def _gmm_from_memberships(data, memberships, covariance_type):
clusters = set(memberships)
n_clusters = len(clusters)
gmm = GMM(n_components=n_clusters, params='m')
gmm.weights_ = np.ones([n_clusters])/n_clusters
gmm.means_ = np.zeros([n_clusters, data.shape[1]])
if covariance_type == 'diag':
gmm.covars_ = np.zeros([n_clusters, data.shape[1]])
if covariance_type == 'spherical':
gmm.covars_ = np.zeros([n_clusters])
if covariance_type == 'full':
gmm.covars_ = np.zeros([n_clusters, data.shape[1], data.shape[1]])
for cluster in clusters:
cluster = int(cluster)
indices = (memberships == cluster)
gmm.means_[cluster, :] = data[indices, :].mean(axis=0)
if covariance_type in ['diag', 'spherical']:
#TODO Fix covariance calculation, for now, return cov=1
#D = np.diag(np.cov(data[indices, :].T))
D = np.ones([data.shape[1]])
if covariance_type == 'spherical':
gmm.covars_[cluster] = D.mean()
else:
gmm.covars_[cluster] = D
if covariance_type == 'full':
cov_estimator = OAS()
cov_estimator.fit(data[indices, :])
gmm.covars_[cluster] = cov_estimator.covariance_
return gmm
def fit_base(self, X, y):
"""
Fit the SLDA model to the base data.
:param X: an Nxd torch tensor of base initialization data
:param y: an Nx1-dimensional torch tensor of the associated labels for X
:return: None
"""
print('\nFitting Base...')
X = X.to(self.device)
y = y.squeeze()
# update positive and negative means
cls_ix = torch.arange(self.num_classes)
for k in torch.unique(y):
self.posW[k] = X[y == k].mean(0)
self.posT[k] = X[y == k].shape[0]
for k in cls_ix:
self.negW[k] = X[y != k].mean(0)
self.negT[k] = X[y != k].shape[0]
self.num_updates = X.shape[0]
print('\nEstimating initial covariance matrix...')
from sklearn.covariance import OAS
cov_estimator = OAS(assume_centered=True)
cov_estimator.fit((X - self.posW[y]).cpu().numpy())
self.Sigma = torch.from_numpy(cov_estimator.covariance_).float().to(
self.device)
print('\nBuilding initial OOD threshold(s)...')
self.ood_predict(X, y)
print('')
def _gmm_from_memberships(data, memberships, covariance_type):
clusters = set(memberships)
n_clusters = len(clusters)
gmm = GMM(n_components=n_clusters, params='m')
gmm.weights_ = np.ones([n_clusters]) / n_clusters
gmm.means_ = np.zeros([n_clusters, data.shape[1]])
if covariance_type == 'diag':
gmm.covars_ = np.zeros([n_clusters, data.shape[1]])
if covariance_type == 'spherical':
gmm.covars_ = np.zeros([n_clusters])
if covariance_type == 'full':
gmm.covars_ = np.zeros([n_clusters, data.shape[1], data.shape[1]])
for cluster in clusters:
cluster = int(cluster)
indices = (memberships == cluster)
gmm.means_[cluster, :] = data[indices, :].mean(axis=0)
if covariance_type in ['diag', 'spherical']:
#TODO Fix covariance calculation, for now, return cov=1
#D = np.diag(np.cov(data[indices, :].T))
D = np.ones([data.shape[1]])
if covariance_type == 'spherical':
gmm.covars_[cluster] = D.mean()
else:
gmm.covars_[cluster] = D
if covariance_type == 'full':
cov_estimator = OAS()
cov_estimator.fit(data[indices, :])
gmm.covars_[cluster] = cov_estimator.covariance_
return gmm
def _shrink_covariance(asset_returns):
"""
Regularise/Shrink the asset covariances.
:param asset_returns: (pd.Dataframe) Asset returns
:return: (pd.Dataframe) Shrinked asset returns covariances
"""
oas = OAS()
oas.fit(asset_returns)
shrinked_covariance = oas.covariance_
return shrinked_covariance
def _shrink_covariance(covariance):
"""
Regularise/Shrink the asset covariances.
:param covariance: (pd.Dataframe) asset returns covariances
:return: (pd.Dataframe) shrinked asset returns covariances
"""
oas = OAS()
oas.fit(covariance)
shrinked_covariance = oas.covariance_
return pd.DataFrame(shrinked_covariance, index=covariance.columns, columns=covariance.columns)
def lw_covars(returns):
"""
Calculates a constrained covariance matrix between the returns.
:return: A pandas dataframe of the covariance between the returns
"""
co_vars = returns.cov() * WEEKDAYS_PER_YEAR
if logger.isEnabledFor(logging.DEBUG):
logger.debug("Calcing covars as table: {}".format(
returns.to_dict('list')))
# Shrink the covars (Ledoit and Wolff)
sk = OAS(assume_centered=True)
sk.fit(returns.values)
return (1 - sk.shrinkage_) * co_vars + sk.shrinkage_ * np.trace(
co_vars) / len(co_vars) * np.identity(len(co_vars))
def OAS_est(X):
'''
OAS coefficient estimate
X_size = (n_samples, n_features)
'''
oa = OAS()
cov_oa = oa.fit(X).covariance_
return cov_oa
def fit_base(self, X, y):
"""
Fit the SLDA model to the base data.
