def test_covariance():
"""Tests Covariance module on a simple dataset.
"""
# test covariance fit from data
cov = EmpiricalCovariance()
cov.fit(X)
assert_array_almost_equal(empirical_covariance(X), cov.covariance_, 4)
assert_almost_equal(cov.error_norm(empirical_covariance(X)), 0)
assert_almost_equal(
cov.error_norm(empirical_covariance(X), norm='spectral'), 0)
assert_almost_equal(
cov.error_norm(empirical_covariance(X), norm='frobenius'), 0)
assert_almost_equal(
cov.error_norm(empirical_covariance(X), scaling=False), 0)
assert_almost_equal(
cov.error_norm(empirical_covariance(X), squared=False), 0)
# Mahalanobis distances computation test
mahal_dist = cov.mahalanobis(X)
assert(np.amax(mahal_dist) < 250)
assert(np.amin(mahal_dist) > 50)
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
cov = EmpiricalCovariance()
cov.fit(X_1d)
assert_array_almost_equal(empirical_covariance(X_1d), cov.covariance_, 4)
assert_almost_equal(cov.error_norm(empirical_covariance(X_1d)), 0)
assert_almost_equal(
cov.error_norm(empirical_covariance(X_1d), norm='spectral'), 0)
# test integer type
X_integer = np.asarray([[0, 1], [1, 0]])
result = np.asarray([[0.25, -0.25], [-0.25, 0.25]])
assert_array_almost_equal(empirical_covariance(X_integer), result)
def test_suffstat_sk_full():
# compare the EmpiricalCovariance.covariance fitted on X*sqrt(resp)
# with _sufficient_sk_full, n_components=1
rng = np.random.RandomState(0)
n_samples, n_features = 500, 2
# special case 1, assuming data is "centered"
X = rng.rand(n_samples, n_features)
resp = rng.rand(n_samples, 1)
X_resp = np.sqrt(resp) * X
nk = np.array([n_samples])
xk = np.zeros((1, n_features))
covars_pred = _estimate_gaussian_covariance_full(resp, X, nk, xk, 0)
ecov = EmpiricalCovariance(assume_centered=True)
ecov.fit(X_resp)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='spectral'), 0)
# special case 2, assuming resp are all ones
resp = np.ones((n_samples, 1))
nk = np.array([n_samples])
xk = X.mean().reshape((1, -1))
covars_pred = _estimate_gaussian_covariance_full(resp, X, nk, xk, 0)
ecov = EmpiricalCovariance(assume_centered=False)
ecov.fit(X)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='spectral'), 0)
def fit(self, X, n_jobs=-1):
EmpiricalCovariance.fit(self, X)
if not self.no_fit:
CovarianceOutlierDetectionMixin.set_threshold(self,
X,
n_jobs=n_jobs)
return self
def calc_full_covs(net, trainloader, n_classes, layers):
net.eval()
layers_centers = []
layers_precisions = []
for l in range(layers):
outputs_list = []
target_list = []
with torch.no_grad():
for (inputs, targets) in trainloader:
inputs, targets = inputs.to(device), targets.to(device)
outputs = net.intermediate_forward(inputs, layer_index=l)
outputs_list.append(outputs)
target_list.append(targets)
outputs = torch.cat(outputs_list, axis=0)
target_list = torch.cat(target_list)
x_dim = outputs.size(1)
centers = torch.zeros(n_classes, x_dim).cuda()
normlized_outputs = []
for c in range(n_classes):
class_points = outputs[c == target_list]
centers[c] = torch.mean(class_points, axis=0)
normlized_outputs.append(
class_points -
centers[c].unsqueeze(0).expand(class_points.size(0), -1))
normlized_outputs = torch.cat(normlized_outputs, axis=0).cpu()
covs_lasso = EmpiricalCovariance(assume_centered=False)
covs_lasso.fit(normlized_outputs.cpu().numpy())
precision = torch.from_numpy(covs_lasso.precision_).float().cuda()
layers_centers.append(centers)
layers_precisions.append(precision)
return layers_precisions, layers_centers
def test_covariance():
"""Tests Covariance module on a simple dataset.
"""
# test covariance fit from data
cov = EmpiricalCovariance()
cov.fit(X)
assert_array_almost_equal(empirical_covariance(X), cov.covariance_, 4)
assert_almost_equal(cov.error_norm(empirical_covariance(X)), 0)
assert_almost_equal(
cov.error_norm(empirical_covariance(X), norm='spectral'), 0)
assert_almost_equal(
cov.error_norm(empirical_covariance(X), norm='frobenius'), 0)
assert_almost_equal(
cov.error_norm(empirical_covariance(X), scaling=False), 0)
assert_almost_equal(
cov.error_norm(empirical_covariance(X), squared=False), 0)
# Mahalanobis distances computation test
mahal_dist = cov.mahalanobis(X)
assert(np.amax(mahal_dist) < 250)
assert(np.amin(mahal_dist) > 50)
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
cov = EmpiricalCovariance()
cov.fit(X_1d)
assert_array_almost_equal(empirical_covariance(X_1d), cov.covariance_, 4)
assert_almost_equal(cov.error_norm(empirical_covariance(X_1d)), 0)
assert_almost_equal(
cov.error_norm(empirical_covariance(X_1d), norm='spectral'), 0)
# test integer type
X_integer = np.asarray([[0, 1], [1, 0]])
result = np.asarray([[0.25, -0.25], [-0.25, 0.25]])
assert_array_almost_equal(empirical_covariance(X_integer), result)
class CovEmbedding(BaseEstimator, TransformerMixin):
""" Tranformer that returns the coefficients on a flat space to
perform the analysis.
"""
def __init__(self, base_estimator=None, kind='tangent'):
self.base_estimator = base_estimator
self.kind = kind
# if self.base_estimator == None:
# self.base_estimator_ = ...
# else:
# self.base_estimator_ = clone(base_estimator)
def fit(self, X, y=None):
if self.base_estimator is None:
self.base_estimator_ = EmpiricalCovariance(
assume_centered=True)
else:
self.base_estimator_ = clone(self.base_estimator)
if self.kind == 'tangent':
# self.mean_cov = mean_cov = spd_manifold.log_mean(covs)
# Euclidean mean as an approximation to the geodesic
covs = [self.base_estimator_.fit(x).covariance_ for x in X]
covs = my_stack(covs)
mean_cov = np.mean(covs, axis=0)
self.whitening_ = inv_sqrtm(mean_cov)
return self
def transform(self, X):
"""Apply transform to covariances
Parameters
----------
covs: list of array
list of covariance matrices, shape (n_rois, n_rois)
Returns
-------
list of array, transformed covariance matrices,
shape (n_rois * (n_rois+1)/2,)
"""
covs = [self.base_estimator_.fit(x).covariance_ for x in X]
covs = my_stack(covs)
p = covs.shape[-1]
if self.kind == 'tangent':
id_ = np.identity(p)
covs = [self.whitening_.dot(c.dot(self.whitening_)) - id_
for c in covs]
elif self.kind == 'partial correlation':
covs = [cov_to_corr(inv(g)) for g in covs]
elif self.kind == 'correlation':
covs = [cov_to_corr(g) for g in covs]
return np.array([sym_to_vec(c) for c in covs])
def printSciKitCovarianceMatrixs():
#does not work, ValueError: setting an array element with a sequence.
xMaker = RSTCovarianceMatrixMaker()
nums, data, ilabels = getLabeledRSTData(False)
for i,d in enumerate(data):
d['ratio'] = ilabels[i]
xMaker.setInstanceNums(nums)
xMaker.fit(data)
X = xMaker.transform(data)
correlator = EmpiricalCovariance()
correlator.fit(X)
print correlator.covariance_
class CovEmbedding(BaseEstimator, TransformerMixin):
""" Tranformer that returns the coefficients on a flat space to
perform the analysis.
"""
def __init__(self, cov_estimator=None, kind='tangent'):
self.cov_estimator = cov_estimator
self.kind = kind
def fit(self, X, y=None):
if self.cov_estimator is None:
self.cov_estimator_ = EmpiricalCovariance(
assume_centered=True)
else:
self.cov_estimator_ = clone(self.cov_estimator)
if self.kind == 'tangent':
covs = [self.cov_estimator_.fit(x).covariance_ for x in X]
self.mean_cov_ = spd_mfd.frechet_mean(covs, max_iter=30, tol=1e-7)
self.whitening_ = spd_mfd.inv_sqrtm(self.mean_cov_)
return self
def transform(self, X):
"""Apply transform to covariances
Parameters
----------
covs: list of array
list of covariance matrices, shape (n_rois, n_rois)
Returns
-------
list of array, transformed covariance matrices,
shape (n_rois * (n_rois+1)/2,)
"""
covs = [self.cov_estimator_.fit(x).covariance_ for x in X]
covs = spd_mfd.my_stack(covs)
if self.kind == 'tangent':
covs = [spd_mfd.logm(self.whitening_.dot(c).dot(self.whitening_))
for c in covs]
elif self.kind == 'precision':
covs = [spd_mfd.inv(g) for g in covs]
elif self.kind == 'partial correlation':
covs = [prec_to_partial(spd_mfd.inv(g)) for g in covs]
elif self.kind == 'correlation':
covs = [cov_to_corr(g) for g in covs]
else:
raise ValueError("Unknown connectivity measure.")
return np.array([sym_to_vec(c) for c in covs])
def init_w_kmeans(data):
"""Calculate initialization values using K-Means"""
# initialize means
km = KMeans(n_clusters=CLUSTERS)
labs = km.fit_predict(data)
means = km.cluster_centers_
# initialize covariaces
covs = np.empty((CLUSTERS, DIMENSIONS, DIMENSIONS))
for l in np.unique(labs.ravel()):
ce = EmpiricalCovariance()
ce.fit(data[labs==l, :])
ce.fit(data)
covs[l,:,:] = ce.covariance_
return means, covs
def main():
print ("Running CV on Mahalanobis Distance based approach.")
mahanalobis()
start_time = time.time()
totalX = []
totalY = []
flag = True
countTrain = 228000
print ("\n\nNow testing on separate data.")
with open("creditcard.csv", "rb") as f:
data = csv.reader(f)
for row in data:
if flag:
flag = False
continue
countTrain += 1
if countTrain > 228000: #CV on 80% of data
totalX.append([float(i) for i in row[:-1]])
totalY.append(int(row[-1]))
print ("Data Loaded")
totalX = scalar.fit_transform(totalX)
clf = EmpiricalCovariance()
clf.fit(totalX)
distances = clf.mahalanobis(totalX)
Y = []
for i in range(len(totalY)):
if np.log10(distances[i]) > 1.838:
Y.append(1)
else:
Y.append(0)
print("%s seconds" % (time.time() - start_time))
print ("Results")
auc = roc_auc_score(totalY, Y)
print("Area under curve : " + str(auc))
fpr, tpr, _ = roc_curve(totalY, Y)
print ("False Positive Rate : " + str(fpr[1]))
_, recall, _ = precision_recall_curve(totalY, Y)
print ("Recall : " + str(recall[1]))
plt.title('Receiver Operating Characteristic')
plt.plot(fpr, tpr, color='darkorange', label='ROC curve (area = %0.3f)' % auc)
plt.ylabel('True Positive Rate')
plt.xlabel('False Positive Rate')
plt.legend(loc="lower right")
plt.show()
class Mahalanobis(BaseEstimator):
"""Mahalanobis distance estimator. Uses Covariance estimate
to compute mahalanobis distance of the observations
from the model.
