tf.compat.v1.distributions.Dirichlet Dirichlet distribution. Inherits From: Distribution
tf.compat.v1.distributions.Dirichlet(
    concentration, validate_args=False, allow_nan_stats=True,
    name='Dirichlet'
)
 The Dirichlet distribution is defined over the (k-1)-simplex using a positive, length-k vector concentration (k > 1). The Dirichlet is identically the Beta distribution when k = 2. Mathematical Details The Dirichlet is a distribution over the open (k-1)-simplex, i.e., S^{k-1} = { (x_0, ..., x_{k-1}) in R^k : sum_j x_j = 1 and all_j x_j > 0 }.
 The probability density function (pdf) is, pdf(x; alpha) = prod_j x_j**(alpha_j - 1) / Z
Z = prod_j Gamma(alpha_j) / Gamma(sum_j alpha_j)
 where:
x in S^{k-1}, i.e., the (k-1)-simplex,
concentration = alpha = [alpha_0, ..., alpha_{k-1}], alpha_j > 0,
Z is the normalization constant aka the multivariate beta function, and,
Gamma is the gamma function.  The concentration represents mean total counts of class occurrence, i.e., concentration = alpha = mean * total_concentration
 where mean in S^{k-1} and total_concentration is a positive real number representing a mean total count. Distribution parameters are automatically broadcast in all functions; see examples for details. Warning: Some components of the samples can be zero due to finite precision. This happens more often when some of the concentrations are very small. Make sure to round the samples to np.finfo(dtype).tiny before computing the density. Samples of this distribution are reparameterized (pathwise differentiable). The derivatives are computed using the approach described in (Figurnov et al., 2018). Examples import tensorflow_probability as tfp
tfd = tfp.distributions

# Create a single trivariate Dirichlet, with the 3rd class being three times
# more frequent than the first. I.e., batch_shape=[], event_shape=[3].
alpha = [1., 2, 3]
dist = tfd.Dirichlet(alpha)

dist.sample([4, 5])  # shape: [4, 5, 3]

# x has one sample, one batch, three classes:
x = [.2, .3, .5]   # shape: [3]
dist.prob(x)       # shape: []

# x has two samples from one batch:
x = [[.1, .4, .5],
     [.2, .3, .5]]
dist.prob(x)         # shape: [2]

# alpha will be broadcast to shape [5, 7, 3] to match x.
x = [[...]]   # shape: [5, 7, 3]
dist.prob(x)  # shape: [5, 7]

# Create batch_shape=[2], event_shape=[3]:
alpha = [[1., 2, 3],
         [4, 5, 6]]   # shape: [2, 3]
dist = tfd.Dirichlet(alpha)

dist.sample([4, 5])  # shape: [4, 5, 2, 3]

x = [.2, .3, .5]
# x will be broadcast as [[.2, .3, .5],
#                         [.2, .3, .5]],
# thus matching batch_shape [2, 3].
dist.prob(x)         # shape: [2]
 Compute the gradients of samples w.r.t. the parameters: alpha = tf.constant([1.0, 2.0, 3.0])
dist = tfd.Dirichlet(alpha)
samples = dist.sample(5)  # Shape [5, 3]
loss = tf.reduce_mean(tf.square(samples))  # Arbitrary loss function
# Unbiased stochastic gradients of the loss function
grads = tf.gradients(loss, alpha)
 References: Implicit Reparameterization Gradients: Figurnov et al., 2018 (pdf)

 Args
  concentration   Positive floating-point Tensor indicating mean number of class occurrences; aka "alpha". Implies self.dtype, and self.batch_shape, self.event_shape, i.e., if concentration.shape = [N1, N2, ..., Nm, k] then batch_shape = [N1, N2, ..., Nm] and event_shape = [k].
  validate_args   Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
  allow_nan_stats   Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value "NaN" to indicate the result is undefined. When False, an exception is raised if one or more of the statistic's batch members are undefined.
  name   Python str name prefixed to Ops created by this class.

 Attributes
  allow_nan_stats   Python bool describing behavior when a stat is undefined. Stats return +/- infinity when it makes sense. E.g., the variance of a Cauchy distribution is infinity. However, sometimes the statistic is undefined, e.g., if a distribution's pdf does not achieve a maximum within the support of the distribution, the mode is undefined. If the mean is undefined, then by definition the variance is undefined. E.g. the mean for Student's T for df = 1 is undefined (no clear way to say it is either + or - infinity), so the variance = E[(X - mean)**2] is also undefined.

  batch_shape   Shape of a single sample from a single event index as a TensorShape. May be partially defined or unknown. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.

  concentration   Concentration parameter; expected counts for that coordinate.
  dtype   The DType of Tensors handled by this Distribution.
  event_shape   Shape of a single sample from a single batch as a TensorShape. May be partially defined or unknown.

  name   Name prepended to all ops created by this Distribution.
  parameters   Dictionary of parameters used to instantiate this Distribution.
  reparameterization_type   Describes how samples from the distribution are reparameterized. Currently this is one of the static instances distributions.FULLY_REPARAMETERIZED or distributions.NOT_REPARAMETERIZED.

  total_concentration   Sum of last dim of concentration parameter.
  validate_args   Python bool indicating possibly expensive checks are enabled.    Methods batch_shape_tensor View source
batch_shape_tensor(
    name='batch_shape_tensor'
)
 Shape of a single sample from a single event index as a 1-D Tensor. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.

 Args
  name   name to give to the op

 Returns
  batch_shape   Tensor.    cdf View source
cdf(
    value, name='cdf'
)
 Cumulative distribution function. Given random variable X, the cumulative distribution function cdf is: cdf(x) := P[X <= x]

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  cdf   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    copy View source
copy(
    **override_parameters_kwargs
)
 Creates a deep copy of the distribution.
Note: the copy distribution may continue to depend on the original initialization arguments.

 Args
  **override_parameters_kwargs   String/value dictionary of initialization arguments to override with new values.

