def apply_ktst(K, y, iterations=10000, subjects=False, verbose=True):
"""
Compute MMD^2_u, its null distribution and the p-value of the
kernel two-sample test.
Parameters:
----------
K: array-like
Kernel matrix
y: array_like
class labels
verbose: bool
Verbosity
Returns:
-------
mmd2u: float
MMD^2_u value.
acc_null: array
Null distribution of the MMD^2_u
p_value: float
p-value
"""
assert len(np.unique(y)) == 2, 'KTST only works on binary problems'
# Assuming that the first m rows of the kernel matrix are from one
# class and the other n rows from the second class.
m = len(y[y == 0])
n = len(y[y == 1])
mmd2u = MMD2u(K, m, n)
if verbose:
print("MMD^2_u = %s" % mmd2u)
print("Computing the null distribution.")
if subjects:
perms = [permutation_subjects_ktst(y) for i in range(iterations)]
mmd2u_null = compute_null_distribution_given_permutations(
K, m, n, perms, iterations)
else:
mmd2u_null = compute_null_distribution(K,
m,
n,
iterations,
verbose=verbose)
p_value = max(1.0 / iterations,
(mmd2u_null > mmd2u).sum() / float(iterations))
if verbose:
print("p-value ~= %s \t (resolution : %s)" %
(p_value, 1.0 / iterations))
return mmd2u, mmd2u_null, p_value
def apply_ktst(K, y, iterations=10000, subjects=False, verbose=True):
"""
Compute MMD^2_u, its null distribution and the p-value of the
kernel two-sample test.
Parameters:
----------
K: array-like
Kernel matrix
y: array_like
class labels
verbose: bool
Verbosity
Returns:
-------
mmd2u: float
MMD^2_u value.
acc_null: array
Null distribution of the MMD^2_u
p_value: float
p-value
"""
assert len(np.unique(y)) == 2, 'KTST only works on binary problems'
# Assuming that the first m rows of the kernel matrix are from one
# class and the other n rows from the second class.
m = len(y[y == 0])
n = len(y[y == 1])
mmd2u = MMD2u(K, m, n)
if verbose:
print("MMD^2_u = %s" % mmd2u)
print("Computing the null distribution.")
if subjects:
perms = [permutation_subjects_ktst(y) for i in range(iterations)]
mmd2u_null = compute_null_distribution_given_permutations(K, m, n,
perms,
iterations)
else:
mmd2u_null = compute_null_distribution(K, m, n, iterations,
verbose=verbose)
p_value = max(1.0/iterations, (mmd2u_null > mmd2u).sum()
/ float(iterations))
if verbose:
print("p-value ~= %s \t (resolution : %s)" % (p_value, 1.0/iterations))
return mmd2u, mmd2u_null, p_value
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))
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)
def compute_mmd_struc_func(k_mat,
struc_b6,
struc_btbr,
func_b6,
func_btbr,
iterations=100000):
"""
Computes the mmd values for the structural and functional problems and plot
them with the null distributions.
Parameters:
----------
k_mat: ndarray
Kernel matrix
struc_b6: array like
Structural vectors for B6 class
struc_btbr: array like
Structural vectors for BTBR class
func_b6: array like
Functional vectors for B6 class
func_btbr: array like
Functional vectors for BTBR class
"""
#Computing the number of samples belonging to structural data in order
#to split the kernel matrix.
l_struc = len(struc_b6) + len(struc_btbr)
#Computing MMD values
struc_mmd = MMD2u(k_mat[:l_struc][:, :l_struc], len(struc_b6),
len(struc_btbr))
func_mmd = MMD2u(k_mat[l_struc:][:, l_struc:], len(func_b6),
len(func_btbr))
print "struc_mmd = %s, func_mmd = %s" % (struc_mmd, func_mmd)
#Computing the null-distribution
mmd2u_null_all = compute_null_distribution(
k_mat,
struc_b6.shape[0] + func_b6.shape[0],
struc_btbr.shape[0] + func_btbr.shape[0],
iterations,
seed=123,
verbose=False)
#Computing the p-value
struc_p_value = max(1.0 / iterations,
(mmd2u_null_all > struc_mmd).sum() / float(iterations))
print("struc_p-value ~= %s \t (resolution : %s)" %
(struc_p_value, 1.0 / iterations))
func_p_value = max(1.0 / iterations,
(mmd2u_null_all > func_mmd).sum() / float(iterations))
print("func_p-value ~= %s \t (resolution : %s)" %
(func_p_value, 1.0 / iterations))
fig = plt.figure()
ax = fig.add_subplot(111)
prob, bins, patches = plt.hist(mmd2u_null_all, bins=50, normed=True)
ax.plot(struc_mmd,
prob.max() / 30,
'w*',
markersize=15,
markeredgecolor='k',
markeredgewidth=2,
label="$Structural MMD^2_u = %s$" % struc_mmd)
ax.plot(func_mmd,
prob.max() / 30,
'w^',
markersize=15,
markeredgecolor='k',
markeredgewidth=2,
label="$Functional MMD^2_u = %s$" % func_mmd)
plt.xlabel('$MMD^2_u$')
plt.ylabel('$p(MMD^2_u)$')
plt.title('$MMD^2_u$: null-distribution and observed values')
ax.annotate(
'p-value: %s' % (struc_p_value),
xy=(float(struc_mmd), 4.),
xycoords='data',
xytext=(-105, 30),
textcoords='offset points',
bbox=dict(boxstyle="round", fc="1."),
arrowprops=dict(arrowstyle="->",
connectionstyle="angle,angleA=0,angleB=90,rad=10"),
)
ax.annotate(
'p-value: %s' % (func_p_value),
xy=(float(func_mmd), 4.),
xycoords='data',
xytext=(10, 30),
textcoords='offset points',
bbox=dict(boxstyle="round", fc="1."),
arrowprops=dict(arrowstyle="->",
connectionstyle="angle,angleA=0,angleB=90,rad=10"),
)
plt.legend(numpoints=1)