Parameters
----------
robust : boolean to determine wheter to use robust estimator
based on Minimum Covariance Determinant computation
"""
def __init__(self, robust=False):
if not robust:
from sklearn.covariance import EmpiricalCovariance as CovarianceEstimator #
else:
from sklearn.covariance import MinCovDet as CovarianceEstimator #
self.model = CovarianceEstimator()
self.cov = None
def fit(self, X, y=None, **params):
"""Fits the covariance model according to the given training
data and parameters.
Parameters
----------
X : array-like, shape = [n_samples, n_features]
Training data, where n_samples is the number of samples and
n_features is the number of features.
Returns
-------
self : object
Returns self.
"""
self.cov = self.model.fit(X)
return self
def score(self, X, y=None):
"""Computes the mahalanobis distances of given observations.
The provided observations are assumed to be centered. One may want to
center them using a location estimate first.
Parameters
----------
X : array-like, shape = [n_samples, n_features]
The observations, the Mahalanobis distances of the which we compute.
Returns
-------
mahalanobis_distance : array, shape = [n_observations,]
Mahalanobis distances of the observations.
"""
#return self.model.score(X,assume_centered=True)
return -self.model.mahalanobis(X - self.model.location_)**0.33
def phd(X, Y, **kwargs):
"""
Parameters
----------
X : array-like, shape = [n_features, n_samples]
Training data, where n_samples is the number of samples and
n_features is the number of features.
Y : array-like, shape = [n_samples]
Response variable, where n_samples is the number of samples
Argument dictionary should contain:
kwargs = {
'd' : intrinsic dimension (int)
'residuals' : If True, creates PHDs from the residuals of linear regression
(defaults to False)
'return_mat' : Boolean whether key PHD matrix should be returned (defaults
to False).
}
Returns
-----------
proj_vecs : array-like, shape = [n_features, d]
Orthonormal system spanning the sufficient dimension subspace, where
d refers to the intrinsic dimension.
}
"""
# Extract arguments from dictionary
d = kwargs['d']
residuals = kwargs.get('residuals', False)
return_mat = kwargs.get('return_mat', False)
D, N = X.shape
# Calculate covariance matrix and empirical covariance matrix
emc = EmpiricalCovariance()
emc = emc.fit(X.T) # Covariance of all samples
cov_all = emc.covariance_
weighted_cov = np.zeros(cov_all.shape)
if residuals:
linreg = LinearRegression()
linreg = linreg.fit(X.T, Y)
res = Y - linreg.predict(X.T)
Y = res
Ymean = np.mean(Y)
mean_all = np.mean(X, axis=1)
for i in range(N):
weighted_cov += (Y[i] - Ymean) * np.outer(X[:, i] - mean_all,
X[:, i] - mean_all)
weighted_cov = weighted_cov / float(N)
vals, vecs = eig(weighted_cov, cov_all)
order = np.argsort(np.abs(vals))[::-1]
proj_vecs = vecs[:, order[:d]]
if return_mat:
return proj_vecs, weighted_cov
else:
return proj_vecs
class Mahalanobis (BaseEstimator):
"""Mahalanobis distance estimator. Uses Covariance estimate
to compute mahalanobis distance of the observations
from the model.
Parameters
----------
robust : boolean to determine wheter to use robust estimator
based on Minimum Covariance Determinant computation
"""
def __init__(self, robust=False):
if not robust:
from sklearn.covariance import EmpiricalCovariance as CovarianceEstimator #
else:
from sklearn.covariance import MinCovDet as CovarianceEstimator #
self.model = CovarianceEstimator()
self.cov = None
def fit(self, X, y=None, **params):
"""Fits the covariance model according to the given training
data and parameters.
Parameters
----------
X : array-like, shape = [n_samples, n_features]
Training data, where n_samples is the number of samples and
n_features is the number of features.
Returns
-------
self : object
Returns self.
"""
self.cov = self.model.fit(X)
return self
def score(self, X, y=None):
"""Computes the mahalanobis distances of given observations.
The provided observations are assumed to be centered. One may want to
center them using a location estimate first.
Parameters
----------
X : array-like, shape = [n_samples, n_features]
The observations, the Mahalanobis distances of the which we compute.
Returns
-------
mahalanobis_distance : array, shape = [n_observations,]
Mahalanobis distances of the observations.
"""
#return self.model.score(X,assume_centered=True)
return - self.model.mahalanobis(X-self.model.location_) ** 0.33
def test_suffstat_sk_full():
# compare the precision matrix compute from the
# EmpiricalCovariance.covariance fitted on X*sqrt(resp)
# with _sufficient_sk_full, n_components=1
rng = np.random.RandomState(0)
n_samples, n_features = 500, 2
# special case 1, assuming data is "centered"
X = rng.rand(n_samples, n_features)
resp = rng.rand(n_samples, 1)
X_resp = np.sqrt(resp) * X
nk = np.array([n_samples])
xk = np.zeros((1, n_features))
covars_pred = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
ecov = EmpiricalCovariance(assume_centered=True)
ecov.fit(X_resp)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='spectral'), 0)
# check the precision computation
precs_chol_pred = _compute_precision_cholesky(covars_pred, 'full')
precs_pred = np.array([np.dot(prec, prec.T) for prec in precs_chol_pred])
precs_est = np.array([linalg.inv(cov) for cov in covars_pred])
assert_array_almost_equal(precs_est, precs_pred)
# special case 2, assuming resp are all ones
resp = np.ones((n_samples, 1))
nk = np.array([n_samples])
xk = X.mean(axis=0).reshape((1, -1))
covars_pred = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
ecov = EmpiricalCovariance(assume_centered=False)
ecov.fit(X)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='spectral'), 0)
# check the precision computation
precs_chol_pred = _compute_precision_cholesky(covars_pred, 'full')
precs_pred = np.array([np.dot(prec, prec.T) for prec in precs_chol_pred])
precs_est = np.array([linalg.inv(cov) for cov in covars_pred])
assert_array_almost_equal(precs_est, precs_pred)
def test_suffstat_sk_full():
# compare the precision matrix compute from the
# EmpiricalCovariance.covariance fitted on X*sqrt(resp)
# with _sufficient_sk_full, n_components=1
rng = np.random.RandomState(0)
n_samples, n_features = 500, 2
# special case 1, assuming data is "centered"
X = rng.rand(n_samples, n_features)
resp = rng.rand(n_samples, 1)
X_resp = np.sqrt(resp) * X
nk = np.array([n_samples])
xk = np.zeros((1, n_features))
covars_pred = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
ecov = EmpiricalCovariance(assume_centered=True)
ecov.fit(X_resp)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='spectral'), 0)
# check the precision computation
precs_chol_pred = _compute_precision_cholesky(covars_pred, 'full')
precs_pred = np.array([np.dot(prec, prec.T) for prec in precs_chol_pred])
precs_est = np.array([linalg.inv(cov) for cov in covars_pred])
assert_array_almost_equal(precs_est, precs_pred)
# special case 2, assuming resp are all ones
resp = np.ones((n_samples, 1))
nk = np.array([n_samples])
xk = X.mean(axis=0).reshape((1, -1))
covars_pred = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
ecov = EmpiricalCovariance(assume_centered=False)
ecov.fit(X)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='spectral'), 0)
# check the precision computation
precs_chol_pred = _compute_precision_cholesky(covars_pred, 'full')
precs_pred = np.array([np.dot(prec, prec.T) for prec in precs_chol_pred])
precs_est = np.array([linalg.inv(cov) for cov in covars_pred])
assert_array_almost_equal(precs_est, precs_pred)
def peakSSV(X, Y, **kwargs):
"""
Parameters
----------
X : array-like, shape = [n_features, n_samples]
Training data, where n_samples is the number of samples and
n_features is the number of features.
Y : array-like, shape = [n_samples]
Response variable, where n_samples is the number of samples
Argument dictionary should contain:
kwargs = {
'd' : intrinsic dimension (int)
'n_samples' : Number of samples around the maximum Y to take.
'rescale' : Boolean whether standardization should be performed (True
for yes).
}
Returns
-----------
proj_vecs : array-like, shape = [n_features, d]
Orthonormal system spanning the sufficient dimension subspace, where
d refers to the intrinsic dimension.
}
"""
# Extract arguments from dictionary
d = kwargs['d']
n_samples = kwargs['n_samples']
rescale = kwargs['rescale']
return_mat = kwargs.get('return_mat', False)
D, N = X.shape
# Standardize X
emc = EmpiricalCovariance()
emc = emc.fit(X.T) # Covariance of all samples
mean_all = np.mean(X, axis=0)
cov_all = emc.covariance_
scaler = StandardScaler()
if rescale:
Z = scaler.fit_transform(X.T).T
pca = PCA()
order = np.argsort(Y)
XO = X[:, order]
pca = pca.fit(X[:, -n_samples:].T)
U = pca.components_[-d:, :].T
if rescale:
# Apply inverse transformation
vecs = sqrtm(scipy.linalg.inv(cov_all)).dot(U[:, :d])
proj_vecs, dummy = np.linalg.qr(vecs)
else:
proj_vecs = U[:, :d]
return proj_vecs
def shape_(data):
ec = EC()
centre = np.mean(data, axis=0)
covar = ec.fit(data).covariance_
v, w = linalg.eigh(covar)
v = 2. * np.sqrt(2.) * np.sqrt(v)
u = w[0] / linalg.norm(w[0])
angle = np.arctan(u[1] / u[0])
angle = 180. * angle / np.pi
circ = geometry.Point(centre).buffer(1)
ellipse = affinity.scale(circ, float(v[0]), float(v[1]))
return affinity.rotate(ellipse, angle)
def test_covariance():
"""Tests Covariance module on a simple dataset.