 Returns
  distribution   A new instance of type(self) initialized from the union of self.parameters and override_parameters_kwargs, i.e., dict(self.parameters, **override_parameters_kwargs).    covariance View source
covariance(
    name='covariance'
)
 Covariance. Covariance is (possibly) defined only for non-scalar-event distributions. For example, for a length-k, vector-valued distribution, it is calculated as, Cov[i, j] = Covariance(X_i, X_j) = E[(X_i - E[X_i]) (X_j - E[X_j])]
 where Cov is a (batch of) k x k matrix, 0 <= (i, j) < k, and E denotes expectation. Alternatively, for non-vector, multivariate distributions (e.g., matrix-valued, Wishart), Covariance shall return a (batch of) matrices under some vectorization of the events, i.e., Cov[i, j] = Covariance(Vec(X)_i, Vec(X)_j) = [as above]
 where Cov is a (batch of) k' x k' matrices, 0 <= (i, j) < k' = reduce_prod(event_shape), and Vec is some function mapping indices of this distribution's event dimensions to indices of a length-k' vector.

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  covariance   Floating-point Tensor with shape [B1, ..., Bn, k', k'] where the first n dimensions are batch coordinates and k' = reduce_prod(self.event_shape).    cross_entropy View source
cross_entropy(
    other, name='cross_entropy'
)
 Computes the (Shannon) cross entropy. Denote this distribution (self) by P and the other distribution by Q. Assuming P, Q are absolutely continuous with respect to one another and permit densities p(x) dr(x) and q(x) dr(x), (Shanon) cross entropy is defined as: H[P, Q] = E_p[-log q(X)] = -int_F p(x) log q(x) dr(x)
 where F denotes the support of the random variable X ~ P.

 Args
  other   tfp.distributions.Distribution instance.
  name   Python str prepended to names of ops created by this function.

 Returns
  cross_entropy   self.dtype Tensor with shape [B1, ..., Bn] representing n different calculations of (Shanon) cross entropy.    entropy View source
entropy(
    name='entropy'
)
 Shannon entropy in nats. event_shape_tensor View source
event_shape_tensor(
    name='event_shape_tensor'
)
 Shape of a single sample from a single batch as a 1-D int32 Tensor.

 Args
  name   name to give to the op

 Returns
  event_shape   Tensor.    is_scalar_batch View source
is_scalar_batch(
    name='is_scalar_batch'
)
 Indicates that batch_shape == [].

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  is_scalar_batch   bool scalar Tensor.    is_scalar_event View source
is_scalar_event(
    name='is_scalar_event'
)
 Indicates that event_shape == [].

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  is_scalar_event   bool scalar Tensor.    kl_divergence View source
kl_divergence(
    other, name='kl_divergence'
)
 Computes the Kullback--Leibler divergence. Denote this distribution (self) by p and the other distribution by q. Assuming p, q are absolutely continuous with respect to reference measure r, the KL divergence is defined as: KL[p, q] = E_p[log(p(X)/q(X))]
         = -int_F p(x) log q(x) dr(x) + int_F p(x) log p(x) dr(x)
         = H[p, q] - H[p]
 where F denotes the support of the random variable X ~ p, H[., .] denotes (Shanon) cross entropy, and H[.] denotes (Shanon) entropy.

 Args
  other   tfp.distributions.Distribution instance.
  name   Python str prepended to names of ops created by this function.

 Returns
  kl_divergence   self.dtype Tensor with shape [B1, ..., Bn] representing n different calculations of the Kullback-Leibler divergence.    log_cdf View source
log_cdf(
    value, name='log_cdf'
)
 Log cumulative distribution function. Given random variable X, the cumulative distribution function cdf is: log_cdf(x) := Log[ P[X <= x] ]
 Often, a numerical approximation can be used for log_cdf(x) that yields a more accurate answer than simply taking the logarithm of the cdf when x << -1.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  logcdf   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    log_prob View source
log_prob(
    value, name='log_prob'
)
 Log probability density/mass function. Additional documentation from Dirichlet:
Note: value must be a non-negative tensor with dtype self.dtype and be in the (self.event_shape() - 1)-simplex, i.e., tf.reduce_sum(value, -1) = 1. It must have a shape compatible with self.batch_shape() + self.event_shape().

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  log_prob   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    log_survival_function View source
log_survival_function(
    value, name='log_survival_function'
)
 Log survival function. Given random variable X, the survival function is defined: log_survival_function(x) = Log[ P[X > x] ]
                         = Log[ 1 - P[X <= x] ]
                         = Log[ 1 - cdf(x) ]
 Typically, different numerical approximations can be used for the log survival function, which are more accurate than 1 - cdf(x) when x >> 1.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns   Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.
 mean View source
mean(
    name='mean'
)
 Mean. mode View source
mode(
    name='mode'
)
 Mode. Additional documentation from Dirichlet:
Note: The mode is undefined when any concentration <= 1. If self.allow_nan_stats is True, NaN is used for undefined modes. If self.allow_nan_stats is False an exception is raised when one or more modes are undefined.
 param_shapes View source
@classmethod
param_shapes(
    sample_shape, name='DistributionParamShapes'
)
 Shapes of parameters given the desired shape of a call to sample(). This is a class method that describes what key/value arguments are required to instantiate the given Distribution so that a particular shape is returned for that instance's call to sample(). Subclasses should override class method _param_shapes.

 Args
  sample_shape   Tensor or python list/tuple. Desired shape of a call to sample().
  name   name to prepend ops with.

 Returns   dict of parameter name to Tensor shapes.
 param_static_shapes View source
@classmethod
param_static_shapes(
    sample_shape
)
 param_shapes with static (i.e. TensorShape) shapes. This is a class method that describes what key/value arguments are required to instantiate the given Distribution so that a particular shape is returned for that instance's call to sample(). Assumes that the sample's shape is known statically. Subclasses should override class method _param_shapes to return constant-valued tensors when constant values are fed.

 Args
  sample_shape   TensorShape or python list/tuple. Desired shape of a call to sample().

 Returns   dict of parameter name to TensorShape.

 Raises
  ValueError   if sample_shape is a TensorShape and is not fully defined.    prob View source
prob(
    value, name='prob'
)
 Probability density/mass function. Additional documentation from Dirichlet:
Note: value must be a non-negative tensor with dtype self.dtype and be in the (self.event_shape() - 1)-simplex, i.e., tf.reduce_sum(value, -1) = 1. It must have a shape compatible with self.batch_shape() + self.event_shape().

