
from modshogun 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 evaluation_clustering(features=fea, ground_truth=gnd_raw, ncenters=10):
from modshogun import ClusteringAccuracy, ClusteringMutualInformation
from modshogun import MulticlassLabels
from modshogun 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 regression_gaussian_process_modular (n=100,n_test=100, \
x_range=6,x_range_test=10,noise_var=0.5,width=1, seed=1):
from modshogun import RealFeatures, RegressionLabels, GaussianKernel, Math
try:
from modshogun import GaussianLikelihood, ZeroMean, \
ExactInferenceMethod, GaussianProcessRegression
except ImportError:
print("Eigen3 needed for Gaussian Processes")
return
# reproducable results
random.seed(seed)
Math.init_random(17)
# easy regression data: one dimensional noisy sine wave
X=random.rand(1,n)*x_range
X_test=array([[float(i)/n_test*x_range_test for i in range(n_test)]])
Y_test=sin(X_test)
Y=sin(X)+random.randn(n)*noise_var
# shogun representation
labels=RegressionLabels(Y[0])
feats_train=RealFeatures(X)
feats_test=RealFeatures(X_test)
# GP specification
shogun_width=width*width*2
kernel=GaussianKernel(10, shogun_width)
zmean = ZeroMean()
lik = GaussianLikelihood()
lik.set_sigma(noise_var)
inf = ExactInferenceMethod(kernel, feats_train, zmean, labels, lik)
# train GP
gp = GaussianProcessRegression(inf)
gp.train()
# some things we can do
alpha = inf.get_alpha()
diagonal = inf.get_diagonal_vector()
cholesky = inf.get_cholesky()
# get mean and variance vectors
mean = gp.get_mean_vector(feats_test)
variance = gp.get_variance_vector(feats_test)
# plot results
#plot(X[0],Y[0],'x') # training observations
#plot(X_test[0],Y_test[0],'-') # ground truth of test
#plot(X_test[0],mean, '-') # mean predictions of test
#fill_between(X_test[0],mean-1.96*sqrt(variance),mean+1.96*sqrt(variance),color='grey') # 95% confidence interval
#legend(["training", "ground truth", "mean predictions"])
#show()
return alpha, diagonal, round(variance,12), round(mean,12), cholesky
def regression_gaussian_process_modular (n=100,n_test=100, \
x_range=6,x_range_test=10,noise_var=0.5,width=1, seed=1):
from modshogun import RealFeatures, RegressionLabels, GaussianKernel, Math
try:
from modshogun import GaussianLikelihood, ZeroMean, \
ExactInferenceMethod, GaussianProcessRegression
except ImportError:
print("Eigen3 needed for Gaussian Processes")
return
# reproducable results
random.seed(seed)
Math.init_random(17)
# easy regression data: one dimensional noisy sine wave
X = random.rand(1, n) * x_range
X_test = array([[float(i) / n_test * x_range_test for i in range(n_test)]])
Y_test = sin(X_test)
Y = sin(X) + random.randn(n) * noise_var
# shogun representation
labels = RegressionLabels(Y[0])
feats_train = RealFeatures(X)
feats_test = RealFeatures(X_test)
# GP specification
shogun_width = width * width * 2
kernel = GaussianKernel(10, shogun_width)
zmean = ZeroMean()
lik = GaussianLikelihood()
lik.set_sigma(noise_var)
inf = ExactInferenceMethod(kernel, feats_train, zmean, labels, lik)
# train GP
gp = GaussianProcessRegression(inf)
gp.train()
# some things we can do
alpha = inf.get_alpha()
diagonal = inf.get_diagonal_vector()
cholesky = inf.get_cholesky()
# get mean and variance vectors
mean = gp.get_mean_vector(feats_test)
variance = gp.get_variance_vector(feats_test)
# plot results
#plot(X[0],Y[0],'x') # training observations
#plot(X_test[0],Y_test[0],'-') # ground truth of test
#plot(X_test[0],mean, '-') # mean predictions of test
#fill_between(X_test[0],mean-1.96*sqrt(variance),mean+1.96*sqrt(variance),color='grey') # 95% confidence interval
#legend(["training", "ground truth", "mean predictions"])
#show()
return alpha, diagonal, round(variance, 12), round(mean, 12), cholesky
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(cross, param_tree)
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 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(cross, param_tree)
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 modshogun import ClusteringAccuracy, ClusteringMutualInformation
