def rings_log_pdf_grad(X, sigma=0.1, radia=np.array([1, 3])):
weights = 2 * np.pi * radia
weights /= np.sum(weights)
norms = np.linalg.norm(X[:, :2], axis=1)
result = np.zeros(np.shape(X))
grads = []
for i in range(len(X)):
log_pdf_components = -0.5 * (norms[i] - radia)**2 / (sigma**2)
log_pdf = logsumexp(log_pdf_components + np.log(weights))
neg_log_neg_ratios = log_pdf_components - log_pdf
gs_inner = np.zeros((len(radia), 1))
for k in range(len(gs_inner)):
gs_inner[k] = -(norms[i] - radia[k]) / (sigma**2)
grad_1d = np.dot(gs_inner.T,
np.exp(neg_log_neg_ratios + np.log(weights)))
angle = np.arctan2(X[i, 1], X[i, 0])
grad_2d = np.array([np.cos(angle), np.sin(angle)]) * grad_1d
grads += [grad_2d]
result[:, :2] = np.array(grads)
if X.shape[1] > 2:
# standard normal log pdf gradient
result[:, 2:] = -X[:, 2:] / (sigma**2)
return result
def calculate_marginal_and_conditional(self, confidence_mass):
assert len(self.received_msgs) == len(self.neighbours), "message from at least one factor is missing"
if self.clamped_value is not None:
marginal = np.zeros(1)
conditional = np.zeros(1)
else:
marginal = np.zeros(self.n_states)
conditional = np.zeros(self.n_states)
for fac in self.factors:
fac_msg_sp, fac_msg_ms = self.received_msgs[fac]
marginal += fac_msg_sp
conditional += fac_msg_ms
# renormalize
self.log_marginal = marginal - logsumexp(marginal)
self.log_conditional = conditional - logsumexp(conditional)
self.marginal = np.exp(self.log_marginal)
self.conditional = np.exp(self.log_conditional)
# calculate means and variances
vals = np.arange(self.n_states)
self.marginal_mean = np.sum(self.marginal * vals)
self.marginal_variance = np.sum(self.marginal * vals**2) - self.marginal_mean**2
self.conditional_mean = np.sum(self.conditional * vals)
self.conditional_variance = np.sum(self.conditional * vals**2) - self.conditional_mean**2
# calculate confidence interval
if not np.all(np.isnan(self.conditional)):
center = np.nanargmax(self.conditional)
conditional_cdf = np.cumsum(self.conditional)
# debug
# if self.name == "f_40":
# import matplotlib.pyplot as plt
# plt.plot(self.conditional)
# plt.figure()
# plt.plot(conditional_cdf)
# plt.figure()
left, right = self.cumulate_mass_around(conditional_cdf, confidence_mass, center)
self.conditional_conf_lower = center - left
self.conditional_conf_upper = right - center
else:
self.conditional_conf_upper = 0
self.conditional_conf_lower = 0
def update(self, Z, num_new=1, log_weights=None):
assert (len(Z) >= num_new)
# dont do anything if no data observed
if num_new == 0:
return
if log_weights is not None:
assert len(log_weights) == len(Z)
else:
log_weights = np.zeros(len(Z))
Z_new = Z[-num_new:]
log_weights_new = log_weights[-num_new:]
# first update: use first of X and log_weights, and then discard
if self.log_sum_weights is None:
# assume have observed fake terms, which is needed for making the system well-posed
# the L_C says that the fake terms had covariance self.lmbda, which is a regulariser
self.L_C = np.eye(self.D) * np.sqrt(self.gamma2)
self.log_sum_weights = log_weights_new[0]
self.mu = Z_new[0]
Z_new = Z_new[1:]
log_weights_new = log_weights_new[1:]
num_new -= 1
# dont do anything if no data observed
if len(Z_new) == 0:
return
# generate lmbdas that correspond to weighted averages
lmbdas = log_weights_to_lmbdas(self.log_sum_weights, log_weights_new)
# low-rank update of Cholesky, costs O(d^2) only
old_L_C = np.array(self.L_C, copy=True)
self.mu, self.L_C = update_mean_cov_L_lmbda(Z_new, self.mu, self.L_C,
lmbdas)
if np.any(np.isnan(self.L_C)) or np.any(np.isinf(self.L_C)):
logger.warning(
"Numerical error while updating Cholesky factor of C.\n"
"Before update:\n%s\n"
"After update:\n%s\n"
"Updating data:\n%s\n"
"Updating log weights:\n%s\n"
"Updating lmbdas:\n%s\n" % (str(old_L_C), str(
self.L_C), str(Z_new), str(log_weights_new), str(lmbdas)))
raise RuntimeError(
"Numerical error while updating Cholesky factor of C.")
