def linear_mmd_test(X, Y, null_samples=1000):
mmd = sg.QuadraticTimeMMD()
mmd.set_p(sg.RealFeatures(X.T.astype(np.float64)))
mmd.set_q(sg.RealFeatures(Y.T.astype(np.float64)))
mmd.set_kernel(sg.LinearKernel())
mmd.set_num_null_samples(null_samples)
samps = mmd.sample_null()
stat = mmd.compute_statistic()
p_val = np.mean(stat <= samps)
return p_val, stat, samps
def shogun_mmd(X, Y, kernel_width, null_samples=1000, median_samples=1000,
cache_size=32):
'''
Run an MMD test using a Gaussian kernel.
Parameters
----------
X : row-instance feature array
Y : row-instance feature array
kernel_width : float
The bandwidth of the RBF kernel (sigma).
null_samples : int
How many times to sample from the null distribution.
Returns
-------
p_val : float
The obtained p value of the test.
stat : float
The test statistic.
null_samples : array of length null_samples
The samples from the null distribution.
'''
import modshogun as sg
mmd = sg.QuadraticTimeMMD()
mmd.set_p(sg.RealFeatures(X.T.astype(np.float64)))
mmd.set_q(sg.RealFeatures(Y.T.astype(np.float64)))
mmd.set_kernel(sg.GaussianKernel(cache_size, float(kernel_width)))
mmd.set_num_null_samples(null_samples)
samps = mmd.sample_null()
stat = mmd.compute_statistic()
p_val = np.mean(stat <= samps)
return p_val, stat, samps
import numpy as np import modshogun as sg X = np.random.randn(100, 3) Y = np.random.randn(100, 3) + .5 mmd = sg.QuadraticTimeMMD() mmd.set_p(sg.RealFeatures(X.T)) mmd.set_q(sg.RealFeatures(Y.T)) mmd.set_kernel(sg.GaussianKernel(32, 1)) mmd.set_num_null_samples(200) samps = mmd.sample_null() stat = mmd.compute_statistic()
def rbf_mmd_test(X,
Y,
bandwidth='median',
null_samples=1000,
median_samples=1000,
cache_size=32):
'''
Run an MMD test using a Gaussian kernel.
Parameters
----------
X : row-instance feature array
Y : row-instance feature array
bandwidth : float or 'median'
The bandwidth of the RBF kernel (sigma).
If 'median', estimates the median pairwise distance in the
aggregate sample and uses that.
null_samples : int
How many times to sample from the null distribution.
median_samples : int
How many points to use for estimating the bandwidth.
Returns
-------
p_val : float
The obtained p value of the test.
stat : float
The test statistic.
null_samples : array of length null_samples
The samples from the null distribution.
bandwidth : float
The used kernel bandwidth
'''
if bandwidth == 'median':
from sklearn.metrics.pairwise import euclidean_distances
sub = lambda feats, n: feats[np.random.choice(
feats.shape[0], min(feats.shape[0], n), replace=False)]
Z = np.r_[sub(X, median_samples // 2), sub(Y, median_samples // 2)]
D2 = euclidean_distances(Z, squared=True)
upper = D2[np.triu_indices_from(D2, k=1)]
kernel_width = np.median(upper, overwrite_input=True)
bandwidth = np.sqrt(kernel_width / 2)
# sigma = median / sqrt(2); works better, sometimes at least
del Z, D2, upper
else:
kernel_width = 2 * bandwidth**2
mmd = sg.QuadraticTimeMMD()
mmd.set_p(sg.RealFeatures(X.T.astype(np.float64)))
mmd.set_q(sg.RealFeatures(Y.T.astype(np.float64)))
mmd.set_kernel(sg.GaussianKernel(cache_size, kernel_width))
mmd.set_num_null_samples(null_samples)
samps = mmd.sample_null()
stat = mmd.compute_statistic()
p_val = np.mean(stat <= samps)
return p_val, stat, samps, bandwidth
def get_estimates(gen, sigmas=None, n_reps=100, n_null_samps=1000,
cache_size=64, rep_states=False, name=None,
save_samps=False, thresh_levels=(.2, .1, .05, .01)):
if sigmas is None:
sigmas = np.logspace(-1.7, 1.7, num=30)
sigmas = np.asarray(sigmas)
mmd = sg.QuadraticTimeMMD()
mmd.set_num_null_samples(n_null_samps)
mmd_mk = mmd.multikernel()
for s in sigmas:
mmd_mk.add_kernel(sg.GaussianKernel(cache_size, 2 * s**2))
info = OrderedDict()
for k in 'sigma rep mmd_est var_est p'.split():
info[k] = []
thresh_names = []
for l in thresh_levels:
s = 'thresh_{}'.format(l)
thresh_names.append(s)
info[s] = []
if save_samps:
info['samps'] = []
thresh_prob = 1 - np.asarray(thresh_levels)
bar = pb.ProgressBar()
if name is not None:
bar.start()
bar.widgets.insert(0, '{} '.format(name))
for rep in bar(xrange(n_reps)):
if rep_states:
rep = np.random.randint(0, 2**32)
X, Y = gen(rs=rep)
else:
X, Y = gen()
n = X.shape[0]
assert Y.shape[0] == n
mmd.set_p(sg.RealFeatures(X.T))
mmd.set_q(sg.RealFeatures(Y.T))
info['sigma'].extend(sigmas)
info['rep'].extend([rep] * len(sigmas))
stat = mmd_mk.compute_statistic()
info['mmd_est'].extend(stat / (n / 2))
samps = mmd_mk.sample_null()
info['p'].extend(np.mean(samps >= stat, axis=0))
if save_samps:
info['samps'].extend(samps.T)
info['var_est'].extend(mmd_mk.compute_variance_h1())
threshes = np.asarray(mquantiles(samps, prob=thresh_prob, axis=0))
for s, t in zip(thresh_names, threshes):
info[s].extend(t)
info = pd.DataFrame(info)
info.set_index(['sigma', 'rep'], inplace=True)
return info