def estimation(self, y1, y2):
""" Estimate Sharma-Mittal divergence.
Parameters
----------
y1 : (number of samples1, dimension)-ndarray
One row of y1 corresponds to one sample.
y2 : (number of samples2, dimension)-ndarray
One row of y2 corresponds to one sample.
Returns
-------
d : float
Estimated Sharma-Mittal divergence.
References
----------
Barnabas Poczos, Zoltan Szabo, Jeff Schneider. Nonparametric
divergence estimators for Independent Subspace Analysis. European
Signal Processing Conference (EUSIPCO), pages 1849-1853, 2011.
Barnabas Poczos, Jeff Schneider. On the Estimation of
alpha-Divergences. International conference on Artificial
Intelligence and Statistics (AISTATS), pages 609-617, 2011.
Marco Massi. A step beyond Tsallis and Renyi entropies. Physics
Letters A, 338:217-224, 2005. (Sharma-Mittal divergence definition)
Examples
--------
d = co.estimation(y1,y2)
"""
# verification:
self.verification_equal_d_subspaces(y1, y2)
d_temp1 = estimate_d_temp1(y1, y2, self)
d = (d_temp1**((1 - self.beta) / (1 - self.alpha)) - 1) /\
(self.beta - 1)
return d
def estimation(self, y1, y2):
""" Estimate Renyi divergence.
Parameters
----------
y1 : (number of samples1, dimension)-ndarray
One row of y1 corresponds to one sample.
y2 : (number of samples2, dimension)-ndarray
One row of y2 corresponds to one sample.
Returns
-------
d : float
Estimated Renyi divergence.
References
----------
Barnabas Poczos, Zoltan Szabo, Jeff Schneider. Nonparametric
divergence estimators for Independent Subspace Analysis. European
Signal Processing Conference (EUSIPCO), pages 1849-1853, 2011.
Barnabas Poczos, Jeff Schneider. On the Estimation of
alpha-Divergences. International conference on Artificial
Intelligence and Statistics (AISTATS), pages 609-617, 2011.
Barnabas Poczos, Liang Xiong, Jeff Schneider. Nonparametric
Divergence: Estimation with Applications to Machine Learning on
Distributions. Uncertainty in Artificial Intelligence (UAI), 2011.
Examples
--------
d = co.estimation(y1,y2)
"""
# verification:
self.verification_equal_d_subspaces(y1, y2)
d_temp1 = estimate_d_temp1(y1, y2, self)
d = log(d_temp1) / (self.alpha - 1)
return d