:param X: an Nxd torch tensor of base initialization data
:param y: an Nx1-dimensional torch tensor of the associated labels for X
:return: None
"""
print('\nFitting Base...')
# update class means
for k in torch.unique(y):
self.muK[k] = X[y == k].mean(0)
self.cK[k] = X[y == k].shape[0]
self.num_updates = X.shape[0]
print('\nEstimating initial covariance matrix...')
from sklearn.covariance import OAS
cov_estimator = OAS(assume_centered=True)
cov_estimator.fit((X - self.muK[y]).cpu().numpy())
self.Sigma = torch.from_numpy(cov_estimator.covariance_).float().to(
self.device)
def correlations(df, categorical_portions):
# The more samples, the slower, but the more accurate the categorical correlation
NUM_CATEGORICAL_SAMPLES = 5
for i in range(NUM_CATEGORICAL_SAMPLES):
df = df.append(df, ignore_index=True)
categorical_cols = list(categorical_portions.keys())
# First generate continuous samples for categorical values. We do this by sampling from
# a truncated normal distribution in the range for that continous variable.
for categorical_col in categorical_cols:
portions = categorical_portions[categorical_col]
# The values of the categorical variable in order
portions_keys = [val for val, frac in portions]
for i, cat_val in enumerate(df[categorical_col]):
if len(portions) == 1:
# Normal sample
df.loc[i, categorical_col] = norm.rvs()
continue
ind = portions_keys.index(cat_val)
# Get sums of prev portions including and not including this portion
sum_a = sum(map(lambda i: portions[i][1], range(ind)))
sum_b = sum_a + portions[ind][1]
# Get thresholds
threshold_a = norm.ppf(sum_a, loc=0.0, scale=1.0)
threshold_b = norm.ppf(sum_b, loc=0.0, scale=1.0)
# Sample truncated norm
df.loc[i, categorical_col] = truncnorm.rvs(threshold_a,
threshold_b)
# estimate covariance matrix
estimator = OAS()
estimator.fit(df.values)
cov = pd.DataFrame(estimator.covariance_,
index=df.columns,
columns=df.columns)
return cov
def test_oas():
"""Tests OAS module on a simple dataset.
"""
# test shrinkage coeff on a simple data set
oa = OAS()
oa.fit(X, assume_centered=True)
assert_almost_equal(oa.shrinkage_, 0.018740, 4)
assert_almost_equal(oa.score(X, assume_centered=True), -5.03605, 4)
# compare shrunk covariance obtained from data and from MLE estimate
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X, assume_centered=True)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
# compare estimates given by OAS and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=oa.shrinkage_)
scov.fit(X, assume_centered=True)
assert_array_almost_equal(scov.covariance_, oa.covariance_, 4)
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
oa = OAS()
oa.fit(X_1d, assume_centered=True)
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X_1d, assume_centered=True)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
assert_array_almost_equal((X_1d ** 2).sum() / n_samples, oa.covariance_, 4)
# test shrinkage coeff on a simple data set (without saving precision)
oa = OAS(store_precision=False)
oa.fit(X, assume_centered=True)
assert_almost_equal(oa.score(X, assume_centered=True), -5.03605, 4)
assert(oa.precision_ is None)
### Same tests without assuming centered data
# test shrinkage coeff on a simple data set
oa = OAS()
oa.fit(X)
assert_almost_equal(oa.shrinkage_, 0.020236, 4)
assert_almost_equal(oa.score(X), 2.079025, 4)
# compare shrunk covariance obtained from data and from MLE estimate
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
# compare estimates given by OAS and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=oa.shrinkage_)
scov.fit(X)
assert_array_almost_equal(scov.covariance_, oa.covariance_, 4)
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
oa = OAS()
oa.fit(X_1d)
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X_1d)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
assert_array_almost_equal(empirical_covariance(X_1d), oa.covariance_, 4)
# test shrinkage coeff on a simple data set (without saving precision)
oa = OAS(store_precision=False)
oa.fit(X)
assert_almost_equal(oa.score(X), 2.079025, 4)
assert(oa.precision_ is None)
lw_mse = np.zeros((n_samples_range.size, repeat))
oa_mse = np.zeros((n_samples_range.size, repeat))
lw_shrinkage = np.zeros((n_samples_range.size, repeat))
oa_shrinkage = np.zeros((n_samples_range.size, repeat))
for i, n_samples in enumerate(n_samples_range):
for j in range(repeat):
X = np.dot(
np.random.normal(size=(n_samples, n_features)), coloring_matrix.T)
lw = LedoitWolf(store_precision=False)
lw.fit(X, assume_centered=True)
lw_mse[i,j] = lw.error_norm(real_cov, scaling=False)
lw_shrinkage[i,j] = lw.shrinkage_
oa = OAS(store_precision=False)
oa.fit(X, assume_centered=True)
oa_mse[i,j] = oa.error_norm(real_cov, scaling=False)
oa_shrinkage[i,j] = oa.shrinkage_
# plot MSE
pl.subplot(2,1,1)
pl.errorbar(n_samples_range, lw_mse.mean(1), yerr=lw_mse.std(1),
label='Ledoit-Wolf', color='g')
pl.errorbar(n_samples_range, oa_mse.mean(1), yerr=oa_mse.std(1),
label='OAS', color='r')
pl.ylabel("Squared error")
pl.legend(loc="upper right")
pl.title("Comparison of covariance estimators")
pl.xlim(5, 31)
# plot shrinkage coefficient
def test_oas():
"""Tests OAS module on a simple dataset.