"""
# test covariance fit from data
cov = EmpiricalCovariance()
cov.fit(X)
emp_cov = empirical_covariance(X)
assert_array_almost_equal(emp_cov, cov.covariance_, 4)
assert_almost_equal(cov.error_norm(emp_cov), 0)
assert_almost_equal(
cov.error_norm(emp_cov, norm='spectral'), 0)
assert_almost_equal(
cov.error_norm(emp_cov, norm='frobenius'), 0)
assert_almost_equal(
cov.error_norm(emp_cov, scaling=False), 0)
assert_almost_equal(
cov.error_norm(emp_cov, squared=False), 0)
assert_raises(NotImplementedError,
cov.error_norm, emp_cov, norm='foo')
# Mahalanobis distances computation test
mahal_dist = cov.mahalanobis(X)
print np.amin(mahal_dist), np.amax(mahal_dist)
assert(np.amin(mahal_dist) > 0)
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
cov = EmpiricalCovariance()
cov.fit(X_1d)
assert_array_almost_equal(empirical_covariance(X_1d), cov.covariance_, 4)
assert_almost_equal(cov.error_norm(empirical_covariance(X_1d)), 0)
assert_almost_equal(
cov.error_norm(empirical_covariance(X_1d), norm='spectral'), 0)
# test with one sample
X_1sample = np.arange(5)
cov = EmpiricalCovariance()
with warnings.catch_warnings(record=True):
cov.fit(X_1sample)
# test integer type
X_integer = np.asarray([[0, 1], [1, 0]])
result = np.asarray([[0.25, -0.25], [-0.25, 0.25]])
assert_array_almost_equal(empirical_covariance(X_integer), result)
# test centered case
cov = EmpiricalCovariance(assume_centered=True)
cov.fit(X)
assert_equal(cov.location_, np.zeros(X.shape[1]))
def test_covariance():
# Tests Covariance module on a simple dataset.
# test covariance fit from data
cov = EmpiricalCovariance()
cov.fit(X)
emp_cov = empirical_covariance(X)
assert_array_almost_equal(emp_cov, cov.covariance_, 4)
assert_almost_equal(cov.error_norm(emp_cov), 0)
assert_almost_equal(cov.error_norm(emp_cov, norm='spectral'), 0)
assert_almost_equal(cov.error_norm(emp_cov, norm='frobenius'), 0)
assert_almost_equal(cov.error_norm(emp_cov, scaling=False), 0)
assert_almost_equal(cov.error_norm(emp_cov, squared=False), 0)
with pytest.raises(NotImplementedError):
cov.error_norm(emp_cov, norm='foo')
# Mahalanobis distances computation test
mahal_dist = cov.mahalanobis(X)
assert np.amin(mahal_dist) > 0
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
cov = EmpiricalCovariance()
cov.fit(X_1d)
assert_array_almost_equal(empirical_covariance(X_1d), cov.covariance_, 4)
assert_almost_equal(cov.error_norm(empirical_covariance(X_1d)), 0)
assert_almost_equal(
cov.error_norm(empirical_covariance(X_1d), norm='spectral'), 0)
# test with one sample
# Create X with 1 sample and 5 features
X_1sample = np.arange(5).reshape(1, 5)
cov = EmpiricalCovariance()
warn_msg = (
"Only one sample available. You may want to reshape your data array")
with pytest.warns(UserWarning, match=warn_msg):
cov.fit(X_1sample)
assert_array_almost_equal(cov.covariance_,
np.zeros(shape=(5, 5), dtype=np.float64))
# test integer type
X_integer = np.asarray([[0, 1], [1, 0]])
result = np.asarray([[0.25, -0.25], [-0.25, 0.25]])
assert_array_almost_equal(empirical_covariance(X_integer), result)
# test centered case
cov = EmpiricalCovariance(assume_centered=True)
cov.fit(X)
assert_array_equal(cov.location_, np.zeros(X.shape[1]))
class MahalanobisDistance(DimReducer):
"""
Computes a person's Mahalanobis distance
using the mean and covariance estimated from a set of young people.
Uses sklearn; verified this matches up with the normal matrix computation.
"""
def __init__(self, age_lower, age_upper):
self.age_lower = age_lower
self.age_upper = age_upper
self.need_ages = True
self.k = 1
def _fit_from_processed_data(self, X, ages):
young_people = (ages >= self.age_lower) & (ages <= self.age_upper)
print("%i people between %s and %s used for mean/cov calculation" %
(young_people.sum(), self.age_lower, self.age_upper))
assert young_people.sum() > 1000
self.model = EmpiricalCovariance(assume_centered=False)
self.model.fit(X[young_people, :])
def _get_projections_from_processed_data(self, X):
md = np.sqrt(self.model.mahalanobis(X)).reshape([-1, 1])
return md
def mahanalobis():
totalX = []
totalY = []
flag = True
countTrain = 0
with open("creditcard.csv", "rb") as f:
data = csv.reader(f)
for row in data:
if flag:
flag = False
continue
if countTrain >= 228000: #test on 20% of data
break
countTrain += 1
totalX.append([float(i) for i in row[:-1]])
totalY.append(int(row[-1]))
totalX = scalar.fit_transform(totalX)
print ("Data Loaded")
clf = EmpiricalCovariance()
clf.fit(totalX)
distances = clf.mahalanobis(totalX)
Y = []
for i in range(len(totalY)):
if np.log10(distances[i]) > 1.838:
Y.append(1)
else:
Y.append(0)
print ("Results")
auc = roc_auc_score(totalY, Y)
print(auc)
fpr, _, _ = roc_curve(totalY, Y)
print (fpr[1])
_, recall, _ = precision_recall_curve(totalY, Y)
print (recall[1])
return auc, fpr[1], recall[1]
def detect_bad_channels(inst, pick_types=None, threshold=.2):
from sklearn.preprocessing import RobustScaler
from sklearn.covariance import EmpiricalCovariance
from jr.stats import median_abs_deviation
if pick_types is None:
pick_types = dict(meg='mag')
inst = inst.pick_types(copy=True, **pick_types)
cov = EmpiricalCovariance()
cov.fit(inst._data.T)
cov = cov.covariance_
# center
scaler = RobustScaler()
cov = scaler.fit_transform(cov).T
cov /= median_abs_deviation(cov)
cov -= np.median(cov)
# compute robust summary metrics
mu = np.median(cov, axis=0)
sigma = median_abs_deviation(cov, axis=0)
mu /= median_abs_deviation(mu)
sigma /= median_abs_deviation(sigma)
distance = np.sqrt(mu ** 2 + sigma ** 2)
bad = np.where(distance < threshold)[0]
bad = [inst.ch_names[ch] for ch in bad]
return bad
def detect_bad_channels(inst, pick_types=None, threshold=.2):
from sklearn.preprocessing import RobustScaler
from sklearn.covariance import EmpiricalCovariance
from jr.stats import median_abs_deviation
if pick_types is None:
pick_types = dict(meg='mag')
inst = inst.pick_types(copy=True, **pick_types)
cov = EmpiricalCovariance()
cov.fit(inst._data.T)
cov = cov.covariance_
# center
scaler = RobustScaler()
cov = scaler.fit_transform(cov).T
cov /= median_abs_deviation(cov)
cov -= np.median(cov)
# compute robust summary metrics
mu = np.median(cov, axis=0)
sigma = median_abs_deviation(cov, axis=0)
mu /= median_abs_deviation(mu)
sigma /= median_abs_deviation(sigma)
distance = np.sqrt(mu ** 2 + sigma ** 2)
bad = np.where(distance < threshold)[0]
bad = [inst.ch_names[ch] for ch in bad]
return bad
def pca(X, **kwargs):
"""
Parameters
----------
X : array-like, shape = [n_features, n_samples]
Training data, where n_samples is the number of samples and
n_features is the number of features.
Argument dictionary should contain:
kwargs = {
'd' : intrinsic dimension (int)
'rescale' : Boolean whether standardization should be performed (True
for yes).
'return_mat' : Boolean whether key SIR matrix should be returned (defaults
to False).
Returns
-----------
proj_vecs : array-like, shape = [n_features, d]
Orthonormal system spanning the sufficient dimension subspace, where
d refers to the intrinsic dimension.
}
"""
d = kwargs['d']
return_mat = kwargs['return_mat']
rescale = kwargs['rescale']
scaler = StandardScaler()
if rescale:
emc = EmpiricalCovariance()
emc = emc.fit(X.T) # Covariance of all samples
cov_all = emc.covariance_
Z = scaler.fit_transform(X.T).T
pca = PCA(svd_solver='full')
pca = pca.fit(Z.T)
proj_vecs = pca.components_[:d, :].T
# Apply inverse transformation
vecs = sqrtm(scipy.linalg.inv(cov_all)).dot(proj_vecs)
proj_vecs, dummy = np.linalg.qr(vecs)
else:
pca = PCA(svd_solver='full')
pca = pca.fit(X.T)
proj_vecs = pca.components_[:d, :].T
if return_mat:
return proj_vecs, X.dot(X.T)
else:
return proj_vecs
class ChangeDetector(object):
"""
Joint Gaussian Change detector using a scikit learn style interface
This class is really a wrapper around the methods in scikit learn for estimating covariance using
robust or empirical methods and calculating the mahalanobis distances.
"""
def __init__(self, method='robust', estimator_kw_args={}):
if method is 'robust':
self.covariance_estimator_ = MinCovDet(**estimator_kw_args)
elif method is 'empirical':
self.covariance_estimator_ = EmpiricalCovariance(
**estimator_kw_args)
else:
raise ValueError(
"{} is not a valid method. Must be one of 'robust' or 'empirical'"
.format(method))
def fit(self, X):
"""
Fits the estimator.
Parameters:
-----------
X - array of time series, shape (n_series, len_series)
"""
self.covariance_estimator_ = self.covariance_estimator_.fit(X)
return self
def predict(self, X, threshold):
"""
Returns true for each time series predicted as change. Also returns the mahalanobis distances
parameters:
-----------
X - array of time series, shape (n_series, len_series)
threshold - float
returns:
y_pred - shape (n_time_series), true of change detected
distances - shape (n_time_series). The mahanobis distances of each time series under the fitted distribution
"""
distances = self.covariance_estimator_.mahalanobis(X)
return distances > threshold, distances
def test_covariance():
# Tests Covariance module on a simple dataset.
# test covariance fit from data
cov = EmpiricalCovariance()
cov.fit(X)
emp_cov = empirical_covariance(X)
assert_array_almost_equal(emp_cov, cov.covariance_, 4)
assert_almost_equal(cov.error_norm(emp_cov), 0)
assert_almost_equal(
cov.error_norm(emp_cov, norm='spectral'), 0)
assert_almost_equal(
cov.error_norm(emp_cov, norm='frobenius'), 0)
assert_almost_equal(
cov.error_norm(emp_cov, scaling=False), 0)
assert_almost_equal(
cov.error_norm(emp_cov, squared=False), 0)
assert_raises(NotImplementedError,
cov.error_norm, emp_cov, norm='foo')
# Mahalanobis distances computation test
mahal_dist = cov.mahalanobis(X)
assert_greater(np.amin(mahal_dist), 0)
# test with n_features = 1
X_1d = X[:, 0].reshape((-1, 1))
cov = EmpiricalCovariance()
cov.fit(X_1d)
assert_array_almost_equal(empirical_covariance(X_1d), cov.covariance_, 4)
assert_almost_equal(cov.error_norm(empirical_covariance(X_1d)), 0)
assert_almost_equal(
cov.error_norm(empirical_covariance(X_1d), norm='spectral'), 0)
# test with one sample
# Create X with 1 sample and 5 features
X_1sample = np.arange(5).reshape(1, 5)
cov = EmpiricalCovariance()
assert_warns(UserWarning, cov.fit, X_1sample)
assert_array_almost_equal(cov.covariance_,
np.zeros(shape=(5, 5), dtype=np.float64))
# test integer type
X_integer = np.asarray([[0, 1], [1, 0]])
result = np.asarray([[0.25, -0.25], [-0.25, 0.25]])
assert_array_almost_equal(empirical_covariance(X_integer), result)
# test centered case
cov = EmpiricalCovariance(assume_centered=True)
cov.fit(X)
assert_array_equal(cov.location_, np.zeros(X.shape[1]))
def save(X, Y, **kwargs):
"""
Parameters
----------
X : array-like, shape = [n_features, n_samples]
Training data, where n_samples is the number of samples and
n_features is the number of features.