from modshogun import MulticlassLabels, GaussianBlobsDataGenerator
from modshogun 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 modshogun import ClusteringAccuracy, ClusteringMutualInformation
from modshogun import MulticlassLabels, GaussianBlobsDataGenerator
from modshogun 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_multiclassovrevaluation_modular(train_fname=traindat, label_fname=label_traindat): from modshogun import MulticlassOVREvaluation,ROCEvaluation from modshogun import MulticlassLibLinear,RealFeatures,ContingencyTableEvaluation,ACCURACY from modshogun import MulticlassLabels, Math, CSVFile Math.init_random(1) ground_truth_labels = MulticlassLabels(CSVFile(label_fname)) svm = MulticlassLibLinear(1.0,RealFeatures(CSVFile(train_fname)),ground_truth_labels) 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 generate_gmm_classification_data(request):
from modshogun import GMM, Math
num_classes = int(request.POST['num_classes'])
gmm = GMM(num_classes)
total = 40
rng = 4.0
num = total / num_classes
for i in xrange(num_classes):
gmm.set_nth_mean(np.array([Math.random(-rng, rng) for j in xrange(2)]),
i)
cov_tmp = Math.normal_random(0.2, 0.1)
cov = np.array([[1.0, cov_tmp], [cov_tmp, 1.0]], dtype=float)
gmm.set_nth_cov(cov, i)
data = []
labels = []
for i in xrange(num_classes):
coef = np.zeros(num_classes)
coef[i] = 1.0
gmm.set_coef(coef)
data.append(np.array([gmm.sample() for j in xrange(num)]).T)
labels.append(np.array([i for j in xrange(num)]))
data = np.hstack(data)
data = data / (2.0 * rng)
xmin = np.min(data[0, :])
ymin = np.min(data[1, :])
labels = np.hstack(labels)
toy_data = []
for i in xrange(num_classes * num):
toy_data.append({
'x': data[0, i] - xmin,
'y': data[1, i] - ymin,
'label': float(labels[i])
})
return HttpResponse(json.dumps(toy_data))
def statistics_quadratic_time_mmd (m,dim,difference): from modshogun import RealFeatures from modshogun import MeanShiftDataGenerator from modshogun import GaussianKernel, CustomKernel from modshogun import QuadraticTimeMMD from modshogun import PERMUTATION, MMD2_SPECTRUM, MMD2_GAMMA, BIASED, BIASED_DEPRECATED from modshogun import Statistics, IntVector, RealVector, Math # init seed for reproducability Math.init_random(1) random.seed(17) # number of examples kept low in order to make things fast # streaming data generator for mean shift distributions gen_p=MeanShiftDataGenerator(0, dim); #gen_p.parallel.set_num_threads(1) 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 permutation (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(PERMUTATION); mmd.set_num_null_samples(3); p_value_null=mmd.perform_test(); # reject if p-value is smaller than test level #print "bootstrap: p!=q: ", p_value_null<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 . mmd.set_statistic_type(BIASED); mmd.set_null_approximation_method(MMD2_SPECTRUM); mmd.set_num_eigenvalues_spectrum(3); mmd.set_num_samples_spectrum(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_DEPRECATED statistic mmd.set_statistic_type(BIASED_DEPRECATED); 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 permutation. 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_statistic_type(BIASED); mmd.set_null_approximation_method(PERMUTATION); mmd.set_num_null_samples(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_null,p_value_spectrum,p_value_gamma,
def gen_data(ftype, num_samples, show_data=False):
from modshogun import Math
from modshogun import FactorType, Factor, TableFactorType, FactorGraph
from modshogun import FactorGraphObservation, FactorGraphLabels, FactorGraphFeatures
from modshogun import MAPInference, TREE_MAX_PROD
Math.init_random(17)
samples = FactorGraphFeatures(num_samples)
labels = FactorGraphLabels(num_samples)
for i in range(num_samples):
vc = np.array([2, 2, 2], np.int32)
fg = FactorGraph(vc)
data1 = np.array([2.0 * Math.random(0.0, 1.0) - 1.0 for i in range(2)])
vind1 = np.array([0, 1], np.int32)
fac1 = Factor(ftype[0], vind1, data1)
fg.add_factor(fac1)
data2 = np.array([2.0 * Math.random(0.0, 1.0) - 1.0 for i in range(2)])