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  prob   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    quantile View source
quantile(
    value, name='quantile'
)
 Quantile function. Aka "inverse cdf" or "percent point function". Given random variable X and p in [0, 1], the quantile is: quantile(p) := x such that P[X <= x] == p

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  quantile   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    sample View source
sample(
    sample_shape=(), seed=None, name='sample'
)
 Generate samples of the specified shape. Note that a call to sample() without arguments will generate a single sample.

 Args
  sample_shape   0D or 1D int32 Tensor. Shape of the generated samples.
  seed   Python integer seed for RNG
  name   name to give to the op.

 Returns
  samples   a Tensor with prepended dimensions sample_shape.    stddev View source
stddev(
    name='stddev'
)
 Standard deviation. Standard deviation is defined as, stddev = E[(X - E[X])**2]**0.5
 where X is the random variable associated with this distribution, E denotes expectation, and stddev.shape = batch_shape + event_shape.

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  stddev   Floating-point Tensor with shape identical to batch_shape + event_shape, i.e., the same shape as self.mean().    survival_function View source
survival_function(
    value, name='survival_function'
)
 Survival function. Given random variable X, the survival function is defined: survival_function(x) = P[X > x]
                     = 1 - P[X <= x]
                     = 1 - cdf(x).

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns   Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.
 variance View source
variance(
    name='variance'
)
 Variance. Variance is defined as, Var = E[(X - E[X])**2]
 where X is the random variable associated with this distribution, E denotes expectation, and Var.shape = batch_shape + event_shape.

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  variance   Floating-point Tensor with shape identical to batch_shape + event_shape, i.e., the same shape as self.mean().


tf.compat.v1.distributions.DirichletMultinomial Dirichlet-Multinomial compound distribution. Inherits From: Distribution
tf.compat.v1.distributions.DirichletMultinomial(
    total_count, concentration, validate_args=False, allow_nan_stats=True,
    name='DirichletMultinomial'
)
 The Dirichlet-Multinomial distribution is parameterized by a (batch of) length-K concentration vectors (K > 1) and a total_count number of trials, i.e., the number of trials per draw from the DirichletMultinomial. It is defined over a (batch of) length-K vector counts such that tf.reduce_sum(counts, -1) = total_count. The Dirichlet-Multinomial is identically the Beta-Binomial distribution when K = 2. Mathematical Details The Dirichlet-Multinomial is a distribution over K-class counts, i.e., a length-K vector of non-negative integer counts = n = [n_0, ..., n_{K-1}]. The probability mass function (pmf) is, pmf(n; alpha, N) = Beta(alpha + n) / (prod_j n_j!) / Z
Z = Beta(alpha) / N!
 where:
concentration = alpha = [alpha_0, ..., alpha_{K-1}], alpha_j > 0,
total_count = N, N a positive integer,
N! is N factorial, and,
Beta(x) = prod_j Gamma(x_j) / Gamma(sum_j x_j) is the multivariate beta function, and,
Gamma is the gamma function.  Dirichlet-Multinomial is a compound distribution, i.e., its samples are generated as follows.  Choose class probabilities: probs = [p_0,...,p_{K-1}] ~ Dir(concentration)
 Draw integers: counts = [n_0,...,n_{K-1}] ~ Multinomial(total_count, probs)
  The last concentration dimension parametrizes a single Dirichlet-Multinomial distribution. When calling distribution functions (e.g., dist.prob(counts)), concentration, total_count and counts are broadcast to the same shape. The last dimension of counts corresponds single Dirichlet-Multinomial distributions. Distribution parameters are automatically broadcast in all functions; see examples for details. Pitfalls The number of classes, K, must not exceed:  the largest integer representable by self.dtype, i.e., 2**(mantissa_bits+1) (IEE754), the maximum Tensor index, i.e., 2**31-1.  In other words, K <= min(2**31-1, {
  tf.float16: 2**11,
  tf.float32: 2**24,
  tf.float64: 2**53 }[param.dtype])

Note: This condition is validated only when self.validate_args = True.
 Examples alpha = [1., 2., 3.]
n = 2.
dist = DirichletMultinomial(n, alpha)
 Creates a 3-class distribution, with the 3rd class is most likely to be drawn. The distribution functions can be evaluated on counts. # counts same shape as alpha.
counts = [0., 0., 2.]
dist.prob(counts)  # Shape []

# alpha will be broadcast to [[1., 2., 3.], [1., 2., 3.]] to match counts.
counts = [[1., 1., 0.], [1., 0., 1.]]
dist.prob(counts)  # Shape [2]

# alpha will be broadcast to shape [5, 7, 3] to match counts.
counts = [[...]]  # Shape [5, 7, 3]
dist.prob(counts)  # Shape [5, 7]
 Creates a 2-batch of 3-class distributions. alpha = [[1., 2., 3.], [4., 5., 6.]]  # Shape [2, 3]
n = [3., 3.]
dist = DirichletMultinomial(n, alpha)

# counts will be broadcast to [[2., 1., 0.], [2., 1., 0.]] to match alpha.
counts = [2., 1., 0.]
dist.prob(counts)  # Shape [2]

 Args
  total_count   Non-negative floating point tensor, whose dtype is the same as concentration. The shape is broadcastable to [N1,..., Nm] with m >= 0. Defines this as a batch of N1 x ... x Nm different Dirichlet multinomial distributions. Its components should be equal to integer values.
  concentration   Positive floating point tensor, whose dtype is the same as n with shape broadcastable to [N1,..., Nm, K] m >= 0. Defines this as a batch of N1 x ... x Nm different K class Dirichlet multinomial distributions.
  validate_args   Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
  allow_nan_stats   Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value "NaN" to indicate the result is undefined. When False, an exception is raised if one or more of the statistic's batch members are undefined.
  name   Python str name prefixed to Ops created by this class.