Y : array-like, shape = [n_samples]
Response variable, where n_samples is the number of samples
Argument dictionary should contain:
kwargs = {
'd' : intrinsic dimension (int)
'n_levelsets' : number of slices to use (int)
'rescale' : Boolean whether standardization should be performed (True
for yes).
'return_mat' : Boolean whether key SIR matrix should be returned (defaults
to False).
}
Returns
-----------
proj_vecs : array-like, shape = [n_features, d]
Orthonormal system spanning the sufficient dimension subspace, where
d refers to the intrinsic dimension.
}
"""
# Extract arguments from dictionary
d = kwargs['d']
n_levelsets = kwargs['n_levelsets']
rescale = kwargs['rescale']
return_mat = kwargs.get('return_mat', False)
D, N = X.shape
# Standardize X
emc = EmpiricalCovariance()
emc = emc.fit(X.T) # Covariance of all samples
mean_all = np.mean(X, axis = 0)
cov_all = emc.covariance_
scaler = StandardScaler()
if rescale:
Z = scaler.fit_transform(X.T).T
labels, n_levelsets = split_statistically_equivalent_blocks(X, Y, n_levelsets)
M = np.zeros((D, D)) # Key matrix in SAVE
empirical_probabilities = np.zeros(n_levelsets)
for i in range(n_levelsets):
empirical_probabilities[i] = float(len(np.where(labels == i)[0]))/float(N)
if rescale:
emc = emc.fit(Z[:,labels == i].T) # Covariance of all samples
cov_sub = emc.covariance_
M += empirical_probabilities[i] * (np.eye(D) - cov_sub).dot((cov_all - cov_sub))
else:
emc = emc.fit(X[:,labels == i].T) # Covariance of all samples
cov_sub = emc.covariance_
M += empirical_probabilities[i] * (cov_all - cov_sub).dot((cov_all - cov_sub))
U, S, V = np.linalg.svd(M)
if rescale:
# Apply inverse transformation
vecs = sqrtm(scipy.linalg.inv(cov_all)).dot(U[:,:d])
proj_vecs, dummy = np.linalg.qr(vecs)
else:
proj_vecs = U[:,:d]
if return_mat:
return proj_vecs, M
else:
return proj_vecs
def optimalShrinkage(X, return_covariance=False, method='rie'):
"""This function computes a cleaned, optimal shrinkage,
rotationally-invariant estimator (RIE) of the true correlation
matrix C underlying the noisy, in-sample estimate
E = 1/T X * transpose(X)
associated to a design matrix X of shape (T, N) (T measurements
and N features).
One approach to getting a cleaned estimator that predates the
optimal shrinkage, RIE estimator consists in inverting the
Marcenko-Pastur equation so as to replace the eigenvalues
from the spectrum of E by an estimation of the true ones.
This approach is known to be numerically-unstable, in addition
to failing to account for the overlap between the sample eigenvectors
and the true eigenvectors. How to compute such overlaps was first
explained by Ledoit and Peche (cf. reference below). Their procedure
was extended by Bun, Bouchaud and Potters, who also correct
for a systematic downward bias in small eigenvalues.
It is this debiased, optimal shrinkage, rotationally-invariant
estimator that the function at hand implements.
In addition to above method, this funtion also provides access to:
- The finite N regularization of the optimal RIE for small eigenvalues
as provided in section 8.1 of [3] a.k.a the inverse wishart (IW) regularization.
- The direct kernel method of O. Ledoit and M. Wolf in their 2017 paper [4].
This is a direct port of their Matlab code.
Parameters
----------
X: design matrix, of shape (T, N), where T denotes the number
of samples (think measurements in a time series), while N
stands for the number of features (think of stock tickers).
return_covariance: type bool (default: False)
If set to True, compute the standard deviations of each individual
feature across observations, clean the underlying matrix
of pairwise correlations, then re-apply the standard
deviations and return a cleaned variance-covariance matrix.
method: type string, optional (default="rie")
- If "rie" : optimal shrinkage in the manner of Bun & al.
with no regularisation
- If "iw" : optimal shrinkage in the manner of Bun & al.
with the so called Inverse Wishart regularization
- If 'kernel': Direct kernel method of Ledoit Wolf.
Returns
-------
E_RIE: type numpy.ndarray, shape (N, N)
Cleaned estimator of the true correlation matrix C. A sample
estimator of C is the empirical covariance matrix E
estimated from X. E is corrupted by in-sample noise.
E_RIE is the optimal shrinkage, rotationally-invariant estimator
(RIE) of C computed following the procedure of Joel Bun
and colleagues (cf. references below).
If return_covariance=True, E_clipped corresponds to a cleaned
variance-covariance matrix.
References
----------
1 "Eigenvectors of some large sample covariance matrix ensembles",
O. Ledoit and S. Peche
Probability Theory and Related Fields, Vol. 151 (1), pp 233-264
2 "Rotational invariant estimator for general noisy matrices",
J. Bun, R. Allez, J.-P. Bouchaud and M. Potters
arXiv: 1502.06736 [cond-mat.stat-mech]
3 "Cleaning large Correlation Matrices: tools from Random Matrix Theory",
J. Bun, J.-P. Bouchaud and M. Potters
arXiv: 1610.08104 [cond-mat.stat-mech]
4 "Direct Nonlinear Shrinkage Estimation of Large-Dimensional Covariance Matrices (September 2017)",
O. Ledoit and M. Wolf https://ssrn.com/abstract=3047302 or http://dx.doi.org/10.2139/ssrn.3047302
"""
try:
assert isinstance(return_covariance, bool)
except AssertionError:
raise
sys.exit(1)
T, N, transpose_flag = checkDesignMatrix(X)
if transpose_flag:
X = X.T
if not return_covariance:
X = StandardScaler(with_mean=False,
with_std=True).fit_transform(X)
ec = EmpiricalCovariance(store_precision=False,
assume_centered=True)
ec.fit(X)
E = ec.covariance_
if return_covariance:
inverse_std = 1./np.sqrt(np.diag(E))
E *= inverse_std
E *= inverse_std.reshape(-1, 1)
eigvals, eigvecs = np.linalg.eigh(E)
eigvecs = eigvecs.T
q = N / float(T)
lambda_N = eigvals[0] # The smallest empirical eigenvalue,
# given that the function used to compute
# the spectrum of a Hermitian or symmetric
# matrix - namely np.linalg.eigh - returns
# the eigenvalues in ascending order.
lambda_hats = None
if method is not 'kernel':
use_inverse_wishart = (method == 'iw')
xis = map(lambda x: xiHelper(x, q, E), eigvals)
Gammas = map(lambda x: gammaHelper(x, q, N, lambda_N, inverse_wishart=use_inverse_wishart), eigvals)
xi_hats = map(lambda a, b: a * b if b > 1 else a, xis, Gammas)
lambda_hats = xi_hats
else:
lambda_hats = directKernel(q, T, N, eigvals)
E_RIE = np.zeros((N, N), dtype=float)
for lambda_hat, eigvec in zip(lambda_hats, eigvecs):
eigvec = eigvec.reshape(-1, 1)
E_RIE += lambda_hat * eigvec.dot(eigvec.T)
# bp()
tmp = 1./np.sqrt(np.diag(E_RIE))
E_RIE *= tmp
E_RIE *= tmp.reshape(-1, 1)
if return_covariance:
std = 1./inverse_std
E_RIE *= std
E_RIE *= std.reshape(-1, 1)
return E_RIE
def clipped(X, alpha=None, return_covariance=False):
"""Clips the eigenvalues of an empirical correlation matrix E
in order to provide a cleaned estimator E_clipped of the
underlying correlation matrix.
Proceeds by keeping the [N * alpha] top eigenvalues and shrinking
the remaining ones by a trace-preserving constant
(i.e. Tr(E_clipped) = Tr(E)).
Parameters
----------
X: design matrix, of shape (T, N), where T denotes the number
of samples (think measurements in a time series), while N
stands for the number of features (think of stock tickers).
alpha: type float or derived from numbers.Real (default: None)
Parameter between 0 and 1, inclusive, determining the fraction
to keep of the top eigenvalues of an empirical correlation matrix.
If left unspecified, alpha is chosen so as to keep all the
empirical eigenvalues greater than the upper limit of
the support to the Marcenko-Pastur spectrum. Indeed, such
eigenvalues can be considered as associated with some signal,
whereas the ones falling inside the Marcenko-Pastur range
should be considered as corrupted with noise and indistinguishable
from the spectrum of the correlation of a random matrix.
This ignores finite-size effects that make it possible
for the eigenvalues to exceed the upper and lower edges
defined by the Marcenko-Pastur spectrum (cf. a set of results
revolving around the Tracy-Widom distribution)
return_covariance: type bool (default: False)
If set to True, compute the standard deviations of each individual
feature across observations, clean the underlying matrix
of pairwise correlations, then re-apply the standard
deviations and return a cleaned variance-covariance matrix.
Returns
-------
E_clipped: type numpy.ndarray, shape (N, N)
Cleaned estimator of the true correlation matrix C underlying
a noisy, in-sample estimate E (empirical correlation matrix
estimated from X). This cleaned estimator proceeds through
a simple eigenvalue clipping procedure (cf. reference below).
If return_covariance=True, E_clipped corresponds to a cleaned
variance-covariance matrix.
Reference
---------
"Financial Applications of Random Matrix Theory: a short review",
J.-P. Bouchaud and M. Potters
arXiv: 0910.1205 [q-fin.ST]
"""
try:
if alpha is not None:
assert isinstance(alpha, Real) and 0 <= alpha <= 1
assert isinstance(return_covariance, bool)
except AssertionError:
raise
sys.exit(1)
T, N, transpose_flag = checkDesignMatrix(X)
if transpose_flag:
X = X.T
if not return_covariance:
X = StandardScaler(with_mean=False,
with_std=True).fit_transform(X)
ec = EmpiricalCovariance(store_precision=False,
assume_centered=True)
ec.fit(X)
E = ec.covariance_
if return_covariance:
inverse_std = 1./np.sqrt(np.diag(E))
E *= inverse_std
E *= inverse_std.reshape(-1, 1)
eigvals, eigvecs = np.linalg.eigh(E)
eigvecs = eigvecs.T
if alpha is None:
(lambda_min, lambda_max), _ = marcenkoPastur(X)
xi_clipped = np.where(eigvals >= lambda_max, eigvals, np.nan)
else:
xi_clipped = np.full(N, np.nan)
threshold = int(ceil(alpha * N))
if threshold > 0:
xi_clipped[-threshold:] = eigvals[-threshold:]
gamma = float(E.trace() - np.nansum(xi_clipped))
gamma /= np.isnan(xi_clipped).sum()
xi_clipped = np.where(np.isnan(xi_clipped), gamma, xi_clipped)
E_clipped = np.zeros((N, N), dtype=float)
for xi, eigvec in zip(xi_clipped, eigvecs):
eigvec = eigvec.reshape(-1, 1)
E_clipped += xi * eigvec.dot(eigvec.T)
tmp = 1./np.sqrt(np.diag(E_clipped))
E_clipped *= tmp
E_clipped *= tmp.reshape(-1, 1)
if return_covariance:
std = 1./inverse_std
E_clipped *= std
E_clipped *= std.reshape(-1, 1)
return E_clipped
class Matching(IndividualOutcomeEstimator):
def __init__(
self,
propensity_transform=None,
caliper=None,
with_replacement=True,
n_neighbors=1,
matching_mode="both",
metric="mahalanobis",
knn_backend="sklearn",
estimate_observed_outcome=False,
):
"""Match treatment and control samples with similar covariates.
