def cdf(self, val):
_cdf = (erf((val - self.mu) / 2**0.5 / self.sigma) - erf(
(self.minimum - self.mu) / 2**0.5 /
self.sigma)) / 2 / self.normalisation
_cdf[val > self.maximum] = 1
_cdf[val < self.minimum] = 0
return _cdf
def normalisation(self):
""" Calculates the proper normalisation of the truncated Gaussian
Returns
-------
float: Proper normalisation of the truncated Gaussian
"""
return (erf((self.maximum - self.mu) / 2**0.5 / self.sigma) - erf(
(self.minimum - self.mu) / 2**0.5 / self.sigma)) / 2
def cdf(self, val):
if isinstance(val, (float, int)):
if val <= self.minimum:
_cdf = 0.
else:
_cdf = 0.5 + erf((np.log(val) - self.mu) / self.sigma / np.sqrt(2)) / 2
else:
_cdf = np.zeros(val.size)
_cdf[val > self.minimum] = 0.5 + erf((
np.log(val[val > self.minimum]) - self.mu) / self.sigma / np.sqrt(2)) / 2
return _cdf
def theoretical_distribution(self):
x = np.sort(self.sample)
y = np.array([
0.5 * (1 + erf((i - self.mean) / np.sqrt(2 * self.std**2)))
for i in x
])
plt.plot(x, y, 'r-')
def rescale(self, val):
"""
'Rescale' a sample from the unit line element to the appropriate truncated Gaussian prior.
This maps to the inverse CDF. This has been analytically solved for this case.
"""
return erfinv(2 * val * self.normalisation + erf(
(self.minimum - self.mu) / 2 ** 0.5 / self.sigma)) * 2 ** 0.5 * self.sigma + self.mu
def unify(outlying_scores: np.array) -> np.array:
# =======================================================================================================================
# Turn output into probability
# Source: https://github.com/yzhao062/pyod/blob/8fafcbd7c441954b82db27bfd9cd7f0720974d9a/pyod/models/base.py
# Reference:
# Hans-Peter Kriegel, etc. Interpreting and unifying outlier scores. SDM 2011
# =======================================================================================================================
mu = np.mean(outlying_scores)
sigma = np.std(outlying_scores)
if sigma !=0:
pre_erf_score = (outlying_scores - mu) / (sigma * np.sqrt(2))
else:
pre_erf_score = (outlying_scores - mu)
erf_score = erf(pre_erf_score)
return erf_score.clip(0, 1).ravel()
def cdf(self, val):
return (1 - erf((self.mu - val) / 2**0.5 / self.sigma)) / 2