"""
# test shrinkage coeff on a simple data set
X_centered = X - X.mean(axis=0)
oa = OAS(assume_centered=True)
oa.fit(X_centered)
shrinkage_ = oa.shrinkage_
score_ = oa.score(X_centered)
# compare shrunk covariance obtained from data and from MLE estimate
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X_centered,
assume_centered=True)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
# compare estimates given by OAS and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=oa.shrinkage_, assume_centered=True)
scov.fit(X_centered)
assert_array_almost_equal(scov.covariance_, oa.covariance_, 4)
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
oa = OAS(assume_centered=True)
oa.fit(X_1d)
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X_1d, assume_centered=True)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
assert_array_almost_equal((X_1d**2).sum() / n_samples, oa.covariance_, 4)
# test shrinkage coeff on a simple data set (without saving precision)
oa = OAS(store_precision=False, assume_centered=True)
oa.fit(X_centered)
assert_almost_equal(oa.score(X_centered), score_, 4)
assert (oa.precision_ is None)
### Same tests without assuming centered data
# test shrinkage coeff on a simple data set
oa = OAS()
oa.fit(X)
assert_almost_equal(oa.shrinkage_, shrinkage_, 4)
assert_almost_equal(oa.score(X), score_, 4)
# compare shrunk covariance obtained from data and from MLE estimate
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
# compare estimates given by OAS and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=oa.shrinkage_)
scov.fit(X)
assert_array_almost_equal(scov.covariance_, oa.covariance_, 4)
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
oa = OAS()
oa.fit(X_1d)
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X_1d)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
assert_array_almost_equal(empirical_covariance(X_1d), oa.covariance_, 4)
# test with one sample
X_1sample = np.arange(5)
oa = OAS()
with warnings.catch_warnings(record=True):
oa.fit(X_1sample)
# test shrinkage coeff on a simple data set (without saving precision)
oa = OAS(store_precision=False)
oa.fit(X)
assert_almost_equal(oa.score(X), score_, 4)
assert (oa.precision_ is None)
def test_oas():
"""Tests OAS module on a simple dataset.
"""
# test shrinkage coeff on a simple data set
X_centered = X - X.mean(axis=0)
oa = OAS(assume_centered=True)
oa.fit(X_centered)
shrinkage_ = oa.shrinkage_
score_ = oa.score(X_centered)
# compare shrunk covariance obtained from data and from MLE estimate
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X_centered,
assume_centered=True)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
# compare estimates given by OAS and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=oa.shrinkage_, assume_centered=True)
scov.fit(X_centered)
assert_array_almost_equal(scov.covariance_, oa.covariance_, 4)
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
oa = OAS(assume_centered=True)
oa.fit(X_1d)
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X_1d, assume_centered=True)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
assert_array_almost_equal((X_1d ** 2).sum() / n_samples, oa.covariance_, 4)
# test shrinkage coeff on a simple data set (without saving precision)
oa = OAS(store_precision=False, assume_centered=True)
oa.fit(X_centered)
assert_almost_equal(oa.score(X_centered), score_, 4)
assert(oa.precision_ is None)
### Same tests without assuming centered data
# test shrinkage coeff on a simple data set
oa = OAS()
oa.fit(X)
assert_almost_equal(oa.shrinkage_, shrinkage_, 4)
assert_almost_equal(oa.score(X), score_, 4)
# compare shrunk covariance obtained from data and from MLE estimate
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
# compare estimates given by OAS and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=oa.shrinkage_)
scov.fit(X)
assert_array_almost_equal(scov.covariance_, oa.covariance_, 4)
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
oa = OAS()
oa.fit(X_1d)
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X_1d)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
assert_array_almost_equal(empirical_covariance(X_1d), oa.covariance_, 4)
# test with one sample
X_1sample = np.arange(5)
oa = OAS()
with warnings.catch_warnings(record=True):
oa.fit(X_1sample)
# test shrinkage coeff on a simple data set (without saving precision)
oa = OAS(store_precision=False)
oa.fit(X)
assert_almost_equal(oa.score(X), score_, 4)
assert(oa.precision_ is None)
def test_oas():
