def _covariance(self):
# Derivation: https://sachinruk.github.io/blog/von-Mises-Fisher/
event_dimension_static = tf.compat.dimension_value(self.event_shape[0])
mean_direction = tf.convert_to_tensor(self.mean_direction)
concentration = tf.convert_to_tensor(self.concentration)
event_dimension = tf.cast(
self._event_shape_tensor(mean_direction)[0], self.dtype)
safe_conc = tf.where(concentration > 0, concentration,
tf.ones_like(concentration))[..., tf.newaxis]
h = tfp_math.bessel_iv_ratio(event_dimension / 2, safe_conc)
intermediate = (
tf.matmul(mean_direction[..., :, tf.newaxis],
mean_direction[..., tf.newaxis, :]) *
(1 - event_dimension * h / safe_conc - h**2)[..., tf.newaxis])
cov = tf.linalg.set_diag(
intermediate,
tf.linalg.diag_part(intermediate) + (h / safe_conc))
return tf.where(
concentration[..., tf.newaxis, tf.newaxis] > 0., cov,
tf.linalg.eye(event_dimension_static,
batch_shape=self._batch_shape_tensor(
mean_direction=mean_direction,
concentration=concentration)) / event_dimension)
def _covariance(self):
# Derivation: https://sachinruk.github.io/blog/von-Mises-Fisher/
event_dimension_static = tf.compat.dimension_value(self.event_shape[0])
# TODO(b/141142878): Enable this; numerically unstable.
if event_dimension_static is not None and event_dimension_static > 2:
raise NotImplementedError(
'vMF covariance is numerically unstable for dim>2')
mean_direction = tf.convert_to_tensor(self.mean_direction)
concentration = tf.convert_to_tensor(self.concentration)
event_dimension = tf.cast(
self._event_shape_tensor(mean_direction)[0], self.dtype)
safe_conc = tf.where(concentration > 0, concentration,
tf.ones_like(concentration))[..., tf.newaxis]
h = tfp_math.bessel_iv_ratio(event_dimension / 2, safe_conc)
intermediate = (
tf.matmul(mean_direction[..., :, tf.newaxis],
mean_direction[..., tf.newaxis, :]) *
(1 - event_dimension * h / safe_conc - h**2)[..., tf.newaxis])
cov = tf.linalg.set_diag(
intermediate,
tf.linalg.diag_part(intermediate) + (h / safe_conc))
return tf.where(
concentration[..., tf.newaxis, tf.newaxis] > 0., cov,
tf.linalg.eye(event_dimension_static,
batch_shape=self._batch_shape_tensor(
mean_direction=mean_direction,
concentration=concentration)) / event_dimension)
def _mean(self):
# Derivation: https://sachinruk.github.io/blog/von-Mises-Fisher/
concentration = tf.convert_to_tensor(self.concentration)
mean_direction = tf.convert_to_tensor(self.mean_direction)
event_dimension = tf.cast(
self._event_shape_tensor(mean_direction)[0], self.dtype)
safe_conc = tf.where(concentration > 0, concentration,
tf.ones_like(concentration))
safe_mean = mean_direction * (tfp_math.bessel_iv_ratio(
event_dimension / 2., safe_conc)[..., tf.newaxis])
return tf.where(concentration[..., tf.newaxis] > 0., safe_mean,
tf.zeros_like(safe_mean))
def _entropy(self):
mean_direction = tf.convert_to_tensor(self.mean_direction)
event_dimension = tf.cast(
self._event_shape_tensor(mean_direction=mean_direction)[0],
dtype=self.dtype)
concentration = tf.convert_to_tensor(self.concentration)
# Compared to [1] (see the KL(VonMisesFisher || SphericalUniform) for the
# exact reference, we add the log normalization constant rather than
# subtract it. This is because in TFP, we have the convention that we
# normalize our distributions p(x) by a constant 1 / Z. Taking the log
# gives us a negative sign.
entropy = -concentration * tfp_math.bessel_iv_ratio(
event_dimension / 2., concentration) + self._log_normalization(
concentration=concentration)
return tf.broadcast_to(
entropy,
self._batch_shape_tensor(mean_direction=mean_direction,
concentration=concentration))