def dirichlet_log_density(x, alpha, clip_finite=True):
"""
Assumes that x is either a vector or a right-stochastic matrix (i.e., each row is a probability dist), and alpha is broadcastable to the same shape as x.
WARNING: does not enforce sum(x)==1; bad things will happen if this is violated.
"""
if len(x.get_shape()) == 1:
x = tf.reshape(x, (1, -1))
if clip_finite:
logx = tf.log(tf.clip_by_value(x, 1e-37, 1.0), name="dirichlet_logx")
else:
logx = tf.log(x, name="dirichlet_logx")
# force broadcasting alpha
if alpha.get_shape() != x.get_shape():
alpha = tf.zeros_like(x) + alpha
log_z = tf.reduce_sum(gammaln(alpha), axis=1) - gammaln(
tf.reduce_sum(alpha, axis=1))
log_density = tf.reduce_sum((alpha - 1) * logx, axis=1) - log_z
return log_density
def inv_gamma_log_density(x, alpha, beta):
"""Creates a TensorFlow variable representing the sum of one or more
independent inverse Gamma log-densities.
Args:
x (scalar or vector): variable(s) being modeled as InvGamma
alpha (scalar or vector)
beta (scalar or vector)
Each of alpha and beta must either be the same dimension
as x, or a scalar (which will be broadcast as required). They may
be TensorFlow variables or Python/numpy values.
Returns:
lp: TF scalar containing the log probability of x
"""
if isinstance(beta, tf.Tensor):
log_beta = tf.log(beta)
else:
log_beta = np.log(beta)
if isinstance(x, tf.Tensor):
log_x = tf.log(x)
else:
log_x = np.log(x)
if isinstance(alpha, tf.Tensor):
gammaln_alpha = gammaln(alpha)
else:
gammaln_alpha = scipy.special.gammaln(alpha)
lps = -beta / x + alpha * log_beta - (alpha +
1) * tf.log(x) - gammaln_alpha
return lps
def dirichlet_log_density(x, alpha, clip_finite=True):
"""
Assumes that x is a vector, and alpha is a vector of the same length.
WARNING: does not enforce sum(x)==1; bad things will happen if this is violated.
"""
if clip_finite:
logx = tf.log(tf.clip_by_value(x, 1e-37, 1.0), name="dirichlet_logx")
else:
logx = tf.log(x, name="dirichlet_logx")
# force broadcasting alpha
if alpha.get_shape() != x.get_shape():
alpha = tf.zeros_like(x) + alpha
log_z = tf.reduce_sum(gammaln(alpha)) - gammaln(tf.reduce_sum(alpha))
log_density = tf.reduce_sum((alpha - 1) * logx) - log_z
return log_density
def gamma_log_density(x, alpha, beta, parameterization=None):
"""Creates a TensorFlow variable representing the sum of one or more
independent inverse Gamma densities.
Args:
x (scalar or vector): variable(s) being modeled as InvGamma
alpha (scalar or vector):
beta (scalar or vector):
Each of alpha and beta must either be the same dimension
as x, or a scalar (which will be broadcast as required). They may
be TensorFlow variables or Python/numpy values.
Returns:
lp: TF scalar containing the log probability of x
"""
try:
dtype = x.dtype
except AttributeError:
try:
dtype = alpha.dtype
except AttributeError:
dtype = beta.dtype
if isinstance(beta, tf.Tensor):
log_beta = tf.log(beta)
else:
log_beta = np.log(beta)
if isinstance(x, tf.Tensor):
log_x = tf.log(x)
else:
log_x = np.log(x)
l1 = -beta * x
l2 = alpha * log_beta
l3 = (alpha - 1) * log_x
if isinstance(alpha, tf.Tensor):
l4 = gammaln(alpha)
else:
l4 = scipy.special.gammaln(alpha)
lps = l1 + l2 + l3 - l4
return lps