# Tests OAS module on a simple dataset.
# test shrinkage coeff on a simple data set
X_centered = X - X.mean(axis=0)
oa = OAS(assume_centered=True)
oa.fit(X_centered)
shrinkage_ = oa.shrinkage_
score_ = oa.score(X_centered)
# compare shrunk covariance obtained from data and from MLE estimate
oa_cov_from_mle, oa_shrinkage_from_mle = oas(X_centered,
assume_centered=True)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shrinkage_from_mle, oa.shrinkage_)
# compare estimates given by OAS and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=oa.shrinkage_, assume_centered=True)
scov.fit(X_centered)
assert_array_almost_equal(scov.covariance_, oa.covariance_, 4)
# test with n_features = 1
X_1d = X[:, 0:1]
oa = OAS(assume_centered=True)
oa.fit(X_1d)
oa_cov_from_mle, oa_shrinkage_from_mle = oas(X_1d, assume_centered=True)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shrinkage_from_mle, oa.shrinkage_)
assert_array_almost_equal((X_1d ** 2).sum() / n_samples, oa.covariance_, 4)
# test shrinkage coeff on a simple data set (without saving precision)
oa = OAS(store_precision=False, assume_centered=True)
oa.fit(X_centered)
assert_almost_equal(oa.score(X_centered), score_, 4)
assert(oa.precision_ is None)
# Same tests without assuming centered data--------------------------------
# test shrinkage coeff on a simple data set
oa = OAS()
oa.fit(X)
assert_almost_equal(oa.shrinkage_, shrinkage_, 4)
assert_almost_equal(oa.score(X), score_, 4)
# compare shrunk covariance obtained from data and from MLE estimate
oa_cov_from_mle, oa_shrinkage_from_mle = oas(X)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shrinkage_from_mle, oa.shrinkage_)
# compare estimates given by OAS and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=oa.shrinkage_)
scov.fit(X)
assert_array_almost_equal(scov.covariance_, oa.covariance_, 4)
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
oa = OAS()
oa.fit(X_1d)
oa_cov_from_mle, oa_shrinkage_from_mle = oas(X_1d)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shrinkage_from_mle, oa.shrinkage_)
assert_array_almost_equal(empirical_covariance(X_1d), oa.covariance_, 4)
# test with one sample
# warning should be raised when using only 1 sample
X_1sample = np.arange(5).reshape(1, 5)
oa = OAS()
assert_warns(UserWarning, oa.fit, X_1sample)
assert_array_almost_equal(oa.covariance_,
np.zeros(shape=(5, 5), dtype=np.float64))
# test shrinkage coeff on a simple data set (without saving precision)
oa = OAS(store_precision=False)
oa.fit(X)
assert_almost_equal(oa.score(X), score_, 4)
assert(oa.precision_ is None)
def BIC(X, Y, Z, p_lambda, mode=0, shrinkage=0):
'''
Bayesian information criterion
delta_BIC = BIC_M1 - BIC_M0
M1: feature vectors X and Y modeled by two multivariate gaussians
M0: Z modeled by one gaussian
delta_BIC > 0: accept M1
delta_BIC < 0: accept M0
covariance matrix dimension size < observation size, rank(cov) <= observation size - 1
rank deficient: http://stats.stackexchange.com/questions/60622/why-is-a-sample-covariance-matrix-singular-when-sample-size-is-less-than-number
mode
0: BIC
1: BICc
2: ABF2
shrinkage
0: no shrinkage
1: Ledoit-Wolf
2: OAS
:param X: frame * feature
:param Y: frame * feature
:param Z: frame * feature
:param p_lambda:
:return:
'''
p = X.shape[1]
N_x = X.shape[0]
N_y = Y.shape[0]
N_z = Z.shape[0]
# centering data
mean_X = np.mean(X, axis=0)
mean_Y = np.mean(Y, axis=0)
mean_Z = np.mean(Z, axis=0)
X = X - mean_X
Y = Y - mean_Y
Z = Z - mean_Z
if shrinkage == 1:
lw = LedoitWolf(store_precision=False, assume_centered=False)
lw.fit(X)
sigma_x = lw.covariance_
lw.fit(Y)
sigma_y = lw.covariance_
lw.fit(Z)
sigma_z = lw.covariance_
elif shrinkage == 2:
oa = OAS(store_precision=False, assume_centered=False)
oa.fit(X)
sigma_x = oa.covariance_
oa.fit(Y)
sigma_y = oa.covariance_
oa.fit(Z)
sigma_z = oa.covariance_
else:
sigma_x = np.cov(X, rowvar=0)
sigma_y = np.cov(Y, rowvar=0)
sigma_z = np.cov(Z, rowvar=0)
sign_z, logdet_z = np.linalg.slogdet(sigma_z)
sign_y, logdet_y = np.linalg.slogdet(sigma_y)
sign_x, logdet_x = np.linalg.slogdet(sigma_x)
# det_z = sign_z*np.exp(logdet_z)
# det_y = sign_y*np.exp(logdet_y)
# det_x = sign_x*np.exp(logdet_x)
R = (N_z/2.0) * logdet_z - \