# update terms and weights
self.log_sum_weights = logsumexp(
list(log_weights) + [self.log_sum_weights])
def update(self, Z, num_new=1, log_weights=None):
assert(len(Z) >= num_new)
# dont do anything if no data observed
if num_new == 0:
return
if log_weights is not None:
assert len(log_weights) == len(Z)
else:
log_weights = np.zeros(len(Z))
Z_new = Z[-num_new:]
log_weights_new = log_weights[-num_new:]
# first update: use first of X and log_weights, and then discard
if self.log_sum_weights is None:
# assume have observed fake terms, which is needed for making the system well-posed
# the L_C says that the fake terms had covariance self.lmbda, which is a regulariser
self.L_C = np.eye(self.D) * np.sqrt(self.gamma2)
self.log_sum_weights = log_weights_new[0]
self.mu = Z_new[0]
Z_new = Z_new[1:]
log_weights_new = log_weights_new[1:]
num_new -= 1
# dont do anything if no data observed
if len(Z_new) == 0:
return
# generate lmbdas that correspond to weighted averages
lmbdas = log_weights_to_lmbdas(self.log_sum_weights, log_weights_new)
# low-rank update of Cholesky, costs O(d^2) only
old_L_C = np.array(self.L_C, copy=True)
self.mu, self.L_C = update_mean_cov_L_lmbda(Z_new, self.mu, self.L_C, lmbdas)
if np.any(np.isnan(self.L_C)) or np.any(np.isinf(self.L_C)):
logger.warning("Numerical error while updating Cholesky factor of C.\n"
"Before update:\n%s\n"
"After update:\n%s\n"
"Updating data:\n%s\n"
"Updating log weights:\n%s\n"
"Updating lmbdas:\n%s\n"
% (str(old_L_C), str(self.L_C), str(Z_new), str(log_weights_new), str(lmbdas))
)
raise RuntimeError("Numerical error while updating Cholesky factor of C.")
# update terms and weights
self.log_sum_weights = logsumexp(list(log_weights) + [self.log_sum_weights])
def log_weights_to_lmbdas(log_sum_old_weights, log_new_weights, boundary_check_min_number=1e-5):
N = len(log_new_weights)
lmbdas = np.zeros(N)
for i, log_new_weight in enumerate(log_new_weights):
log_sum_old_weights = logsumexp([log_sum_old_weights, log_new_weight])
log_lmbda = log_new_weight - log_sum_old_weights
lmbdas[i] = np.exp(log_lmbda)
# numerical checks for lambdas. Must be in (0,1)
lmbdas[lmbdas < boundary_check_min_number] = boundary_check_min_number
lmbdas[(1 - lmbdas) < boundary_check_min_number] = 1 - boundary_check_min_number
return lmbdas
def predict_log_proba(self,X):
if isinstance(X, ndarray):
logps = []
for clazz in self.classes_:
data_object = self.\
_convert_to_data_object_in_scoring(
X,
y=array([clazz]*len(X))
)
logps += [self._anomaly_detector._LogProbabilityOfData(data_object, len(X))]
LogPs = [x-logsumexp(x) for x in array(logps).T]
return array(LogPs)
def log_weights_to_lmbdas(log_sum_old_weights,
log_new_weights,
boundary_check_min_number=1e-5):
N = len(log_new_weights)
lmbdas = np.zeros(N)
for i, log_new_weight in enumerate(log_new_weights):
log_sum_old_weights = logsumexp([log_sum_old_weights, log_new_weight])
log_lmbda = log_new_weight - log_sum_old_weights
lmbdas[i] = np.exp(log_lmbda)
# numerical checks for lambdas. Must be in (0,1)
lmbdas[lmbdas < boundary_check_min_number] = boundary_check_min_number
lmbdas[(1 - lmbdas
) < boundary_check_min_number] = 1 - boundary_check_min_number
return lmbdas
def predict_log_proba(self, X):
if isinstance(X, ndarray):
logps = []
for clazz in self.classes_:
data_object = self.\
_convert_to_data_object_in_scoring(
X,
y=array([clazz]*len(X))
)
logps += [
self._anomaly_detector._LogProbabilityOfData(
data_object, len(X))
]
LogPs = [x - logsumexp(x) for x in array(logps).T]
return array(LogPs)
def _logsum(self, x, dim):
"""Calculates the sum of x[:^(dim-1), i, ...] for each value of i.
Returns a vector of size x.shape[dim]."""
# handle case when there is no summation to be done
if x.ndim == 1 and dim == 0:
return x
# make stationary axis the first one
x = np.rollaxis(x, dim)
# flatten other axes
xflat = np.reshape(x, (x.shape[0], -1))
# calculate sum
x_sum = logsumexp(xflat, axis=1)
return x_sum
def predict_log_proba(self, X):
assert self.class_column > -1
X1 = None
if isinstance(X, pyisc.DataObject):
assert X.class_column == self.class_column
X1 = X.as_2d_array()
elif isinstance(X, ndarray):
X1 = X.copy()
if X1 is not None:
logps = self.compute_logp(X1)
LogPs = [x - logsumexp(x) for x in array(logps).T] #normalized
return array(LogPs)
else:
raise ValueError("Unknown type of data to score:", type(X))