 Attributes
  allow_nan_stats   Python bool describing behavior when a stat is undefined. Stats return +/- infinity when it makes sense. E.g., the variance of a Cauchy distribution is infinity. However, sometimes the statistic is undefined, e.g., if a distribution's pdf does not achieve a maximum within the support of the distribution, the mode is undefined. If the mean is undefined, then by definition the variance is undefined. E.g. the mean for Student's T for df = 1 is undefined (no clear way to say it is either + or - infinity), so the variance = E[(X - mean)**2] is also undefined.

  batch_shape   Shape of a single sample from a single event index as a TensorShape. May be partially defined or unknown. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.

  concentration   Concentration parameter; expected prior counts for that coordinate.
  dtype   The DType of Tensors handled by this Distribution.
  event_shape   Shape of a single sample from a single batch as a TensorShape. May be partially defined or unknown.

  name   Name prepended to all ops created by this Distribution.
  parameters   Dictionary of parameters used to instantiate this Distribution.
  reparameterization_type   Describes how samples from the distribution are reparameterized. Currently this is one of the static instances distributions.FULLY_REPARAMETERIZED or distributions.NOT_REPARAMETERIZED.

  total_concentration   Sum of last dim of concentration parameter.
  total_count   Number of trials used to construct a sample.
  validate_args   Python bool indicating possibly expensive checks are enabled.    Methods batch_shape_tensor View source
batch_shape_tensor(
    name='batch_shape_tensor'
)
 Shape of a single sample from a single event index as a 1-D Tensor. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.

 Args
  name   name to give to the op

 Returns
  batch_shape   Tensor.    cdf View source
cdf(
    value, name='cdf'
)
 Cumulative distribution function. Given random variable X, the cumulative distribution function cdf is: cdf(x) := P[X <= x]

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  cdf   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    copy View source
copy(
    **override_parameters_kwargs
)
 Creates a deep copy of the distribution.
Note: the copy distribution may continue to depend on the original initialization arguments.

 Args
  **override_parameters_kwargs   String/value dictionary of initialization arguments to override with new values.

 Returns
  distribution   A new instance of type(self) initialized from the union of self.parameters and override_parameters_kwargs, i.e., dict(self.parameters, **override_parameters_kwargs).    covariance View source
covariance(
    name='covariance'
)
 Covariance. Covariance is (possibly) defined only for non-scalar-event distributions. For example, for a length-k, vector-valued distribution, it is calculated as, Cov[i, j] = Covariance(X_i, X_j) = E[(X_i - E[X_i]) (X_j - E[X_j])]
 where Cov is a (batch of) k x k matrix, 0 <= (i, j) < k, and E denotes expectation. Alternatively, for non-vector, multivariate distributions (e.g., matrix-valued, Wishart), Covariance shall return a (batch of) matrices under some vectorization of the events, i.e., Cov[i, j] = Covariance(Vec(X)_i, Vec(X)_j) = [as above]
 where Cov is a (batch of) k' x k' matrices, 0 <= (i, j) < k' = reduce_prod(event_shape), and Vec is some function mapping indices of this distribution's event dimensions to indices of a length-k' vector. Additional documentation from DirichletMultinomial: The covariance for each batch member is defined as the following: Var(X_j) = n * alpha_j / alpha_0 * (1 - alpha_j / alpha_0) *
(n + alpha_0) / (1 + alpha_0)
 where concentration = alpha and total_concentration = alpha_0 = sum_j alpha_j. The covariance between elements in a batch is defined as: Cov(X_i, X_j) = -n * alpha_i * alpha_j / alpha_0 ** 2 *
(n + alpha_0) / (1 + alpha_0)

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  covariance   Floating-point Tensor with shape [B1, ..., Bn, k', k'] where the first n dimensions are batch coordinates and k' = reduce_prod(self.event_shape).    cross_entropy View source
cross_entropy(
    other, name='cross_entropy'
)
 Computes the (Shannon) cross entropy. Denote this distribution (self) by P and the other distribution by Q. Assuming P, Q are absolutely continuous with respect to one another and permit densities p(x) dr(x) and q(x) dr(x), (Shanon) cross entropy is defined as: H[P, Q] = E_p[-log q(X)] = -int_F p(x) log q(x) dr(x)
 where F denotes the support of the random variable X ~ P.

 Args
  other   tfp.distributions.Distribution instance.
  name   Python str prepended to names of ops created by this function.

 Returns
  cross_entropy   self.dtype Tensor with shape [B1, ..., Bn] representing n different calculations of (Shanon) cross entropy.    entropy View source
entropy(
    name='entropy'
)
 Shannon entropy in nats. event_shape_tensor View source
event_shape_tensor(
    name='event_shape_tensor'
)
 Shape of a single sample from a single batch as a 1-D int32 Tensor.

 Args
  name   name to give to the op

 Returns
  event_shape   Tensor.    is_scalar_batch View source
is_scalar_batch(
    name='is_scalar_batch'
)
 Indicates that batch_shape == [].

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  is_scalar_batch   bool scalar Tensor.    is_scalar_event View source
is_scalar_event(
    name='is_scalar_event'
)
 Indicates that event_shape == [].

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  is_scalar_event   bool scalar Tensor.    kl_divergence View source
kl_divergence(
    other, name='kl_divergence'
)
 Computes the Kullback--Leibler divergence. Denote this distribution (self) by p and the other distribution by q. Assuming p, q are absolutely continuous with respect to reference measure r, the KL divergence is defined as: KL[p, q] = E_p[log(p(X)/q(X))]
         = -int_F p(x) log q(x) dr(x) + int_F p(x) log p(x) dr(x)
         = H[p, q] - H[p]
 where F denotes the support of the random variable X ~ p, H[., .] denotes (Shanon) cross entropy, and H[.] denotes (Shanon) entropy.

 Args
  other   tfp.distributions.Distribution instance.
  name   Python str prepended to names of ops created by this function.

