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simulation.py
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simulation.py
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"""Simulation estimating Type I and Type II error of CBT and KTST.
Author: Sandro Vega-Pons, Emanuele Olivetti
"""
import numpy as np
from sklearn.metrics.pairwise import pairwise_distances
from kernel_two_sample_test import MMD2u, compute_null_distribution
from sklearn.svm import SVC
from sklearn.grid_search import GridSearchCV
from sklearn.cross_validation import StratifiedKFold, cross_val_score
# from multiprocessing import cpu_count
from joblib import Parallel, delayed
# Temporarily stop warnings to cope with the too verbose sklearn
# GridSearchCV.score warning:
import warnings
warnings.simplefilter("ignore")
# boundaries for seeds generation during parallel processing:
MAX_INT = np.iinfo(np.uint32(1)).max
MIN_INT = np.iinfo(np.uint32(1)).min
def estimate_pvalue(score_unpermuted, scores_null):
iterations = len(scores_null)
p_value = max(1.0/iterations, (scores_null > score_unpermuted).sum() /
float(iterations))
return p_value
def compute_svm_score(K, y, n_folds, scoring='accuracy', random_state=0):
cv = StratifiedKFold(y, n_folds=n_folds, shuffle=True,
random_state=random_state)
clf = SVC(C=1.0, kernel='precomputed')
scores = cross_val_score(clf, K, y, scoring=scoring, cv=cv, n_jobs=1)
score = scores.mean()
return score
def compute_svm_score_nestedCV(K, y, n_folds, scoring='accuracy',
random_state=None,
param_grid=[{'C': np.logspace(-5, 5, 20)}]):
cv = StratifiedKFold(y, n_folds=n_folds, shuffle=True,
random_state=random_state)
scores = np.zeros(n_folds)
for i, (train, test) in enumerate(cv):
cvclf = SVC(kernel='precomputed')
y_train = y[train]
cvcv = StratifiedKFold(y_train, n_folds=n_folds,
shuffle=True,
random_state=random_state)
clf = GridSearchCV(cvclf, param_grid=param_grid, scoring=scoring,
cv=cvcv, n_jobs=1)
clf.fit(K[:, train][train, :], y_train)
scores[i] = clf.score(K[test, :][:, train], y[test])
return scores.mean()
if __name__ == '__main__':
np.random.seed(0)
print("JSTSP Simulation Experiments.")
nA = 20 # size of class A
nB = 20 # size of class B
d = 5 # number of dimensions
# separation between the two normally-distributed classes:
delta = 0.75
twist = np.ones(d)
print("nA = %s" % nA)
print("nB = %s" % nB)
print("d = %s" % d)
print("delta = %s" % delta)
print("twist = %s" % twist)
muA = np.zeros(d)
muB = np.ones(d) * delta
covA = np.eye(d)
covB = np.eye(d) * twist
seed_data = 0 # random generation of data
rng_data = np.random.RandomState(seed_data)
seed_ktst = 0 # random permutations of KTST
rng_ktst = np.random.RandomState(seed_ktst)
seed_cv = 0 # random splits of cross-validation
rng_cv = np.random.RandomState(seed_cv)
svm_param_grid = [{'C': np.logspace(-5, 5, 20)}]
# svm_param_grid = [{'C': np.logspace(-3, 2, 10)}]
repetitions = 100
print("This experiments will be repeated on %s randomly-sampled datasets."