(N_y/2.0) * logdet_y - \
(N_x/2.0) * logdet_x
k_z = (p + p * (p + 1) / 2.0)
if mode == 0:
P = k_z * np.log(N_z) / 2.0
elif mode == 1:
P = k_z * np.log(N_z) * (2.0 / (N_z - 2 * k_z - 1) -
(1.0 / (N_z - k_z - 1))) / 2.0
P *= 10000
elif mode == 2:
P = P_ABF2(mean_X, mean_Y, mean_Z, sigma_x, sigma_y, sigma_z, N_x, N_y,
N_z)
# print R, P, R-p_lambda*P, logdet_z, logdet_y, logdet_x, N_z, N_y, N_x
# if det_z <0: print det_z
# if det_y <0: print det_y
# if det_x <0: print det_x
return R - p_lambda * P
lw_mse = np.zeros((n_samples_range.size, repeat))
oa_mse = np.zeros((n_samples_range.size, repeat))
lw_shrinkage = np.zeros((n_samples_range.size, repeat))
oa_shrinkage = np.zeros((n_samples_range.size, repeat))
for i, n_samples in enumerate(n_samples_range):
for j in range(repeat):
X = np.dot(np.random.normal(size=(n_samples, n_features)),
coloring_matrix.T)
lw = LedoitWolf(store_precision=False, assume_centered=True)
lw.fit(X)
lw_mse[i, j] = lw.error_norm(real_cov, scaling=False)
lw_shrinkage[i, j] = lw.shrinkage_
oa = OAS(store_precision=False, assume_centered=True)
oa.fit(X)
oa_mse[i, j] = oa.error_norm(real_cov, scaling=False)
oa_shrinkage[i, j] = oa.shrinkage_
# plot MSE
plt.subplot(2, 1, 1)
plt.errorbar(
n_samples_range,
lw_mse.mean(1),
yerr=lw_mse.std(1),
label="Ledoit-Wolf",
color="navy",
lw=2,
)
plt.errorbar(
n_samples_range,
lw_mse = np.zeros((n_samples_range.size, repeat))
oa_mse = np.zeros((n_samples_range.size, repeat))
lw_shrinkage = np.zeros((n_samples_range.size, repeat))
oa_shrinkage = np.zeros((n_samples_range.size, repeat))
for i, n_samples in enumerate(n_samples_range):
for j in range(repeat):
X = np.dot(
np.random.normal(size=(n_samples, n_features)), coloring_matrix.T)
lw = LedoitWolf(store_precision=False, assume_centered=True)
lw.fit(X)
lw_mse[i, j] = lw.error_norm(real_cov, scaling=False)
lw_shrinkage[i, j] = lw.shrinkage_
oa = OAS(store_precision=False, assume_centered=True)
oa.fit(X)
oa_mse[i, j] = oa.error_norm(real_cov, scaling=False)
oa_shrinkage[i, j] = oa.shrinkage_
# plot MSE
plt.subplot(2, 1, 1)
plt.errorbar(n_samples_range, lw_mse.mean(1), yerr=lw_mse.std(1),
label='Ledoit-Wolf', color='g')
plt.errorbar(n_samples_range, oa_mse.mean(1), yerr=oa_mse.std(1),
label='OAS', color='r')
plt.ylabel("Squared error")
plt.legend(loc="upper right")
plt.title("Comparison of covariance estimators")
plt.xlim(5, 31)
# plot shrinkage coefficient
print timecourse_files
# roll through the subjects
print np.shape(timecourse_data)[0]
for i in range(np.shape(timecourse_data)[0]) :
#for i in range(10) :
print i
# extract the timecourses for this subejct
subject_timecourses = timecourse_data[i, : ,:]
#print np.shape(subject_timecourses)
# calculate Pearson covariance
X = scale(subject_timecourses, axis=1)
cov = np.dot(X, np.transpose(X)) / np.shape(X)[1]
print cov[:5, :5]
print logm(cov)[:5, :5]
# calculate sparse inverse covariance (precision) matrix
model = OAS(store_precision=False, assume_centered=True)
model.fit(np.transpose(X))
cov = model.covariance_
OAS_matrices[i, :] = np.reshape(cov, (1, 8100))
#print cov[:5, :5]
foo = logm(cov)
#print logm(cov[:5, :5])
## save the data
np.savetxt('/home/jonyoung/IoP_data/Data/connectivity_data/OAS_data.csv', OAS_matrices, delimiter=',')
X_test = np.dot(base_X_test, coloring_matrix)
###############################################################################
# Compute Ledoit-Wolf and Covariances on a grid of shrinkages
from sklearn.covariance import LedoitWolf, OAS, ShrunkCovariance, \
log_likelihood, empirical_covariance
# Ledoit-Wolf optimal shrinkage coefficient estimate
lw = LedoitWolf()
loglik_lw = lw.fit(X_train, assume_centered=True).score(
X_test, assume_centered=True)
# OAS coefficient estimate
oa = OAS()
loglik_oa = oa.fit(X_train, assume_centered=True).score(
X_test, assume_centered=True)
# spanning a range of possible shrinkage coefficient values
shrinkages = np.logspace(-3, 0, 30)
negative_logliks = [-ShrunkCovariance(shrinkage=s).fit(
X_train, assume_centered=True).score(X_test, assume_centered=True) \
for s in shrinkages]
# getting the likelihood under the real model
real_cov = np.dot(coloring_matrix.T, coloring_matrix)