 Returns
  kl_divergence   self.dtype Tensor with shape [B1, ..., Bn] representing n different calculations of the Kullback-Leibler divergence.    log_cdf View source
log_cdf(
    value, name='log_cdf'
)
 Log cumulative distribution function. Given random variable X, the cumulative distribution function cdf is: log_cdf(x) := Log[ P[X <= x] ]
 Often, a numerical approximation can be used for log_cdf(x) that yields a more accurate answer than simply taking the logarithm of the cdf when x << -1.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  logcdf   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    log_prob View source
log_prob(
    value, name='log_prob'
)
 Log probability density/mass function. Additional documentation from DirichletMultinomial: For each batch of counts, value = [n_0, ..., n_{K-1}], P[value] is the probability that after sampling self.total_count draws from this Dirichlet-Multinomial distribution, the number of draws falling in class j is n_j. Since this definition is exchangeable; different sequences have the same counts so the probability includes a combinatorial coefficient.
Note: value must be a non-negative tensor with dtype self.dtype, have no fractional components, and such that tf.reduce_sum(value, -1) = self.total_count. Its shape must be broadcastable with self.concentration and self.total_count.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  log_prob   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    log_survival_function View source
log_survival_function(
    value, name='log_survival_function'
)
 Log survival function. Given random variable X, the survival function is defined: log_survival_function(x) = Log[ P[X > x] ]
                         = Log[ 1 - P[X <= x] ]
                         = Log[ 1 - cdf(x) ]
 Typically, different numerical approximations can be used for the log survival function, which are more accurate than 1 - cdf(x) when x >> 1.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns   Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.
 mean View source
mean(
    name='mean'
)
 Mean. mode View source
mode(
    name='mode'
)
 Mode. param_shapes View source
@classmethod
param_shapes(
    sample_shape, name='DistributionParamShapes'
)
 Shapes of parameters given the desired shape of a call to sample(). This is a class method that describes what key/value arguments are required to instantiate the given Distribution so that a particular shape is returned for that instance's call to sample(). Subclasses should override class method _param_shapes.

 Args
  sample_shape   Tensor or python list/tuple. Desired shape of a call to sample().
  name   name to prepend ops with.

 Returns   dict of parameter name to Tensor shapes.
 param_static_shapes View source
@classmethod
param_static_shapes(
    sample_shape
)
 param_shapes with static (i.e. TensorShape) shapes. This is a class method that describes what key/value arguments are required to instantiate the given Distribution so that a particular shape is returned for that instance's call to sample(). Assumes that the sample's shape is known statically. Subclasses should override class method _param_shapes to return constant-valued tensors when constant values are fed.

 Args
  sample_shape   TensorShape or python list/tuple. Desired shape of a call to sample().

 Returns   dict of parameter name to TensorShape.

 Raises
  ValueError   if sample_shape is a TensorShape and is not fully defined.    prob View source
prob(
    value, name='prob'
)
 Probability density/mass function. Additional documentation from DirichletMultinomial: For each batch of counts, value = [n_0, ..., n_{K-1}], P[value] is the probability that after sampling self.total_count draws from this Dirichlet-Multinomial distribution, the number of draws falling in class j is n_j. Since this definition is exchangeable; different sequences have the same counts so the probability includes a combinatorial coefficient.
Note: value must be a non-negative tensor with dtype self.dtype, have no fractional components, and such that tf.reduce_sum(value, -1) = self.total_count. Its shape must be broadcastable with self.concentration and self.total_count.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  prob   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    quantile View source
quantile(
    value, name='quantile'
)
 Quantile function. Aka "inverse cdf" or "percent point function". Given random variable X and p in [0, 1], the quantile is: quantile(p) := x such that P[X <= x] == p

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  quantile   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    sample View source
sample(
    sample_shape=(), seed=None, name='sample'
)
 Generate samples of the specified shape. Note that a call to sample() without arguments will generate a single sample.

 Args
  sample_shape   0D or 1D int32 Tensor. Shape of the generated samples.
  seed   Python integer seed for RNG
  name   name to give to the op.

 Returns
  samples   a Tensor with prepended dimensions sample_shape.    stddev View source
stddev(
    name='stddev'
)
 Standard deviation. Standard deviation is defined as, stddev = E[(X - E[X])**2]**0.5
 where X is the random variable associated with this distribution, E denotes expectation, and stddev.shape = batch_shape + event_shape.

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  stddev   Floating-point Tensor with shape identical to batch_shape + event_shape, i.e., the same shape as self.mean().    survival_function View source
survival_function(
    value, name='survival_function'
)
 Survival function. Given random variable X, the survival function is defined: survival_function(x) = P[X > x]
                     = 1 - P[X <= x]
                     = 1 - cdf(x).

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns   Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.
 variance View source
variance(
    name='variance'
)
 Variance. Variance is defined as, Var = E[(X - E[X])**2]
 where X is the random variable associated with this distribution, E denotes expectation, and Var.shape = batch_shape + event_shape.

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  variance   Floating-point Tensor with shape identical to batch_shape + event_shape, i.e., the same shape as self.mean().


tf.compat.v1.distributions.Distribution A generic probability distribution base class.
tf.compat.v1.distributions.Distribution(
    dtype, reparameterization_type, validate_args, allow_nan_stats, parameters=None,
    graph_parents=None, name=None
)
 Distribution is a base class for constructing and organizing properties (e.g., mean, variance) of random variables (e.g, Bernoulli, Gaussian). Subclassing Subclasses are expected to implement a leading-underscore version of the same-named function. The argument signature should be identical except for the omission of name="...". For example, to enable log_prob(value, name="log_prob") a subclass should implement _log_prob(value). Subclasses can append to public-level docstrings by providing docstrings for their method specializations. For example: @util.AppendDocstring("Some other details.")
def _log_prob(self, value):
  ...
 would add the string "Some other details." to the log_prob function docstring. This is implemented as a simple decorator to avoid python linter complaining about missing Args/Returns/Raises sections in the partial docstrings. Broadcasting, batching, and shapes All distributions support batches of independent distributions of that type. The batch shape is determined by broadcasting together the parameters. The shape of arguments to __init__, cdf, log_cdf, prob, and log_prob reflect this broadcasting, as does the return value of sample and sample_n. sample_n_shape = [n] + batch_shape + event_shape, where sample_n_shape is the shape of the Tensor returned from sample_n, n is the number of samples, batch_shape defines how many independent distributions there are, and event_shape defines the shape of samples from each of those independent distributions. Samples are independent along the batch_shape dimensions, but not necessarily so along the event_shape dimensions (depending on the particulars of the underlying distribution). Using the Uniform distribution as an example: minval = 3.0
maxval = [[4.0, 6.0],
          [10.0, 12.0]]

# Broadcasting:
# This instance represents 4 Uniform distributions. Each has a lower bound at
# 3.0 as the `minval` parameter was broadcasted to match `maxval`'s shape.
u = Uniform(minval, maxval)

# `event_shape` is `TensorShape([])`.
event_shape = u.event_shape
# `event_shape_t` is a `Tensor` which will evaluate to [].
event_shape_t = u.event_shape_tensor()

# Sampling returns a sample per distribution. `samples` has shape
# [5, 2, 2], which is [n] + batch_shape + event_shape, where n=5,
# batch_shape=[2, 2], and event_shape=[].
samples = u.sample_n(5)

# The broadcasting holds across methods. Here we use `cdf` as an example. The
# same holds for `log_cdf` and the likelihood functions.