% repetitions)
scores = np.zeros(repetitions)
p_value_scores = np.zeros(repetitions)
mmd2us = np.zeros(repetitions)
p_value_mmd2us = np.zeros(repetitions)
for r in range(repetitions):
print("")
print("Repetition %s" % r)
A = rng_data.multivariate_normal(muA, covA, size=nA)
B = rng_data.multivariate_normal(muB, covB, size=nB)
X = np.vstack([A, B])
y = np.concatenate([np.zeros(nA), np.ones(nB)])
distances = pairwise_distances(X, metric='euclidean')
sigma2 = np.median(distances) ** 2.0
K = np.exp(- distances * distances / sigma2)
# K = X.dot(X.T)
iterations = 10000
mmd2u_unpermuted = MMD2u(K, nA, nB)
print("mmd2u: %s" % mmd2u_unpermuted)
mmd2us[r] = mmd2u_unpermuted
mmd2us_null = compute_null_distribution(K, nA, nB, iterations,
random_state=rng_ktst)
p_value_mmd2u = estimate_pvalue(mmd2u_unpermuted, mmd2us_null)
print("mmd2u p-value: %s" % p_value_mmd2u)
p_value_mmd2us[r] = p_value_mmd2u
scoring = 'accuracy'
n_folds = 5
iterations = 1
# score_unpermuted = compute_svm_score_nestedCV(K, y, n_folds,
# scoring=scoring,
# random_state=rng_cv)
rngs = [np.random.RandomState(rng_cv.randint(low=MIN_INT, high=MAX_INT)) for i in range(iterations)]
scores_unpermuted = Parallel(n_jobs=-1)(delayed(compute_svm_score_nestedCV)(K, y, n_folds, scoring, rngs[i], param_grid=svm_param_grid) for i in range(iterations))
score_unpermuted = np.mean(scores_unpermuted)
print("accuracy: %s" % score_unpermuted)
scores[r] = score_unpermuted
# print("Doing permutations:"),
iterations = 100
scores_null = np.zeros(iterations)
# for i in range(iterations):
# if (i % 10) == 0:
# print(i)
# yi = rng_cv.permutation(y)
# scores_null[i] = compute_svm_score_nestedCV(K, yi, n_folds,
# scoring=scoring,
# random_state=rng_cv)
rngs = [np.random.RandomState(rng_cv.randint(low=MIN_INT, high=MAX_INT)) for i in range(iterations)]
yis = [np.random.permutation(y) for i in range(iterations)]
scores_null = Parallel(n_jobs=-1)(delayed(compute_svm_score_nestedCV)(K, yis[i], n_folds, scoring, rngs[i], param_grid=svm_param_grid) for i in range(iterations))
p_value_score = estimate_pvalue(score_unpermuted, scores_null)
p_value_scores[r] = p_value_score
print("%s p-value: %s" % (scoring, p_value_score))
p_value_threshold = 0.05
mmd2u_power = (p_value_mmd2us[:r+1] <= p_value_threshold).mean()
scores_power = (p_value_scores[:r+1] <= p_value_threshold).mean()
print("p_value_threshold: %s" % p_value_threshold)
print("Partial results - MMD2u: %s , %s: %s" %
(mmd2u_power, scoring, scores_power))
print("")
print("FINAL RESULTS:")
p_value_threshold = 0.1
print("p_value_threshold: %s" % p_value_threshold)
mmd2u_power = (p_value_mmd2us <= p_value_threshold).mean()
scores_power = (p_value_scores <= p_value_threshold).mean()
print("MMD2u Power: %s" % mmd2u_power)
print("%s Power: %s" % (scoring, scores_power))
print("")
p_value_threshold = 0.05
print("p_value_threshold: %s" % p_value_threshold)
mmd2u_power = (p_value_mmd2us <= p_value_threshold).mean()
scores_power = (p_value_scores <= p_value_threshold).mean()
print("MMD2u Power: %s" % mmd2u_power)
print("%s Power: %s" % (scoring, scores_power))
print("")
p_value_threshold = 0.01
print("p_value_threshold: %s" % p_value_threshold)
mmd2u_power = (p_value_mmd2us <= p_value_threshold).mean()
scores_power = (p_value_scores <= p_value_threshold).mean()
print("MMD2u Power: %s" % mmd2u_power)
print("%s Power: %s" % (scoring, scores_power))
print("")