Args:
propensity_transform (causallib.transformers.PropensityTransformer):
an object for data preprocessing which adds the propensity
score as a feature (default: None)
caliper (float) : maximal distance for a match to be accepted. If
not defined, all matches will be accepted. If defined, some
samples may not be matched and their outcomes will not be
estimated. (default: None)
with_replacement (bool): whether samples can be used multiple times
for matching. If set to False, the matching process will optimize
the linear sum of distances between pairs of treatment and
control samples and only `min(N_treatment, N_control)` samples
will be estimated. Matching with no replacement does not make
use of the `fit` data and is therefore not implemented for
out-of-sample data (default: True)
n_neighbors (int) : number of nearest neighbors to include in match.
Must be 1 if `with_replacement` is `False.` If larger than 1, the
estimate is calculated using the `regress_agg_function` or
`classify_agg_function` across the `n_neighbors`. Note that when
the `caliper` variable is set, some samples will have fewer than
`n_neighbors` matches. (default: 1).
matching_mode (str) : Direction of matching: `treatment_to_control`,
`control_to_treatment` or `both` to indicate which set should
be matched to which. All sets are cross-matched in `match`
and when `with_replacement` is `False` all matching modes
coincide. With replacement there is a difference.
metric (str) : Distance metric string for calculating distance
between samples. Note: if an external built `knn_backend`
object with a different metric is supplied, `metric` needs to
be changed to reflect that, because `Matching` will set its
inverse covariance matrix if "mahalanobis" is set. (default:
"mahalanobis", also supported: "euclidean")
knn_backend (str or callable) : Backend to use for nearest neighbor
search. Options are "sklearn" or a callable which returns an
object implementing `fit`, `kneighbors` and `set_params`
like the sklearn `NearestNeighbors` object. (default: "sklearn").
estimate_observed_outcome (bool) : Whether to allow a match of a
sample to a sample other than itself when looking within its own
treatment value. If True, the estimated potential outcome for the
observed outcome may differ from the true observed outcome.
(default: False)
Attributes:
classify_agg_function (callable) : Aggregating function for outcome
estimation when classifying. (default: majority_rule)
Usage is determined by type of `y` during `fit`
regress_agg_function (callable) : Aggregating function for outcome
estimation when regressing or predicting prob_a. (default: np.mean)
Usage is determined by type of `y` during `fit`
treatments_ (pd.DataFrame) : DataFrame of treatments (created after `fit`)
outcomes_ (pd.DataFrame) : DataFrame of outcomes (created after `fit`)
match_df_ (pd.DataFrame) : Dataframe of most recently calculated
matches. For details, see `match`. (created after `match`)
samples_used_ (pd.Series) : Series with count of samples used
during most recent match. Series includes a count for each
treatment value. (created after `match`)
"""
self.propensity_transform = propensity_transform
self.covariance_conditioner = EmpiricalCovariance()
self.caliper = caliper
self.with_replacement = with_replacement
self.n_neighbors = n_neighbors
self.matching_mode = matching_mode
self.metric = metric
# if classify task, default aggregation function is majority
self.classify_agg_function = majority_rule
# if regress task, default aggregation function is mean
self.regress_agg_function = np.mean
self.knn_backend = knn_backend
self.estimate_observed_outcome = estimate_observed_outcome
def fit(self, X, a, y, sample_weight=None):
"""Load the treatments and outcomes and fit search trees.
Applies transform to covariates X, initializes search trees for each
treatment value for performing nearest neighbor searches.
Note: Running `fit` a second time overwrites any information from
previous `fit or `match` and re-fits the propensity_transform object.
Args:
X (pd.DataFrame): DataFrame of shape (n,m) containing m covariates
for n samples.
a (pd.Series): Series of shape (n,) containing discrete treatment
values for the n samples.
y (pd.Series): Series of shape (n,) containing outcomes for
the n samples.
sample_weight: IGNORED In signature for compatibility with other
estimators.
Note: `X`, `a` and `y` must share the same index.
Returns:
self (Matching) the fitted object
"""
self._clear_post_fit_variables()
self.outcome_ = y.copy()
self.treatments_ = a.copy()
if self.propensity_transform:
self.propensity_transform.fit(X, a)
X = self.propensity_transform.transform(X)
self.conditioned_covariance_ = self._calculate_covariance(X)
self.treatment_knns_ = {}
for a in self.treatments_.unique():
haystack = X[self.treatments_ == a]
self.treatment_knns_[a] = self._fit_sknn(haystack)
return self
def _execute_matching(self, X, a):
"""Execute matching of samples in X according to the treatment values in a.
Returns a DataFrame including all the results, which is also set as
the attribute `self.match_df_`. The arguments `X` and `a` define the
"needle" where the "haystack" is the data that was previously passed
to fit, for matching with replacement. As such, treatment and control
samples from within `X` will not be matched with each other, unless
the same `X` and `a` were passed to `fit`. For matching without
replacement, the `X` and `a` passed to `match` provide the "needle" and
the "haystack". If the attribute `caliper` is set, the matches are
limited to those with a distance less than `caliper`.
This function ignores the existing `match_df_` and will overwrite it.
It is thus useful for if you have changed the settings and need to
rematch the samples. For most applications, the `match` function is
more convenient.
Args:
X (pd.DataFrame): DataFrame of shape (n,m) containing m covariates
for n samples.
a (pd.Series): Series of shape (n,) containing discrete treatment
values for the n samples.
Note: The args are assumed to share the same index.
Returns:
match_df: The resulting matches DataFrame is indexed so that
` match_df.loc[treatment_value, sample_id]` has columns `matches`
and `distances` containing lists of indices to samples and the
respective distances for the matches discovered for `sample_id`
from within the fitted samples with the given `treatment_value`.
The indices in the `matches` column are from the fitted data,
not the X argument in `match`. If `sample_id` had no match,
`match_df.loc[treatment_value, sample_id].matches = []`.
The DataFrame has shape (n* len(a.unique()), 2 ).
Raises:
NotImplementedError: Raised when with_replacement is False and
n_neighbors is not 1.
"""
if self.n_neighbors != 1 and not self.with_replacement:
raise NotImplementedError(
"Matching more than one neighbor is only implemented for"
"no-replacement")
if self.propensity_transform:
X = self.propensity_transform.transform(X)
if self.with_replacement:
self.match_df_ = self._withreplacement_match(X, a)
else:
self.match_df_ = self._noreplacement_match(X, a)
sample_id_name = X.index.name if X.index.name is not None else "sample_id"
self.match_df_.index.set_names(["match_to_treatment", sample_id_name],
inplace=True)
# we record the number of samples that were successfully matched of
# each treatment value
self.samples_used_ = self._count_samples_used_by_treatment_value(a)
return self.match_df_
def estimate_individual_outcome(self,
X,
a,
y=None,
treatment_values=None,
predict_proba=True,
dropna=True):
"""
Calculate the potential outcome for each sample and treatment value.
Execute match and calculate, for each treatment value and each sample,
the expected outcome.
Note: Out of sample estimation for matching without replacement requires
passing a `y` vector here. If no 'y' is passed here, the values received
by `fit` are used, and if the estimation indices are not a subset of the
fitted indices, the estimation will fail.
If the attribute `estimate_observed_outcome` is
`True`, estimates will be calculated for the observed outcomes as well.
If not, then the observed outcome will be passed through from the
corresponding element of `y` passed to `fit`.
Args:
X (pd.DataFrame): DataFrame of shape (n,m) containing m covariates
for n samples.
a (pd.Series): Series of shape (n,) containing discrete treatment
values for the n samples.
y (pd.Series): Series of shape (n,) containing outcome values for
n samples. This is only used when `with_replacemnt=False`.
Otherwise, the outcome values passed to `fit` are used.
predict_proba (bool) : whether to output classifications or
probabilties for a classification task. If set to False and
data is non-integer, a warning is issued. (default True)
dropna (bool) : For samples that were unmatched due to caliper
restrictions, drop from outcome_df leading to a potentially
smaller sized output, or include them as NaN. (default: True)
treatment_values : IGNORED
Note: The args are assumed to share the same index.
Returns:
outcome_df (pd.DataFrame)
"""
match_df = self.match(X, a, use_cached_result=True)
outcome_df = self._aggregate_match_df_to_generate_outcome_df(
match_df, a, predict_proba)
outcome_df = self._filter_outcome_df_by_matching_mode(outcome_df, a)
if outcome_df.isna().all(axis=None):
raise ValueError("Matching was not successful and no outcomes can"
"be estimated. Check caliper value.")
if dropna:
outcome_df = outcome_df.dropna()
return outcome_df
def match(self,
X,
a,
use_cached_result=True,
successful_matches_only=False):
"""Matching the samples in X according to the treatment values in a.
Returns a DataFrame including all the results, which is also set as
the attribute `self.match_df_`. The arguments `X` and `a` define the
"needle" where the "haystack" is the data that was previously passed
to fit, for matching with replacement. As such, treatment and control
samp les from within `X` will not be matched with each other, unless
the same `X` and `a` were passed to `fit`. For matching without
replacement, the `X` and `a` passed to `match` provide the "needle" and
the "haystack". If the attribute `caliper` is set, the matches are
limited to those with a distance less than `caliper`.
Args:
X (pd.DataFrame): DataFrame of shape (n,m) containing m covariates
for n samples.
a (pd.Series): Series of shape (n,) containing discrete treatment
values for the n samples.
use_cached_result (bool): Whether or not to return the `match_df`
from the most recent matching operation. The cached result will
only be used if the sample indices of `X` and those of `match_df`
are identical, otherwise it will rematch.
successful_matches_only (bool): Whether or not to filter the matches
to those which matched successfully. If set to `False`, the
resulting DataFrame will have shape (n* len(a.unique()), 2 ),
otherwise it may have a smaller shape due to unsuccessful matches.
Note: The args are assumed to share the same index.
Returns:
match_df: The resulting matches DataFrame is indexed so that
` match_df.loc[treatment_value, sample_id]` has columns `matches`
and `distances` containing lists of indices to samples and the
respective distances for the matches discovered for `sample_id`
from within the fitted samples with the given `treatment_value`.