# `cum_prob` has shape [2, 2] as the `value` argument was broadcasted to the
# shape of the `Uniform` instance.
cum_prob_broadcast = u.cdf(4.0)

# `cum_prob`'s shape is [2, 2], one per distribution. No broadcasting
# occurred.
cum_prob_per_dist = u.cdf([[4.0, 5.0],
                           [6.0, 7.0]])

# INVALID as the `value` argument is not broadcastable to the distribution's
# shape.
cum_prob_invalid = u.cdf([4.0, 5.0, 6.0])
 Shapes There are three important concepts associated with TensorFlow Distributions shapes:  Event shape describes the shape of a single draw from the distribution; it may be dependent across dimensions. For scalar distributions, the event shape is []. For a 5-dimensional MultivariateNormal, the event shape is [5]. Batch shape describes independent, not identically distributed draws, aka a "collection" or "bunch" of distributions. Sample shape describes independent, identically distributed draws of batches from the distribution family.  The event shape and the batch shape are properties of a Distribution object, whereas the sample shape is associated with a specific call to sample or log_prob. For detailed usage examples of TensorFlow Distributions shapes, see this tutorial Parameter values leading to undefined statistics or distributions. Some distributions do not have well-defined statistics for all initialization parameter values. For example, the beta distribution is parameterized by positive real numbers concentration1 and concentration0, and does not have well-defined mode if concentration1 < 1 or concentration0 < 1. The user is given the option of raising an exception or returning NaN. a = tf.exp(tf.matmul(logits, weights_a))
b = tf.exp(tf.matmul(logits, weights_b))

# Will raise exception if ANY batch member has a < 1 or b < 1.
dist = distributions.beta(a, b, allow_nan_stats=False)
mode = dist.mode().eval()

# Will return NaN for batch members with either a < 1 or b < 1.
dist = distributions.beta(a, b, allow_nan_stats=True)  # Default behavior
mode = dist.mode().eval()
 In all cases, an exception is raised if invalid parameters are passed, e.g. # Will raise an exception if any Op is run.
negative_a = -1.0 * a  # beta distribution by definition has a > 0.
dist = distributions.beta(negative_a, b, allow_nan_stats=True)
dist.mean().eval()

 Args
  dtype   The type of the event samples. None implies no type-enforcement.
  reparameterization_type   Instance of ReparameterizationType. If distributions.FULLY_REPARAMETERIZED, this Distribution can be reparameterized in terms of some standard distribution with a function whose Jacobian is constant for the support of the standard distribution. If distributions.NOT_REPARAMETERIZED, then no such reparameterization is available.
  validate_args   Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
  allow_nan_stats   Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value "NaN" to indicate the result is undefined. When False, an exception is raised if one or more of the statistic's batch members are undefined.
  parameters   Python dict of parameters used to instantiate this Distribution.
  graph_parents   Python list of graph prerequisites of this Distribution.
  name   Python str name prefixed to Ops created by this class. Default: subclass name.

 Raises
  ValueError   if any member of graph_parents is None or not a Tensor.

 Attributes
  allow_nan_stats   Python bool describing behavior when a stat is undefined. Stats return +/- infinity when it makes sense. E.g., the variance of a Cauchy distribution is infinity. However, sometimes the statistic is undefined, e.g., if a distribution's pdf does not achieve a maximum within the support of the distribution, the mode is undefined. If the mean is undefined, then by definition the variance is undefined. E.g. the mean for Student's T for df = 1 is undefined (no clear way to say it is either + or - infinity), so the variance = E[(X - mean)**2] is also undefined.

  batch_shape   Shape of a single sample from a single event index as a TensorShape. May be partially defined or unknown. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.

  dtype   The DType of Tensors handled by this Distribution.
  event_shape   Shape of a single sample from a single batch as a TensorShape. May be partially defined or unknown.

  name   Name prepended to all ops created by this Distribution.
  parameters   Dictionary of parameters used to instantiate this Distribution.
  reparameterization_type   Describes how samples from the distribution are reparameterized. Currently this is one of the static instances distributions.FULLY_REPARAMETERIZED or distributions.NOT_REPARAMETERIZED.

  validate_args   Python bool indicating possibly expensive checks are enabled.    Methods batch_shape_tensor View source
batch_shape_tensor(
    name='batch_shape_tensor'
)
 Shape of a single sample from a single event index as a 1-D Tensor. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.

 Args
  name   name to give to the op

 Returns
  batch_shape   Tensor.    cdf View source
cdf(
    value, name='cdf'
)
 Cumulative distribution function. Given random variable X, the cumulative distribution function cdf is: cdf(x) := P[X <= x]

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  cdf   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    copy View source
copy(
    **override_parameters_kwargs
)
 Creates a deep copy of the distribution.
Note: the copy distribution may continue to depend on the original initialization arguments.

 Args
  **override_parameters_kwargs   String/value dictionary of initialization arguments to override with new values.

 Returns
  distribution   A new instance of type(self) initialized from the union of self.parameters and override_parameters_kwargs, i.e., dict(self.parameters, **override_parameters_kwargs).    covariance View source
covariance(
    name='covariance'
)
 Covariance. Covariance is (possibly) defined only for non-scalar-event distributions. For example, for a length-k, vector-valued distribution, it is calculated as, Cov[i, j] = Covariance(X_i, X_j) = E[(X_i - E[X_i]) (X_j - E[X_j])]
 where Cov is a (batch of) k x k matrix, 0 <= (i, j) < k, and E denotes expectation. Alternatively, for non-vector, multivariate distributions (e.g., matrix-valued, Wishart), Covariance shall return a (batch of) matrices under some vectorization of the events, i.e., Cov[i, j] = Covariance(Vec(X)_i, Vec(X)_j) = [as above]
 where Cov is a (batch of) k' x k' matrices, 0 <= (i, j) < k' = reduce_prod(event_shape), and Vec is some function mapping indices of this distribution's event dimensions to indices of a length-k' vector.

