def _kl_beta_beta(dist1, dist2):
dist1_apb = dist1.a + dist1.b
dist2_apb = dist2.a + dist2.b
return - _lbeta(dist1.a, dist1.b) + _lbeta(dist2.a, dist2.b)\
+ (dist1.a - dist2.a) * digamma.digamma(dist1.a) \
+ (dist1.b - dist2.b) * digamma.digamma(dist1.b) \
+ (dist2_apb - dist1_apb) * digamma.digamma(dist1_apb)
def _kl_beta_beta(dist1, dist2):
dist1_apb = dist1._a_plus_b
dist2_apb = dist2._a_plus_b
return (-_lbeta(dist1.a, dist1.b) + _lbeta(dist2.a, dist2.b) +
(dist1.a - dist2.a) * digamma.digamma(dist1.a) +
(dist1.b - dist2.b) * digamma.digamma(dist1.b) +
(dist2_apb - dist1_apb) * digamma.digamma(dist1_apb))
def _kl_beta_beta(dist1, dist2):
dist1_apb = dist1.a + dist1.b
dist2_apb = dist2.a + dist2.b
return - _lbeta(dist1.a, dist1.b) + _lbeta(dist2.a, dist2.b)\
+ (dist1.a - dist2.a) * digamma.digamma(dist1.a) \
+ (dist1.b - dist2.b) * digamma.digamma(dist1.b) \
+ (dist2_apb - dist1_apb) * digamma.digamma(dist1_apb)
def entropy(self):
return (
_lbeta(self.alpha)
+ ((self.alpha0 - self.event_shape[0])
* digamma.digamma(self.alpha0))
- sum_mod.sum(
(self.alpha - 1) * digamma.digamma(self.alpha),
axis=-1))
def _kl_dirichlet_dirichlet(dist1, dist2):
return (
- _lbeta(dist1.alpha)
+ _lbeta(dist2.alpha)
+ sum_mod.sum(
(dist1.alpha - dist2.alpha)
* (digamma.digamma(dist1.alpha)
- expand_dims.expand_dims(
digamma.digamma(dist1.alpha0),
axis=-1)),
axis=-1))
def entropy(self):
return _lbeta(self.alpha) \
+ (self.alpha0 - self.event_shape[0]) \
* digamma.digamma(self.alpha0) \
- sum_mod.sum((self.alpha - 1)
* digamma.digamma(self.alpha), axis=-1)
def entropy(self):
apb = self.a + self.b
return _lbeta(self.a, self.b) \
- (self.a - 1) * digamma.digamma(self.a) \
- (self.b - 1) * digamma.digamma(self.b) \
+ (apb - 2) * digamma.digamma(apb)
def _kl_gamma_gamma(dist1, dist2):
return (dist1.k - dist2.k) * digamma.digamma(dist1.k) \
- (lgamma.lgamma(dist1.k) - lgamma.lgamma(dist2.k)) \
+ dist2.k\
* (exponential.log(dist2.theta) - exponential.log(dist1.theta)) \
+ dist1.k * (dist1.theta / dist2.theta - 1)
def entropy(self):
return self.k + exponential.log(self.theta) + lgamma.lgamma(self.k) \
+ (1 - self.k) * digamma.digamma(self.k)
def entropy(self):
apb = self.a + self.b
return _lbeta(self.a, self.b) \
- (self.a - 1) * digamma.digamma(self.a) \
- (self.b - 1) * digamma.digamma(self.b) \
+ (apb - 2) * digamma.digamma(apb)
def entropy(self):
return 0.5 * self.k + numpy.log(2.) + lgamma.lgamma(0.5 * self.k) \
+ (1 - 0.5 * self.k) * digamma.digamma(0.5 * self.k)
def entropy(self):
return self._half_k + numpy.log(2.) + lgamma.lgamma(self._half_k) \
+ (1 - self._half_k) * digamma.digamma(self._half_k)
def entropy(self):
return (
self._half_k
+ numpy.log(2.)
+ lgamma.lgamma(self._half_k)
+ (1 - self._half_k) * digamma.digamma(self._half_k))
def entropy(self):
apb = self._a_plus_b
return (_lbeta(self.a, self.b) -
(self.a - 1) * digamma.digamma(self.a) -
(self.b - 1) * digamma.digamma(self.b) +
(apb - 2) * digamma.digamma(apb))
def entropy(self):
return _lbeta(self.alpha) \
+ (self.alpha0 - self.event_shape[0]) \
* digamma.digamma(self.alpha0) \
- sum_mod.sum((self.alpha - 1)
* digamma.digamma(self.alpha), axis=-1)
def _kl_dirichlet_dirichlet(dist1, dist2):
return - _lbeta(dist1.alpha) + _lbeta(dist2.alpha) \
+ sum_mod.sum((dist1.alpha - dist2.alpha) * (
digamma.digamma(dist1.alpha)
- expand_dims.expand_dims(digamma.digamma(
dist1.alpha0), axis=-1)), axis=-1)
def entropy(self):
return self.k + exponential.log(self.theta) + lgamma.lgamma(self.k) \
+ (1 - self.k) * digamma.digamma(self.k)
def _kl_gamma_gamma(dist1, dist2):
return (dist1.k - dist2.k) * digamma.digamma(dist1.k) \
- (lgamma.lgamma(dist1.k) - lgamma.lgamma(dist2.k)) \
+ dist2.k\
* (exponential.log(dist2.theta) - exponential.log(dist1.theta)) \
+ dist1.k * (dist1.theta / dist2.theta - 1)
def entropy(self):
return 0.5 * self.k + numpy.log(2.) + lgamma.lgamma(0.5 * self.k) \
+ (1 - 0.5 * self.k) * digamma.digamma(0.5 * self.k)