The indices in the `matches` column are from the fitted data,
not the X argument in `match`. If `sample_id` had no match,
`match_df.loc[treatment_value, sample_id].matches = []`.
The DataFrame has shape (n* len(a.unique()), 2 ), if
`successful_matches_only` is set to `False.
Raises:
NotImplementedError: Raised when with_replacement is False and
n_neighbors is not 1.
"""
cached_result_available = (hasattr(self, "match_df_") and
X.index.equals(self.match_df_.loc[0].index))
if not (use_cached_result and cached_result_available):
self._execute_matching(X, a)
return self._get_match_df(
successful_matches_only=successful_matches_only)
def matches_to_weights(self, match_df=None):
"""Calculate weights based on a given set of matches.
For each matching from one treatment value to another, a weight vector
is generated. The weights are calculated as the number of times a
sample was selected in a matching, with each occurrence weighted
according to the number of other samples in that matching. The weights
can be used to estimate outcomes or to check covariate balancing. The
function can only be called after `match` has been run.
Args:
match_df (pd.DataFrame) : a DataFrame of matches returned from
`match`. If not supplied, will use the `match_df_` attribute if
available, else raises ValueError. Will not execute `match` to
generate a `match_df`.
Returns:
weights_df (pd.DataFrame): DataFrame of shape (n,M) where M is the
number of permutations of `a.unique()`.
"""
if match_df is None:
match_df = self._get_match_df(successful_matches_only=False)
match_permutations = sorted(permutations(self.treatments_.unique()))
weights_df = pd.DataFrame([
self._matches_to_weights_single_matching(s, t, match_df)
for s, t in match_permutations
], ).T
return weights_df
def get_covariates_of_matches(self, s, t, covariates):
"""
Look up covariates of closest matches for a given matching.
Using `self.match_df_` and the supplied `covariates`, look up
the covariates of the last match. The function can only be called after
`match` has been run.
Args:
s (int) : source treatment value
t (int) : target treatment value
covariates (pd.DataFrame) : The same covariates which were
passed to `fit`.
Returns:
covariate_df (pd.DataFrame) : a DataFrame of size
(n_matched_samples, n_covariates * 3 + 2) with the covariate
values of the sample, covariates of its match, calculated
distance and number of neighbors found within the given
caliper (with no caliper this will equal self.n_neighbors )
"""
match_df = self._get_match_df()
subdf = match_df.loc[s][self.treatments_ == t]
sample_id_name = subdf.index.name
def get_covariate_difference_from_nearest_match(source_row_index):
j = subdf.loc[source_row_index].matches[0]
delta_series = pd.Series(covariates.loc[source_row_index] -
covariates.loc[j])
source_row = covariates.loc[j].copy()
source_row.at[sample_id_name] = j
target_row = covariates.loc[source_row_index].copy()
target_row = target_row
covariate_differences = pd.concat({
t:
target_row,
s:
source_row,
"delta":
delta_series,
"outcomes":
pd.Series({
t: self.outcome_.loc[source_row_index],
s: self.outcome_.loc[j]
}),
"match":
pd.Series(
dict(
n_neighbors=len(subdf.loc[source_row_index].matches),
distance=subdf.loc[source_row_index].distances[0],
)),
})
return covariate_differences
covdf = pd.DataFrame(data=[
get_covariate_difference_from_nearest_match(i) for i in subdf.index
],
index=subdf.index)
covdf = covdf.reset_index()
cols = covdf.columns
covdf.columns = pd.MultiIndex.from_tuples([(t, sample_id_name)] +
list(cols[1:]))
return covdf
def _clear_post_fit_variables(self):
for var in list(vars(self)):
if var[-1] == "_":
self.__delattr__(var)
def _calculate_covariance(self, X):
if len(X.shape) > 1 and X.shape[1] > 1:
V_list = []
for a in self.treatments_.unique():
X_at_a = X[self.treatments_ == a].copy()
current_V = self.covariance_conditioner.fit(X_at_a).covariance_
V_list.append(current_V)
# following Imbens&Rubin, we average across treatment groups
V = np.mean(V_list, axis=0)
else:
# for 1d data revert to euclidean metric
V = np.array(1).reshape(1, 1)
return V
def _aggregate_match_df_to_generate_outcome_df(self, match_df, a,
predict_proba):
agg_function = self._get_agg_function(predict_proba)
def outcome_from_matches_by_idx(x):
return agg_function(self.outcome_.loc[x])
outcomes = {}
for i in sorted(a.unique()):
outcomes[i] = match_df.loc[i].matches.apply(
outcome_from_matches_by_idx)
outcome_df = pd.DataFrame(outcomes)
return outcome_df
def _get_match_df(self, successful_matches_only=True):
if not hasattr(self, "match_df_") or self.match_df_ is None:
raise NotFittedError("You need to run `match` first")
match_df = self.match_df_.copy()
if successful_matches_only:
match_df = match_df[match_df.matches.apply(bool)]
if match_df.empty:
raise ValueError(
"Matching was not successful and no outcomes can be "
"estimated. Check caliper value.")
return match_df
def _filter_outcome_df_by_matching_mode(self, outcome_df, a):
if self.matching_mode == "treatment_to_control":
outcome_df = outcome_df[a == 1]
elif self.matching_mode == "control_to_treatment":
outcome_df = outcome_df[a == 0]
elif self.matching_mode == "both":
pass
else:
raise NotImplementedError(
"Matching mode {} is not implemented. Please select one of "
"'treatment_to_control', 'control_to_treatment, "
"or 'both'.".format(self.matching_mode))
return outcome_df
def _get_agg_function(self, predict_proba):
if predict_proba:
agg_function = self.regress_agg_function
else:
agg_function = self.classify_agg_function
try:
isoutputinteger = np.allclose(self.outcome_.apply(int),
self.outcome_)
if not isoutputinteger:
warnings.warn("Classifying non-categorical outcomes. "
"This is probably a mistake.")
except:
warnings.warn(
"Unable to detect whether outcome is integer-like. ")
return agg_function
def _instantiate_nearest_neighbors_object(self):
backend = self.knn_backend
if backend == "sklearn":
backend_instance = NearestNeighbors(algorithm="auto")
elif callable(backend):
backend_instance = backend()
self.metric = backend_instance.metric
elif hasattr(backend, "fit") and hasattr(backend, "kneighbors"):
backend_instance = sk_clone(backend)
self.metric = backend_instance.metric
else:
raise NotImplementedError(
"`knn_backend` must be either an NearestNeighbors-like object,"
" a callable returning such an object, or the string \"sklearn\""
)
backend_instance.set_params(**self._get_metric_dict())
return backend_instance
def _fit_sknn(self, target_df):
"""
Fit scikit-learn NearestNeighbors object with samples in target_df.
Fits object, adds metric parameters and returns namedtuple which
also includes DataFrame indices so that identities can looked up.
Args:
target_df (pd.DataFrame) : DataFrame of covariates to fit
Returns:
KNN (namedtuple) : Namedtuple with members `learner` and `index`
containing the fitted sklearn object and an index lookup vector,
respectively.
"""
target_array = target_df.values
sknn = self._instantiate_nearest_neighbors_object()
target_array = self._ensure_array_columnlike(target_array)
sknn.fit(target_array)
return KNN(sknn, target_df.index)
@staticmethod
def _ensure_array_columnlike(target_array):
if len(target_array.shape) < 2 or target_array.shape[1] == 1:
target_array = target_array.reshape(-1, 1)
return target_array
def _get_metric_dict(
self,
VI_in_metric_params=True,
):
metric_dict = dict(metric=self.metric)
if self.metric == "mahalanobis":
VI = np.linalg.inv(self.conditioned_covariance_)
if VI_in_metric_params:
metric_dict["metric_params"] = {"VI": VI}
else:
metric_dict["VI"] = VI
return metric_dict
def _kneighbors(self, knn, source_df):
"""Lookup neighbors in knn object.
Args:
knn (namedtuple) : knn named tuple to look for neighbors in. The
object has `learner` and `index` attributes to reference the
original df index.
source_df (pd.DataFrame) : a DataFrame of source data points to use
as "needles" for the knn "haystack."
Returns:
match_df (pd.DataFrame) : a DataFrame of matches
"""
source_array = source_df.values
# 1d data must be in shape (-1, 1) for sklearn.knn
source_array = self._ensure_array_columnlike(source_array)
distances, neighbor_array_indices = knn.learner.kneighbors(
source_array, n_neighbors=self.n_neighbors)
return self._generate_match_df(source_df, knn.index, distances,
neighbor_array_indices)
def _generate_match_df(self, source_df, target_df_index, distances,
neighbor_array_indices):
"""
Take results of matching and build into match_df DataFrame.
For clarity we'll call the samples that are being matched "needles" and
the set of samples that they looked for matches in the "haystack".
Args:
source_df (pd.DataFrame) : Covariate dataframe of N "needles"
target_df_index (np.array) : An array of M indices of the haystack
samples in their original dataframe.
distances (np.array) : An array of N arrays of floats of length K
where K is `self.n_neighbors`.
neighbor_array_indices (np.array) : An array of N arrays of ints of
length K where K is `self.n_neighbors`.
"""
# target is the haystack, source is the needle(s)
# translate array indices back to original indices
matches_dict = {}
for source_idx, distance_row, neighbor_array_index_row in zip(
source_df.index, distances, neighbor_array_indices):
neighbor_df_indices = \
target_df_index[neighbor_array_index_row.flatten()]
if self.caliper is not None:
neighbor_df_indices = [
n for i, n in enumerate(neighbor_df_indices)
if distance_row[i] < self.caliper
]
distance_row = [d for d in distance_row if d < self.caliper]
matches_dict[source_idx] = dict(matches=list(neighbor_df_indices),
distances=list(distance_row))
# convert dict of dicts like { 1: {'matches':[], 'distances':[]}} to df
return pd.DataFrame(matches_dict).T
def _matches_to_weights_single_matching(self, s, t, match_df):
"""
For a given match, calculate the resulting weight vector.
The weight vector adds a count each time a sample is used, weighted by
the number of other neighbors when it was used. This is necessary to
make the weighted sum return the correct effect estimate.
"""
weights = pd.Series(self.treatments_.copy() * 0)
name = {0: "control", 1: "treatment"}
weights.name = "{s}_to_{t}".format(s=name[s], t=name[t])
s_to_t_matches = match_df.loc[t][self.treatments_ == s].matches
for source_idx, matches_list in s_to_t_matches.iteritems():
if matches_list:
weights.loc[source_idx] += 1
for match in matches_list:
weights.loc[match] += 1 / len(matches_list)
return weights
def _get_distance_matrix(self, source_df, target_df):
"""
Create distance matrix for no replacement match.
Combines metric, caliper and source/target data into a
precalculated distance matrix which can be passed to
scipy.optimize.linear_sum_assignment.