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  covariance   Floating-point Tensor with shape [B1, ..., Bn, k', k'] where the first n dimensions are batch coordinates and k' = reduce_prod(self.event_shape).    cross_entropy View source
cross_entropy(
    other, name='cross_entropy'
)
 Computes the (Shannon) cross entropy. Denote this distribution (self) by P and the other distribution by Q. Assuming P, Q are absolutely continuous with respect to one another and permit densities p(x) dr(x) and q(x) dr(x), (Shanon) cross entropy is defined as: H[P, Q] = E_p[-log q(X)] = -int_F p(x) log q(x) dr(x)
 where F denotes the support of the random variable X ~ P.

 Args
  other   tfp.distributions.Distribution instance.
  name   Python str prepended to names of ops created by this function.

 Returns
  cross_entropy   self.dtype Tensor with shape [B1, ..., Bn] representing n different calculations of (Shanon) cross entropy.    entropy View source
entropy(
    name='entropy'
)
 Shannon entropy in nats. event_shape_tensor View source
event_shape_tensor(
    name='event_shape_tensor'
)
 Shape of a single sample from a single batch as a 1-D int32 Tensor.

 Args
  name   name to give to the op

 Returns
  event_shape   Tensor.    is_scalar_batch View source
is_scalar_batch(
    name='is_scalar_batch'
)
 Indicates that batch_shape == [].

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  is_scalar_batch   bool scalar Tensor.    is_scalar_event View source
is_scalar_event(
    name='is_scalar_event'
)
 Indicates that event_shape == [].

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  is_scalar_event   bool scalar Tensor.    kl_divergence View source
kl_divergence(
    other, name='kl_divergence'
)
 Computes the Kullback--Leibler divergence. Denote this distribution (self) by p and the other distribution by q. Assuming p, q are absolutely continuous with respect to reference measure r, the KL divergence is defined as: KL[p, q] = E_p[log(p(X)/q(X))]
         = -int_F p(x) log q(x) dr(x) + int_F p(x) log p(x) dr(x)
         = H[p, q] - H[p]
 where F denotes the support of the random variable X ~ p, H[., .] denotes (Shanon) cross entropy, and H[.] denotes (Shanon) entropy.

 Args
  other   tfp.distributions.Distribution instance.
  name   Python str prepended to names of ops created by this function.

 Returns
  kl_divergence   self.dtype Tensor with shape [B1, ..., Bn] representing n different calculations of the Kullback-Leibler divergence.    log_cdf View source
log_cdf(
    value, name='log_cdf'
)
 Log cumulative distribution function. Given random variable X, the cumulative distribution function cdf is: log_cdf(x) := Log[ P[X <= x] ]
 Often, a numerical approximation can be used for log_cdf(x) that yields a more accurate answer than simply taking the logarithm of the cdf when x << -1.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  logcdf   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    log_prob View source
log_prob(
    value, name='log_prob'
)
 Log probability density/mass function.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  log_prob   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    log_survival_function View source
log_survival_function(
    value, name='log_survival_function'
)
 Log survival function. Given random variable X, the survival function is defined: log_survival_function(x) = Log[ P[X > x] ]
                         = Log[ 1 - P[X <= x] ]
                         = Log[ 1 - cdf(x) ]
 Typically, different numerical approximations can be used for the log survival function, which are more accurate than 1 - cdf(x) when x >> 1.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns   Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.
 mean View source
mean(
    name='mean'
)
 Mean. mode View source
mode(
    name='mode'
)
 Mode. param_shapes View source
@classmethod
param_shapes(
    sample_shape, name='DistributionParamShapes'
)
 Shapes of parameters given the desired shape of a call to sample(). This is a class method that describes what key/value arguments are required to instantiate the given Distribution so that a particular shape is returned for that instance's call to sample(). Subclasses should override class method _param_shapes.

 Args
  sample_shape   Tensor or python list/tuple. Desired shape of a call to sample().
  name   name to prepend ops with.

 Returns   dict of parameter name to Tensor shapes.
 param_static_shapes View source
@classmethod
param_static_shapes(
    sample_shape
)
 param_shapes with static (i.e. TensorShape) shapes. This is a class method that describes what key/value arguments are required to instantiate the given Distribution so that a particular shape is returned for that instance's call to sample(). Assumes that the sample's shape is known statically. Subclasses should override class method _param_shapes to return constant-valued tensors when constant values are fed.

 Args
  sample_shape   TensorShape or python list/tuple. Desired shape of a call to sample().

 Returns   dict of parameter name to TensorShape.

 Raises
  ValueError   if sample_shape is a TensorShape and is not fully defined.    prob View source
prob(
    value, name='prob'
)
 Probability density/mass function.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  prob   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    quantile View source
quantile(
    value, name='quantile'
)
 Quantile function. Aka "inverse cdf" or "percent point function". Given random variable X and p in [0, 1], the quantile is: quantile(p) := x such that P[X <= x] == p

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  quantile   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    sample View source
sample(
    sample_shape=(), seed=None, name='sample'
)
 Generate samples of the specified shape. Note that a call to sample() without arguments will generate a single sample.

 Args
  sample_shape   0D or 1D int32 Tensor. Shape of the generated samples.
  seed   Python integer seed for RNG
  name   name to give to the op.

 Returns
  samples   a Tensor with prepended dimensions sample_shape.    stddev View source
stddev(
    name='stddev'
)
 Standard deviation. Standard deviation is defined as, stddev = E[(X - E[X])**2]**0.5
 where X is the random variable associated with this distribution, E denotes expectation, and stddev.shape = batch_shape + event_shape.

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  stddev   Floating-point Tensor with shape identical to batch_shape + event_shape, i.e., the same shape as self.mean().    survival_function View source
survival_function(
    value, name='survival_function'
)
 Survival function. Given random variable X, the survival function is defined: survival_function(x) = P[X > x]
                     = 1 - P[X <= x]
                     = 1 - cdf(x).

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns   Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.
 variance View source
variance(
    name='variance'
)
 Variance. Variance is defined as, Var = E[(X - E[X])**2]
 where X is the random variable associated with this distribution, E denotes expectation, and Var.shape = batch_shape + event_shape.