emp_cov = empirical_covariance(X_train)
loglik_real = -log_likelihood(emp_cov, linalg.inv(real_cov))
###############################################################################
# Plot results
pl.figure(-1)
repeat = 100
lw_mse = np.zeros((n_samples_range.size, repeat))
oas_mse = np.zeros((n_samples_range.size, repeat))
lw_shrinkage = np.zeros((n_samples_range.size, repeat))
oas_shrinkage = np.zeros((n_samples_range.size, repeat))
for i, n_samples in enumerate(n_samples_range):
for j in range(repeat):
X = np.dot(np.random.normal(size=(n_samples, n_features)),
coloring_matrix)
lw = LedoitWolf(store_precision=False, assume_centered=True)
lw.fit(X)
lw_mse[i, j] = lw.error_norm(real_cov, scaling=False)
lw_shrinkage[i, j] = lw.shrinkage_
oas = OAS(store_precision=False, assume_centered=True)
oas.fit(X)
oas_mse[i, j] = oas.error_norm(real_cov, scaling=False)
oas_shrinkage[i, j] = oas.shrinkage_
# plot MSE
plt.subplot(211)
plt.errorbar(n_samples_range,
lw_mse.mean(1),
yerr=lw_mse.std(1),
label='Ledoit-Wolf',
color='navy',
lw=2)
plt.errorbar(n_samples_range,
oas_mse.mean(1),
yerr=oas_mse.std(1),
label='OAS',
def test_oas():
"""Tests OAS module on a simple dataset.
"""
# test shrinkage coeff on a simple data set
oa = OAS()
oa.fit(X, assume_centered=True)
assert_almost_equal(oa.shrinkage_, 0.018740, 4)
assert_almost_equal(oa.score(X, assume_centered=True), -5.03605, 4)
# compare shrunk covariance obtained from data and from MLE estimate
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X, assume_centered=True)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
# compare estimates given by OAS and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=oa.shrinkage_)
scov.fit(X, assume_centered=True)
assert_array_almost_equal(scov.covariance_, oa.covariance_, 4)
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
oa = OAS()
oa.fit(X_1d, assume_centered=True)
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X_1d, assume_centered=True)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
assert_array_almost_equal((X_1d ** 2).sum() / n_samples, oa.covariance_, 4)
# test shrinkage coeff on a simple data set (without saving precision)
oa = OAS(store_precision=False)
oa.fit(X, assume_centered=True)
assert_almost_equal(oa.score(X, assume_centered=True), -5.03605, 4)
assert(oa.precision_ is None)
### Same tests without assuming centered data
# test shrinkage coeff on a simple data set
oa = OAS()
oa.fit(X)
assert_almost_equal(oa.shrinkage_, 0.020236, 4)
assert_almost_equal(oa.score(X), 2.079025, 4)
# compare shrunk covariance obtained from data and from MLE estimate
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
# compare estimates given by OAS and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=oa.shrinkage_)
scov.fit(X)
assert_array_almost_equal(scov.covariance_, oa.covariance_, 4)
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
oa = OAS()
oa.fit(X_1d)
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X_1d)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
assert_array_almost_equal(empirical_covariance(X_1d), oa.covariance_, 4)
# test shrinkage coeff on a simple data set (without saving precision)
oa = OAS(store_precision=False)
oa.fit(X)
assert_almost_equal(oa.score(X), 2.079025, 4)
assert(oa.precision_ is None)
def cov2corr(cov):
std_ = np.sqrt(np.diag(cov))
corr = cov / np.outer(std_, std_)
return corr
if has_sklearn:
from sklearn.covariance import LedoitWolf, OAS, MCD
lw = LedoitWolf(store_precision=False)
lw.fit(rr, assume_centered=False)
cov_lw = lw.covariance_
corr_lw = cov2corr(cov_lw)
oas = OAS(store_precision=False)
oas.fit(rr, assume_centered=False)
cov_oas = oas.covariance_
corr_oas = cov2corr(cov_oas)
mcd = MCD() #.fit(rr, reweight=None)
mcd.fit(rr, assume_centered=False)
cov_mcd = mcd.covariance_
corr_mcd = cov2corr(cov_mcd)
titles = ['raw correlation', 'lw', 'oas', 'mcd']
normcolor = None
fig = plt.figure()
for i, c in enumerate([rrcorr, corr_lw, corr_oas, corr_mcd]):
#for i, c in enumerate([np.cov(rr, rowvar=0), cov_lw, cov_oas, cov_mcd]):
ax = fig.add_subplot(2, 2, i + 1)
plot_corr(c, xnames=None, title=titles[i], normcolor=normcolor, ax=ax)
def test_oas():