"""
cdist_args = dict(
XA=self._ensure_array_columnlike(source_df.values),
XB=self._ensure_array_columnlike(target_df.values),
)
cdist_args.update(self._get_metric_dict(False))
distance_matrix = distance.cdist(**cdist_args)
if self.caliper is not None:
distance_matrix[distance_matrix > self.caliper] = VERY_LARGE_NUMBER
return distance_matrix
def _withreplacement_match(self, X, a):
matches = {} # maps treatment value to list of matches TO that value
for treatment_value, knn in self.treatment_knns_.items():
matches[treatment_value] = self._kneighbors(knn, X)
# when producing potential outcomes we may want to force the
# value of the observed outcome to be the actual observed
# outcome, and not an average of the k nearest samples.
if not self.estimate_observed_outcome:
def limit_within_treatment_matches_to_self_only(row):
if (a.loc[row.name] == treatment_value
and row.name in row.matches):
row.matches = [row.name]
row.distances = [0]
return row
matches[treatment_value] = matches[treatment_value].apply(
limit_within_treatment_matches_to_self_only, axis=1)
return pd.concat(matches, sort=True)
def _noreplacement_match(self, X, a):
match_combinations = sorted(combinations(a.unique(), 2))
matches = {}
for s, t in match_combinations:
distance_matrix = self._get_distance_matrix(X[a == s], X[a == t])
source_array, neighbor_array_indices, distances = \
self._optimally_match_distance_matrix(distance_matrix)
source_df = X[a == s].iloc[np.array(source_array)]
target_df = X[a == t].iloc[np.array(neighbor_array_indices)]
if t in matches or s in matches:
warnings.warn("No-replacement matching for more than "
"2 treatment values is not supported")
matches[t] = self._create_match_df_for_no_replacement(
a, source_df, target_df, distances)
matches[s] = self._create_match_df_for_no_replacement(
a, target_df, source_df, distances)
match_df = pd.concat(matches, sort=True)
return match_df
def _optimally_match_distance_matrix(self, distance_matrix):
source_array, neighbor_array_indices = linear_sum_assignment(
distance_matrix)
distances = [[
distance_matrix[s_idx, t_idx]
] for s_idx, t_idx in zip(source_array, neighbor_array_indices)]
source_array, neighbor_array_indices, distances = \
self._filter_noreplacement_matches_using_caliper(
source_array, neighbor_array_indices, distances)
return source_array, neighbor_array_indices, distances
def _filter_noreplacement_matches_using_caliper(self, source_array,
neighbor_array_indices,
distances):
if self.caliper is None:
return source_array, neighbor_array_indices, distances
keep_indices = [
i for i, d in enumerate(distances) if d[0] <= self.caliper
]
source_array = source_array[keep_indices]
neighbor_array_indices = neighbor_array_indices[keep_indices]
distances = [distances[i] for i in keep_indices]
if not keep_indices:
warnings.warn("No matches found, check caliper."
"No estimation possible.")
return source_array, neighbor_array_indices, distances
@staticmethod
def _create_match_df_for_no_replacement(base_series, source_df, target_df,
distances):
match_sub_df = pd.DataFrame(
index=base_series.index,
columns=[
"matches",
"distances",
],
data=base_series.apply(lambda x: pd.Series([[], []])).values,
dtype="object",
)
# matching from source to target: read distances
match_sub_df.loc[source_df.index] = pd.DataFrame(
data=dict(
matches=[[tidx] for tidx in target_df.index],
distances=distances,
),
index=source_df.index,
)
# matching from target to target: fill with zeros
match_sub_df.loc[target_df.index] = pd.DataFrame(
data=dict(
matches=[[tidx] for tidx in target_df.index],
distances=[[0]] * len(distances),
),
index=target_df.index,
)
return match_sub_df
def _count_samples_used_by_treatment_value(self, a):
# we record the number of samples that were successfully matched of
# each treatment value
samples_used = {
treatment_value: self.match_df_.loc[treatment_value][
a != treatment_value].matches.apply(bool).sum()
for treatment_value in sorted(a.unique(), reverse=True)
}
return pd.Series(samples_used)
###### Likelyhood Computation ######
# Fold the angles in params into proper range, such that
# they centered at the mean.
N_CYCLE_FOLD_ANGLE = 10
for j in xrange(N_CYCLE_FOLD_ANGLE):
mean = np.mean(params, axis=0)
for i in xrange(3, 6): # index 3,4,5 are angles, others are distances
params[:, i][params[:, i] > mean[i] + np.pi] -= 2 * np.pi
params[:, i][params[:, i] < mean[i] - np.pi] += 2 * np.pi
if PARAMS_TLR[i] > mean[i] + np.pi:
PARAMS_TLR[i] += 2 * np.pi
if PARAMS_TLR[i] < mean[i] - np.pi:
PARAMS_TLR[i] -= 2 * np.pi
est = EmpiricalCovariance(True, False)
est.fit(params)
log_likelyhood = est.score(PARAMS_TLR[None, :])
KT = 0.59
free_e = -log_likelyhood * KT
print 'Log likelyhood score:', log_likelyhood
print 'Free energy:', free_e
###### Output the best conformer to pdb ######
def generate_bp_par_file(params, bps, out_name):
assert(len(params) == len(bps))
n_bp = len(params)
# convert from radians to degrees
params[:, 3:] = np.degrees(params[:, 3:])
import numpy as np
from scipy.io import loadmat
from sklearn.covariance import EmpiricalCovariance, EllipticEnvelope
from sklearn.metrics import accuracy_score, classification_report
cardio_data = loadmat('cardio.mat')
estimator = EmpiricalCovariance()
cov = estimator.fit(cardio_data['X'])
mahal_cov = cov.mahalanobis(cardio_data['X'])
# sort values and extract n maximum values
# number of outliers in cardio data = 176
indexes = np.argpartition(mahal_cov, 176)[-176:]
y_pred = np.zeros(cardio_data['y'].shape)
y_pred[indexes] = 1
print(classification_report(cardio_data['y'], y_pred))
print(accuracy_score(cardio_data['y'], y_pred))
cov = EllipticEnvelope().fit(np.dot(cardio_data['X'].T, cardio_data['X']))
mahal_cov = cov.mahalanobis(cardio_data['X'])
indexes = np.argpartition(mahal_cov, 176)[-176:]
y_pred = np.zeros(cardio_data['y'].shape)
y_pred[indexes] = 1
print(classification_report(cardio_data['y'], y_pred))
print(accuracy_score(cardio_data['y'], y_pred))
# ####################################
# PLSR - Marco
# ####################################
plsr = PLSR(X, Y)
plsr.Initialize()
plsr.EvaluateComponents()
weights = plsr.GetWeights()
comps = plsr.ReturnComponents()
print('Covariance X (XX\'):\n %s' % str(X.dot(X.T).shape))
print('Covariance X (plsr):\n %s' % str(plsr._covX.shape))
print('Covariance X (numpy):\n %s' % np.cov(X, rowvar=False))
print('Covariance X (pandas):\n %s' % dfx.cov().values)
cov = EmpiricalCovariance(assume_centered=True)
cov.fit(X)
print('Covariance X (sklearn):\n %s' % cov.covariance_)
# print('weigths 0:\n %s' % weights[0])
# print('weigths 1:\n %s' % weights[1])
# print('Y Scores:\n %s' % comps[0])
# print('Components Y:\n %s' % comps[1])
# ####################################
# PLSR - SKLEARN
# ####################################
# print('\n\nPLS-SVD')
# plsr = PLSSVD(n_components=2, scale=False)
# plsr.fit(X,Y)
def get_covariance(X):
cov = EmpiricalCovariance(assume_centered=True)
cov.fit(X)
return cov.covariance_
def fit(self, X, n_jobs=-1):
EmpiricalCovariance.fit(self, X)
if not self.no_fit:
CovarianceOutlierDetectionMixin.set_threshold(
self, X, n_jobs=n_jobs)
return self
hPurity_disc.Divide(hPurity_discDen)
hPurity_disc.Draw()
c.Print("purity_disc.png")
hMVAdisc_pt.Draw("colz")
c.Print("discriminator_vs_candPt.png")
from sklearn.covariance import EmpiricalCovariance
npRocInput = numpy.array(rocInput)
npRocAnswers = numpy.array(rocScore)
slimNpData0 = npRocInput[npRocAnswers == 0]
slimNpData1 = npRocInput[npRocAnswers == 1]
ecv = EmpiricalCovariance()
ecv.fit(slimNpData0)
from scipy.linalg import fractional_matrix_power
def diagElements(m):
size = m.shape[0]
return numpy.matrix(numpy.diag([m[i, i] for i in xrange(size)]))
def corrMat(m):
sqrt_diag = fractional_matrix_power(diagElements(m), -0.5)
return numpy.array(sqrt_diag * m * sqrt_diag)
corr0 = corrMat(numpy.matrix(ecv.covariance_))