vind2 = np.array([1, 2], np.int32)
fac2 = Factor(ftype[0], vind2, data2)
fg.add_factor(fac2)
data3 = np.array([2.0 * Math.random(0.0, 1.0) - 1.0 for i in range(2)])
vind3 = np.array([0], np.int32)
fac3 = Factor(ftype[1], vind3, data3)
fg.add_factor(fac3)
data4 = np.array([2.0 * Math.random(0.0, 1.0) - 1.0 for i in range(2)])
vind4 = np.array([1], np.int32)
fac4 = Factor(ftype[1], vind4, data4)
fg.add_factor(fac4)
data5 = np.array([2.0 * Math.random(0.0, 1.0) - 1.0 for i in range(2)])
vind5 = np.array([2], np.int32)
fac5 = Factor(ftype[1], vind5, data5)
fg.add_factor(fac5)
data6 = np.array([1.0])
vind6 = np.array([0], np.int32)
fac6 = Factor(ftype[2], vind6, data6)
fg.add_factor(fac6)
data7 = np.array([1.0])
vind7 = np.array([2], np.int32)
fac7 = Factor(ftype[2], vind7, data7)
fg.add_factor(fac7)
samples.add_sample(fg)
fg.connect_components()
fg.compute_energies()
infer_met = MAPInference(fg, TREE_MAX_PROD)
infer_met.inference()
fg_obs = infer_met.get_structured_outputs()
labels.add_label(fg_obs)
if show_data:
state = fg_obs.get_data()
print(state)
return samples, labels
def statistics_linear_time_mmd (n,dim,difference): from modshogun import RealFeatures from modshogun import MeanShiftDataGenerator from modshogun import GaussianKernel from modshogun import LinearTimeMMD from modshogun import PERMUTATION, MMD1_GAUSSIAN from modshogun import EuclideanDistance from modshogun 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 # sampling null and gaussian approximation (ony for really large samples) alpha=0.05 #print "computing p-value using sampling null" mmd.set_null_approximation_method(PERMUTATION) mmd.set_num_null_samples(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(PERMUTATION) mmd.set_num_null_samples(10) # normally, far more iterations are needed null_samples=mmd.sample_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
def statistics_quadratic_time_mmd(m, dim, difference):
from modshogun import RealFeatures
from modshogun import MeanShiftDataGenerator
from modshogun import GaussianKernel, CustomKernel
from modshogun import QuadraticTimeMMD
from modshogun import BOOTSTRAP, MMD2_SPECTRUM, MMD2_GAMMA, BIASED, UNBIASED
from modshogun import Statistics, IntVector, RealVector, Math
# init seed for reproducability
Math.init_random(1)
random.seed(17)
# number of examples kept low in order to make things fast
# streaming data generator for mean shift distributions
gen_p = MeanShiftDataGenerator(0, dim)
#gen_p.parallel.set_num_threads(1)
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_hsic(n, difference, angle):
from modshogun import RealFeatures
from modshogun import DataGenerator
from modshogun import GaussianKernel
from modshogun import HSIC
from modshogun import PERMUTATION, HSIC_GAMMA
from modshogun import EuclideanDistance
from modshogun import Statistics, Math
# for reproducable results (the numpy one might not be reproducible across
# different OS/Python-distributions
Math.init_random(1)
np.random.seed(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(np.array([data[0]]))
features_y = RealFeatures(np.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 = np.random.permutation(features_x.get_num_vectors()).astype(
np.int32)
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 = np.median(distances)
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 = np.median(distances)
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 sampling null"
hsic.set_null_approximation_method(PERMUTATION)
# normally, at least 250 iterations should be done, but that takes long
hsic.set_num_null_samples(100)
# sampling null 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
# sampling null, biased statistic
#print "sampling null distribution using sample_null"
hsic.set_null_approximation_method(PERMUTATION)
hsic.set_num_null_samples(100)
null_samples = hsic.sample_null()
#print "null mean:", np.mean(null_samples)
#print "null variance:", np.var(null_samples)
#hist(null_samples, 100); show()
return p_value_boot, thresh_boot, p_value_gamma, thresh_gamma, statistic, null_samples