# Tests OAS module on a simple dataset.
# test shrinkage coeff on a simple data set
X_centered = X - X.mean(axis=0)
oa = OAS(assume_centered=True)
oa.fit(X_centered)
shrinkage_ = oa.shrinkage_
score_ = oa.score(X_centered)
# compare shrunk covariance obtained from data and from MLE estimate
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X_centered,
assume_centered=True)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
# compare estimates given by OAS and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=oa.shrinkage_, assume_centered=True)
scov.fit(X_centered)
assert_array_almost_equal(scov.covariance_, oa.covariance_, 4)
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
oa = OAS(assume_centered=True)
oa.fit(X_1d)
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X_1d, assume_centered=True)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
assert_array_almost_equal((X_1d**2).sum() / n_samples, oa.covariance_, 4)
# test shrinkage coeff on a simple data set (without saving precision)
oa = OAS(store_precision=False, assume_centered=True)
oa.fit(X_centered)
assert_almost_equal(oa.score(X_centered), score_, 4)
assert (oa.precision_ is None)
# Same tests without assuming centered data--------------------------------
# test shrinkage coeff on a simple data set
oa = OAS()
oa.fit(X)
assert_almost_equal(oa.shrinkage_, shrinkage_, 4)
assert_almost_equal(oa.score(X), score_, 4)
# compare shrunk covariance obtained from data and from MLE estimate
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
# compare estimates given by OAS and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=oa.shrinkage_)
scov.fit(X)
assert_array_almost_equal(scov.covariance_, oa.covariance_, 4)
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
oa = OAS()
oa.fit(X_1d)
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X_1d)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
assert_array_almost_equal(empirical_covariance(X_1d), oa.covariance_, 4)
# test with one sample
# FIXME I don't know what this test does
X_1sample = np.arange(5)
oa = OAS()
assert_warns(UserWarning, oa.fit, X_1sample)
assert_array_almost_equal(oa.covariance_,
np.zeros(shape=(5, 5), dtype=np.float64))
# test shrinkage coeff on a simple data set (without saving precision)
oa = OAS(store_precision=False)
oa.fit(X)
assert_almost_equal(oa.score(X), score_, 4)
assert (oa.precision_ is None)
# #############################################################################
# Compare different approaches to setting the parameter
# GridSearch for an optimal shrinkage coefficient
tuned_parameters = [{'shrinkage': shrinkages}]
cv = GridSearchCV(ShrunkCovariance(), tuned_parameters, cv=5)
cv.fit(X_train)
# Ledoit-Wolf optimal shrinkage coefficient estimate
lw = LedoitWolf()
loglik_lw = lw.fit(X_train).score(X_test)
# OAS coefficient estimate
oa = OAS()
loglik_oa = oa.fit(X_train).score(X_test)
# #############################################################################
# Plot results
fig = plt.figure()
plt.title("Regularized covariance: likelihood and shrinkage coefficient")
plt.xlabel('Regularization parameter: shrinkage coefficient')
plt.ylabel('Error: negative log-likelihood on test data')
# range shrinkage curve
plt.loglog(shrinkages, negative_logliks, label="Negative log-likelihood")
plt.plot(plt.xlim(), 2 * [loglik_real], '--r',
label="Real covariance likelihood")
# adjust view
lik_max = np.amax(negative_logliks)
if args.verbose:
print('sys.argv:')
print(sys.argv)
print()
print('numpy version:', np.__version__)
print('pandas version:', pd.__version__)
print('scipy version:', sp.__version__)
print()
gene_expr_raw = pd.read_table(args.data)
gene_expr = gene_expr_raw.T
X_centered = (gene_expr - gene_expr.mean()) / np.sqrt(gene_expr.var())
oa = OAS(store_precision=True, assume_centered=True)
gene_expr_OAS_corr = oa.fit(X_centered)
n_genes = gene_expr_OAS_corr.covariance_.shape[1]
g = Graph(directed=False)
g.add_vertex(n=n_genes)
spearman = g.new_ep("double", 0)
pval = g.new_ep("double", 0)
genes = g.new_vertex_property(
"string", np.array(np.array(gene_expr.columns, dtype="str")))
g.vertex_properties["genes"] = genes
for i in range(n_genes):
for j in range(i):
spearman_r = sp.stats.spearmanr(X_centered.iloc[:, i],
X_centered.iloc[:, j])
lw_mse = np.zeros((n_samples_range.size, repeat))
