def _forward_log_det_jacobian(self, x):
# y = sinh((arcsinh(x) + skewness) * tailweight) * multiplier
# Using sinh' = cosh, arcsinh'(x) = 1 / sqrt(x**2 + 1),
# dy/dx
# = cosh((arcsinh(x) + skewness) * tailweight) * tailweight / sqrt(x**2 + 1)
# * multiplier
tailweight = tf.convert_to_tensor(self.tailweight)
return (tfp_math.log_cosh((tf.asinh(x) + self.skewness) * tailweight) -
0.5 * tfp_math.log1psquare(x) + tf.math.log(tailweight) +
tf.math.log(self._output_multiplier(tailweight)))
def _inverse_log_det_jacobian(self, y):
# x = sinh(arcsinh(y / multiplier) / tailweight - skewness)
# Using sinh' = cosh, arcsinh'(y) = 1 / sqrt(y**2 + 1),
# dx/dy
# = cosh(arcsinh(y / multiplier) / tailweight - skewness)
# / (tailweight * sqrt((y / multiplier)**2 + 1)) / multiplier
tailweight = tf.convert_to_tensor(self.tailweight)
multiplier = self._output_multiplier(tailweight)
y = y / multiplier
return (tfp_math.log_cosh(tf.asinh(y) / tailweight - self.skewness) -
0.5 * tfp_math.log1psquare(y) - tf.math.log(tailweight) -
tf.math.log(multiplier))
def _forward_log_det_jacobian(self, x):
return tfp_math.log_cosh(x)