def statistics_mmd_kernel_selection_single(m,distance,stretch,num_blobs,angle,selection_method):
from modshogun import RealFeatures
from modshogun import GaussianBlobsDataGenerator
from modshogun import GaussianKernel, CombinedKernel
from modshogun import LinearTimeMMD
from modshogun import MMDKernelSelectionMedian
from modshogun import MMDKernelSelectionMax
from modshogun import MMDKernelSelectionOpt
from modshogun import PERMUTATION, MMD1_GAUSSIAN
from modshogun import EuclideanDistance
from modshogun 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 gen_data(ftype, num_samples, show_data = False): from modshogun import Math from modshogun import FactorType, Factor, TableFactorType, FactorGraph from modshogun import FactorGraphObservation, FactorGraphLabels, FactorGraphFeatures from modshogun import MAPInference, TREE_MAX_PROD Math.init_random(17) samples = FactorGraphFeatures(num_samples) labels = FactorGraphLabels(num_samples) for i in xrange(num_samples): vc = np.array([2,2,2], np.int32) fg = FactorGraph(vc) data1 = np.array([2.0*Math.random(0.0,1.0)-1.0 for i in xrange(2)]) vind1 = np.array([0,1], np.int32) fac1 = Factor(ftype[0], vind1, data1) fg.add_factor(fac1) data2 = np.array([2.0*Math.random(0.0,1.0)-1.0 for i in xrange(2)]) vind2 = np.array([1,2], np.int32) fac2 = Factor(ftype[0], vind2, data2) fg.add_factor(fac2) data3 = np.array([2.0*Math.random(0.0,1.0)-1.0 for i in xrange(2)]) vind3 = np.array([0], np.int32) fac3 = Factor(ftype[1], vind3, data3) fg.add_factor(fac3) data4 = np.array([2.0*Math.random(0.0,1.0)-1.0 for i in xrange(2)]) vind4 = np.array([1], np.int32) fac4 = Factor(ftype[1], vind4, data4) fg.add_factor(fac4) data5 = np.array([2.0*Math.random(0.0,1.0)-1.0 for i in xrange(2)]) vind5 = np.array([2], np.int32) fac5 = Factor(ftype[1], vind5, data5) fg.add_factor(fac5) data6 = np.array([1.0]) vind6 = np.array([0], np.int32) fac6 = Factor(ftype[2], vind6, data6) fg.add_factor(fac6) data7 = np.array([1.0]) vind7 = np.array([2], np.int32) fac7 = Factor(ftype[2], vind7, data7) fg.add_factor(fac7) samples.add_sample(fg) fg.connect_components() fg.compute_energies() infer_met = MAPInference(fg, TREE_MAX_PROD) infer_met.inference() fg_obs = infer_met.get_structured_outputs() labels.add_label(fg_obs) if show_data: state = fg_obs.get_data() print state return samples, labels
def statistics_linear_time_mmd(n, dim, difference):
from modshogun import RealFeatures
from modshogun import MeanShiftDataGenerator
from modshogun import GaussianKernel
from modshogun import LinearTimeMMD
from modshogun import PERMUTATION, MMD1_GAUSSIAN
from modshogun import EuclideanDistance
from modshogun 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
# sampling null and gaussian approximation (ony for really large samples)
alpha = 0.05
#print "computing p-value using sampling null"
mmd.set_null_approximation_method(PERMUTATION)
mmd.set_num_null_samples(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(PERMUTATION)
mmd.set_num_null_samples(10) # normally, far more iterations are needed
null_samples = mmd.sample_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
def evaluation_cross_validation_multiclass_storage (traindat=traindat, label_traindat=label_traindat):
from modshogun import CrossValidation, CrossValidationResult
from modshogun import CrossValidationPrintOutput
from modshogun import CrossValidationMKLStorage, CrossValidationMulticlassStorage
from modshogun import MulticlassAccuracy, F1Measure
from modshogun import StratifiedCrossValidationSplitting
from modshogun import MulticlassLabels
from modshogun import RealFeatures, CombinedFeatures
from modshogun import GaussianKernel, CombinedKernel
from modshogun import MKLMulticlass
from modshogun 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 modshogun import RealFeatures from modshogun import DataGenerator from modshogun import GaussianKernel from modshogun import HSIC from modshogun import BOOTSTRAP, HSIC_GAMMA from modshogun import EuclideanDistance from modshogun 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