###### Likelyhood Computation ######
# Fold the angles in params into proper range, such that
# they centered at the mean.
N_CYCLE_FOLD_ANGLE = 10
for j in xrange(N_CYCLE_FOLD_ANGLE):
mean = np.mean(params, axis=0)
for i in xrange(3, 6): # index 3,4,5 are angles, others are distances
params[:, i][params[:, i] > mean[i] + np.pi] -= 2 * np.pi
params[:, i][params[:, i] < mean[i] - np.pi] += 2 * np.pi
if PARAMS_TLR[i] > mean[i] + np.pi:
PARAMS_TLR[i] += 2 * np.pi
if PARAMS_TLR[i] < mean[i] - np.pi:
PARAMS_TLR[i] -= 2 * np.pi
est = EmpiricalCovariance(True, False)
est.fit(params)
log_likelyhood = est.score(PARAMS_TLR[None, :])
KT = 0.59
free_e = -log_likelyhood * KT
print 'Log likelyhood score:', log_likelyhood
print 'Free energy:', free_e
###### Output the best conformer to pdb ######
def generate_bp_par_file(params, bps, out_name):
assert (len(params) == len(bps))
n_bp = len(params)
# convert from radians to degrees
params[:, 3:] = np.degrees(params[:, 3:])
def fit(self, X):
'''
Copulafit using Gaussian copula with marginals evaluated by Gaussian KDE
Precision matrix is evaluated using specified method, default to graphical LASSO
:param X: input dataset
:return: estimated precision matrix rho
'''
N, d = X.shape
if self.scaler is not None:
X_scale = self.scaler.fit_transform(X)
else:
X_scale = X
if len(self.vertexes) == 0:
self.vertexes = [str(id) for id in range(d)]
self.theta = 1.0 / N
cum_marginals = np.zeros_like(X)
inv_norm_cdf = np.zeros_like(X)
# inv_norm_cdf_scaled = np.zeros_like(X)
self.kernels = list([])
# TODO: complexity O(Nd) is high
if self.verbose:
colored('>> Computing marginals', color='blue')
for j in range(cum_marginals.shape[1]):
self.kernels.append(gaussian_kde(X_scale[:, j]))
cum_pdf_overall = self.kernels[-1].integrate_box_1d(
X_scale[:, j].min(), X_scale[:, j].max())
for i in range(cum_marginals.shape[0]):
cum_marginals[i, j] = self.kernels[-1].integrate_box_1d(
X_scale[:, j].min(), X_scale[i, j]) / cum_pdf_overall
# truncate cumulative marginals
if cum_marginals[i, j] < self.theta:
cum_marginals[i, j] = self.theta
elif cum_marginals[i, j] > 1 - self.theta:
cum_marginals[i, j] = 1 - self.theta
# inverse of normal CDF: \Phi(F_j(x))^{-1}
inv_norm_cdf[i, j] = norm.ppf(cum_marginals[i, j])
# scaled to preserve mean and variance: u_j + \sigma_j*\Phi(F_j(x))^{-1}
# inv_norm_cdf_scaled[i, j] = X_scale[:, j].mean() + X_scale[:, j].std() * inv_norm_cdf[i, j]
if self.method == 'mle':
# maximum-likelihood estiamtor
empirical_cov = EmpiricalCovariance()
empirical_cov.fit(inv_norm_cdf)
if self.verbose:
print colored('>> Running MLE to estiamte precision matrix',
color='blue')
self.est_cov = empirical_cov.covariance_
self.corr = scale_matrix(self.est_cov)
self.precision_ = inv(empirical_cov.covariance_)
if self.method == 'glasso':
if self.verbose:
print colored('>> Running glasso to estiamte precision matrix',
color='blue')
empirical_cov = EmpiricalCovariance()
empirical_cov.fit(inv_norm_cdf)
# shrunk convariance to avoid numerical instability
shrunk_cov = shrunk_covariance(empirical_cov.covariance_,
shrinkage=0.8)
self.est_cov, self.precision_ = graph_lasso(emp_cov=shrunk_cov,
alpha=self.penalty,
verbose=self.verbose,
max_iter=self.max_iter)
self.corr = scale_matrix(self.est_cov)
if self.method == 'ledoit_wolf':
if self.verbose:
print colored(
'>> Running ledoit_wolf to estiamte precision matrix',
color='blue')
self.est_cov, _ = ledoit_wolf(inv_norm_cdf)
self.corr = scale_matrix(self.est_cov)
self.precision_ = linalg.inv(self.est_cov)
if self.method == 'spectral':
'''L2 mehtod, use paper Inverse covariance estimation for high dimension data in linear time and space
:formular: in paper eq(8)
'''
if self.verbose:
print colored(
'>> Running Riccati to estiamte precision matrix',
color='blue')
# TODO: note estimated cov is sample cov
self.est_cov, self.precision_ = spectral(inv_norm_cdf,
rho=2 * self.penalty,
assume_centered=False)
self.corr = scale_matrix(self.est_cov)
if self.method == 'pc':
clf = pgmlearner.PGMLearner()
data_list = list([])
for row_id in range(X_scale.shape[0]):
instance = dict()
for i, n in enumerate(self.vertexes):
instance[n] = X_scale[row_id, i]
data_list.append(instance)
graph = clf.lg_constraint_estimatestruct(data=data_list,
pvalparam=self.pval,
bins=self.bins)
dag = np.zeros(shape=(len(graph.V), len(graph.V)))
for e in graph.E:
dag[self.vertexes.index(e[0]), self.vertexes.index(e[1])] = 1
self.conditional_independences_ = dag
if self.method == 'ic':
df = dict()
variable_types = dict()
for j in range(X_scale.shape[1]):
df[self.vertexes[j]] = X_scale[:, j]
variable_types[self.vertexes[j]] = 'c'
data = pd.DataFrame(df)
# run the search
ic_algorithm = IC(RobustRegressionTest,
data,
variable_types,
alpha=self.pval)
graph = ic_algorithm.search()
dag = np.zeros(shape=(X_scale.shape[1], X_scale.shape[1]))
for e in graph.edges(data=True):
i = self.vertexes.index(e[0])
j = self.vertexes.index(e[1])
dag[i, j] = 1
dag[j, i] = 1
arrows = set(e[2]['arrows'])
head_len = len(arrows)
if head_len > 0:
head = arrows.pop()
if head_len == 1 and head == e[0]:
dag[i, j] = 0
if head_len == 1 and head == e[1]:
dag[j, i] = 0
self.conditional_independences_ = dag
# finally we fit the structure
self.fit_structure(self.precision_)
def optimalShrinkage(X, return_covariance=False):
"""This function computes a cleaned, optimal shrinkage,
rotationally-invariant estimator (RIE) of the true correlation
matrix C underlying the noisy, in-sample estimate
E = 1/T X * transpose(X)
associated to a design matrix X of shape (T, N) (T measurements
and N features).
One approach to getting a cleaned estimator that predates the
optimal shrinkage, RIE estimator consists in inverting the
Marcenko-Pastur equation so as to replace the eigenvalues
from the spectrum of E by an estimation of the true ones.
This approach is known to be numerically-unstable, in addition
to failing to account for the overlap between the sample eigenvectors
and the true eigenvectors. How to compute such overlaps was first
explained by Ledoit and Peche (cf. reference below). Their procedure
was extended by Bun, Bouchaud and Potters, who also correct
for a systematic downward bias in small eigenvalues.
It is this debiased, optimal shrinkage, rotationally-invariant
estimator that the function at hand implements.
Parameter
---------
X: design matrix, of shape (T, N), where T denotes the number
of samples (think measurements in a time series), while N
stands for the number of features (think of stock tickers).
return_covariance: type bool (default: False)
If set to True, compute the standard deviations of each individual
feature across observations, clean the underlying matrix
of pairwise correlations, then re-apply the standard
deviations and return a cleaned variance-covariance matrix.
Returns
-------
E_RIE: type numpy.ndarray, shape (N, N)
Cleaned estimator of the true correlation matrix C. A sample
estimator of C is the empirical covariance matrix E
estimated from X. E is corrupted by in-sample noise.
E_RIE is the optimal shrinkage, rotationally-invariant estimator
(RIE) of C computed following the procedure of Joel Bun
and colleagues (cf. references below).
If return_covariance=True, E_clipped corresponds to a cleaned
variance-covariance matrix.
References
----------
* "Eigenvectors of some large sample covariance matrix ensembles",
O. Ledoit and S. Peche
Probability Theory and Related Fields, Vol. 151 (1), pp 233-264
* "Rotational invariant estimator for general noisy matrices",
J. Bun, R. Allez, J.-P. Bouchaud and M. Potters
arXiv: 1502.06736 [cond-mat.stat-mech]
* "Cleaning large Correlation Matrices: tools from Random Matrix Theory",
J. Bun, J.-P. Bouchaud and M. Potters
arXiv: 1610.08104 [cond-mat.stat-mech]
"""
try:
assert isinstance(return_covariance, bool)
except AssertionError:
raise
sys.exit(1)
T, N, transpose_flag = checkDesignMatrix(X)
if transpose_flag:
X = X.T
if not return_covariance:
X = StandardScaler(with_mean=False,
with_std=True).fit_transform(X)
ec = EmpiricalCovariance(store_precision=False,
assume_centered=True)
ec.fit(X)
E = ec.covariance_
if return_covariance:
inverse_std = 1./np.sqrt(np.diag(E))
E *= inverse_std
E *= inverse_std.reshape(-1, 1)
eigvals, eigvecs = np.linalg.eigh(E)
eigvecs = eigvecs.T
q = N / float(T)
lambda_N = eigvals[0] # The smallest empirical eigenvalue,
# given that the function used to compute
# the spectrum of a Hermitian or symmetric
# matrix - namely np.linalg.eigh - returns
# the eigenvalues in ascending order.
xis = map(lambda x: xiHelper(x, q, E), eigvals)
Gammas = map(lambda x: gammaHelper(x, q, N, lambda_N), eigvals)
xi_hats = map(lambda a, b: a * b if b > 1 else a, xis, Gammas)
E_RIE = np.zeros((N, N), dtype=float)
for xi_hat, eigvec in zip(xi_hats, eigvecs):
eigvec = eigvec.reshape(-1, 1)
E_RIE += xi_hat * eigvec.dot(eigvec.T)
tmp = 1./np.sqrt(np.diag(E_RIE))
E_RIE *= tmp
E_RIE *= tmp.reshape(-1, 1)
if return_covariance:
std = 1./inverse_std
E_RIE *= std
E_RIE *= std.reshape(-1, 1)
return E_RIE
def rand_pts_overall_cov_init(X,
n_components,
cov_est_method='LW',
covariance_type='full',
random_state=None):
"""
Sets the means to randomly selected points. Sets the covariances to the overall covariance matrix.
Parameters
----------
X: (n_samples, n_features)
n_components: int
cov_est_method: str
Must be one of ['emperical', 'LW', 'OAS'] for
empirical covariance matrix estimate, LedoitWolf and
Oracle Approximating Shrinkage Estimator. See
sklean.covariace for details.
random_state: None, int, random seed
Random seed.
"""
assert cov_est_method in ['empirical', 'LW', 'OAS']
assert covariance_type in ['full', 'diag', 'tied', 'spherical']
n_samples = X.shape[0]
# randomly select data points to start cluster centers from
rng = check_random_state(random_state)
# estimate global covariance
if cov_est_method == 'empirical':
cov_estimator = EmpiricalCovariance(store_precision=False)
elif cov_est_method == 'LW':
cov_estimator = LedoitWolf(store_precision=False)
elif cov_est_method == 'OAS':
cov_estimator = OAS(store_precision=False)
cov_estimator.fit(X)
cov_est = cov_estimator.covariance_
# set covariance matrix for each cluster
if covariance_type == 'tied':
covs = cov_est
elif covariance_type == 'full':
covs = np.stack([cov_est for _ in range(n_components)])
elif covariance_type == 'diag':
# each components gets the diagonal of the estimated covariance matrix
covs = np.diag(cov_est)
covs = np.repeat(covs.reshape(1, -1), repeats=n_components, axis=0)
elif covariance_type == 'spherical':
# each components gets the average of the variances
covs = np.diag(cov_est).mean()
covs = np.repeat(covs, repeats=n_components)
# set means to random data points
rand_idxs = rng.choice(range(n_samples), replace=False, size=n_components)
means = [X[pt_idx, ] for pt_idx in rand_idxs]
means = np.array(means)
return means, covs
# save for heuristic correction
age = df_test['var15']
age_ecdf = ECDF(df_train['var15'])
df_train['var15'] = age_ecdf(df_train['var15'])
df_test['var15'] = age_ecdf(df_test['var15'])
# feature engineering
df_train.loc[df_train['var3'] == -999999.000000, 'var3'] = 2.0
df_train['num_zeros'] = (df_train == 0).sum(axis=1)
df_test.loc[df_train['var3'] == -999999.000000, 'var3'] = 2.0
df_test['num_zeros'] = (df_test == 0).sum(axis=1)
# outliers
ec = EmpiricalCovariance()
ec = ec.fit(df_train)
m2 = ec.mahalanobis(df_train)
df_train = df_train[m2 < 40000]
df_target = df_target[m2 < 40000]
# clip
# df_test = df_test.clip(df_train.min(), df_train.max(), axis=1)
# standard preprocessing
prep = Pipeline([
('cd', ColumnDropper(drop=ZERO_VARIANCE_COLUMNS + CORRELATED_COLUMNS)),
('std', StandardScaler())
])
X_train = prep.fit_transform(df_train)
X_test = prep.transform(df_test)