oa_mse = np.zeros((n_samples_range.size, repeat))
lw_shrinkage = np.zeros((n_samples_range.size, repeat))
oa_shrinkage = np.zeros((n_samples_range.size, repeat))
for i, n_samples in enumerate(n_samples_range):
for j in range(repeat):
X = np.dot(np.random.normal(size=(n_samples, n_features)),
coloring_matrix.T)
lw = LedoitWolf(store_precision=False)
lw.fit(X, assume_centered=True)
lw_mse[i, j] = lw.error_norm(real_cov, scaling=False)
lw_shrinkage[i, j] = lw.shrinkage_
oa = OAS(store_precision=False)
oa.fit(X, assume_centered=True)
oa_mse[i, j] = oa.error_norm(real_cov, scaling=False)
oa_shrinkage[i, j] = oa.shrinkage_
# plot MSE
pl.subplot(2, 1, 1)
pl.errorbar(n_samples_range,
lw_mse.mean(1),
yerr=lw_mse.std(1),
label='Ledoit-Wolf',
color='g')
pl.errorbar(n_samples_range,
oa_mse.mean(1),
yerr=oa_mse.std(1),
label='OAS',
color='r')
def cov2corr(cov):
std_ = np.sqrt(np.diag(cov))
corr = cov / np.outer(std_, std_)
return corr
if has_sklearn:
from sklearn.covariance import LedoitWolf, OAS, MCD
lw = LedoitWolf(store_precision=False)
lw.fit(rr, assume_centered=False)
cov_lw = lw.covariance_
corr_lw = cov2corr(cov_lw)
oas = OAS(store_precision=False)
oas.fit(rr, assume_centered=False)
cov_oas = oas.covariance_
corr_oas = cov2corr(cov_oas)
mcd = MCD()#.fit(rr, reweight=None)
mcd.fit(rr, assume_centered=False)
cov_mcd = mcd.covariance_
corr_mcd = cov2corr(cov_mcd)
titles = ['raw correlation', 'lw', 'oas', 'mcd']
normcolor = None
fig = plt.figure()
for i, c in enumerate([rrcorr, corr_lw, corr_oas, corr_mcd]):
#for i, c in enumerate([np.cov(rr, rowvar=0), cov_lw, cov_oas, cov_mcd]):
ax = fig.add_subplot(2,2,i+1)
plot_corr(c, xnames=None, title=titles[i],
def test_oas():
# Tests OAS module on a simple dataset.
# test shrinkage coeff on a simple data set
X_centered = X - X.mean(axis=0)
oa = OAS(assume_centered=True)
oa.fit(X_centered)
shrinkage_ = oa.shrinkage_
score_ = oa.score(X_centered)
# compare shrunk covariance obtained from data and from MLE estimate
oa_cov_from_mle, oa_shrinkage_from_mle = oas(X_centered,
assume_centered=True)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shrinkage_from_mle, oa.shrinkage_)
# compare estimates given by OAS and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=oa.shrinkage_, assume_centered=True)
scov.fit(X_centered)
assert_array_almost_equal(scov.covariance_, oa.covariance_, 4)
# test with n_features = 1
X_1d = X[:, 0:1]
oa = OAS(assume_centered=True)
oa.fit(X_1d)
oa_cov_from_mle, oa_shrinkage_from_mle = oas(X_1d, assume_centered=True)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shrinkage_from_mle, oa.shrinkage_)
assert_array_almost_equal((X_1d**2).sum() / n_samples, oa.covariance_, 4)
# test shrinkage coeff on a simple data set (without saving precision)
oa = OAS(store_precision=False, assume_centered=True)
oa.fit(X_centered)
assert_almost_equal(oa.score(X_centered), score_, 4)
assert (oa.precision_ is None)
# Same tests without assuming centered data--------------------------------
# test shrinkage coeff on a simple data set
oa = OAS()
oa.fit(X)
assert_almost_equal(oa.shrinkage_, shrinkage_, 4)
assert_almost_equal(oa.score(X), score_, 4)
# compare shrunk covariance obtained from data and from MLE estimate
oa_cov_from_mle, oa_shrinkage_from_mle = oas(X)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shrinkage_from_mle, oa.shrinkage_)
# compare estimates given by OAS and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=oa.shrinkage_)
scov.fit(X)
assert_array_almost_equal(scov.covariance_, oa.covariance_, 4)
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
oa = OAS()
oa.fit(X_1d)
oa_cov_from_mle, oa_shrinkage_from_mle = oas(X_1d)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shrinkage_from_mle, oa.shrinkage_)
assert_array_almost_equal(empirical_covariance(X_1d), oa.covariance_, 4)
# test with one sample
# warning should be raised when using only 1 sample
X_1sample = np.arange(5).reshape(1, 5)
oa = OAS()
warn_msg = (
"Only one sample available. You may want to reshape your data array")
with pytest.warns(UserWarning, match=warn_msg):
oa.fit(X_1sample)
assert_array_almost_equal(oa.covariance_,
np.zeros(shape=(5, 5), dtype=np.float64))
# test shrinkage coeff on a simple data set (without saving precision)
oa = OAS(store_precision=False)
oa.fit(X)
assert_almost_equal(oa.score(X), score_, 4)
assert (oa.precision_ is None)