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  variance   Floating-point Tensor with shape identical to batch_shape + event_shape, i.e., the same shape as self.mean().


tf.compat.v1.distributions.Exponential Exponential distribution. Inherits From: Gamma, Distribution
tf.compat.v1.distributions.Exponential(
    rate, validate_args=False, allow_nan_stats=True, name='Exponential'
)
 The Exponential distribution is parameterized by an event rate parameter. Mathematical Details The probability density function (pdf) is, pdf(x; lambda, x > 0) = exp(-lambda x) / Z
Z = 1 / lambda
 where rate = lambda and Z is the normalizaing constant. The Exponential distribution is a special case of the Gamma distribution, i.e., Exponential(rate) = Gamma(concentration=1., rate)
 The Exponential distribution uses a rate parameter, or "inverse scale", which can be intuited as, X ~ Exponential(rate=1)
Y = X / rate

 Args
  rate   Floating point tensor, equivalent to 1 / mean. Must contain only positive values.
  validate_args   Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
  allow_nan_stats   Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value "NaN" to indicate the result is undefined. When False, an exception is raised if one or more of the statistic's batch members are undefined.
  name   Python str name prefixed to Ops created by this class.

 Attributes
  allow_nan_stats   Python bool describing behavior when a stat is undefined. Stats return +/- infinity when it makes sense. E.g., the variance of a Cauchy distribution is infinity. However, sometimes the statistic is undefined, e.g., if a distribution's pdf does not achieve a maximum within the support of the distribution, the mode is undefined. If the mean is undefined, then by definition the variance is undefined. E.g. the mean for Student's T for df = 1 is undefined (no clear way to say it is either + or - infinity), so the variance = E[(X - mean)**2] is also undefined.

  batch_shape   Shape of a single sample from a single event index as a TensorShape. May be partially defined or unknown. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.

  concentration   Concentration parameter.
  dtype   The DType of Tensors handled by this Distribution.
  event_shape   Shape of a single sample from a single batch as a TensorShape. May be partially defined or unknown.

  name   Name prepended to all ops created by this Distribution.
  parameters   Dictionary of parameters used to instantiate this Distribution.
  rate   Rate parameter.
  reparameterization_type   Describes how samples from the distribution are reparameterized. Currently this is one of the static instances distributions.FULLY_REPARAMETERIZED or distributions.NOT_REPARAMETERIZED.

  validate_args   Python bool indicating possibly expensive checks are enabled.    Methods batch_shape_tensor View source
batch_shape_tensor(
    name='batch_shape_tensor'
)
 Shape of a single sample from a single event index as a 1-D Tensor. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.

 Args
  name   name to give to the op

 Returns
  batch_shape   Tensor.    cdf View source
cdf(
    value, name='cdf'
)
 Cumulative distribution function. Given random variable X, the cumulative distribution function cdf is: cdf(x) := P[X <= x]

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  cdf   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    copy View source
copy(
    **override_parameters_kwargs
)
 Creates a deep copy of the distribution.
Note: the copy distribution may continue to depend on the original initialization arguments.

 Args
  **override_parameters_kwargs   String/value dictionary of initialization arguments to override with new values.

 Returns
  distribution   A new instance of type(self) initialized from the union of self.parameters and override_parameters_kwargs, i.e., dict(self.parameters, **override_parameters_kwargs).    covariance View source
covariance(
    name='covariance'
)
 Covariance. Covariance is (possibly) defined only for non-scalar-event distributions. For example, for a length-k, vector-valued distribution, it is calculated as, Cov[i, j] = Covariance(X_i, X_j) = E[(X_i - E[X_i]) (X_j - E[X_j])]
 where Cov is a (batch of) k x k matrix, 0 <= (i, j) < k, and E denotes expectation. Alternatively, for non-vector, multivariate distributions (e.g., matrix-valued, Wishart), Covariance shall return a (batch of) matrices under some vectorization of the events, i.e., Cov[i, j] = Covariance(Vec(X)_i, Vec(X)_j) = [as above]
 where Cov is a (batch of) k' x k' matrices, 0 <= (i, j) < k' = reduce_prod(event_shape), and Vec is some function mapping indices of this distribution's event dimensions to indices of a length-k' vector.

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  covariance   Floating-point Tensor with shape [B1, ..., Bn, k', k'] where the first n dimensions are batch coordinates and k' = reduce_prod(self.event_shape).    cross_entropy View source
cross_entropy(
    other, name='cross_entropy'
)
 Computes the (Shannon) cross entropy. Denote this distribution (self) by P and the other distribution by Q. Assuming P, Q are absolutely continuous with respect to one another and permit densities p(x) dr(x) and q(x) dr(x), (Shanon) cross entropy is defined as: H[P, Q] = E_p[-log q(X)] = -int_F p(x) log q(x) dr(x)
 where F denotes the support of the random variable X ~ P.

 Args
  other   tfp.distributions.Distribution instance.
  name   Python str prepended to names of ops created by this function.

 Returns
  cross_entropy   self.dtype Tensor with shape [B1, ..., Bn] representing n different calculations of (Shanon) cross entropy.    entropy View source
entropy(
    name='entropy'
)
 Shannon entropy in nats. event_shape_tensor View source
event_shape_tensor(
    name='event_shape_tensor'
)
 Shape of a single sample from a single batch as a 1-D int32 Tensor.

 Args
  name   name to give to the op

 Returns
  event_shape   Tensor.    is_scalar_batch View source
is_scalar_batch(
    name='is_scalar_batch'
)
 Indicates that batch_shape == [].

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  is_scalar_batch   bool scalar Tensor.    is_scalar_event View source
is_scalar_event(
    name='is_scalar_event'
)
 Indicates that event_shape == [].

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  is_scalar_event   bool scalar Tensor.    kl_divergence View source
kl_divergence(
    other, name='kl_divergence'
)
 Computes the Kullback--Leibler divergence. Denote this distribution (self) by p and the other distribution by q. Assuming p, q are absolutely continuous with respect to reference measure r, the KL divergence is defined as: KL[p, q] = E_p[log(p(X)/q(X))]
         = -int_F p(x) log q(x) dr(x) + int_F p(x) log p(x) dr(x)
         = H[p, q] - H[p]
 where F denotes the support of the random variable X ~ p, H[., .] denotes (Shanon) cross entropy, and H[.] denotes (Shanon) entropy.

 Args
  other   tfp.distributions.Distribution instance.
  name   Python str prepended to names of ops created by this function.

 Returns
  kl_divergence   self.dtype Tensor with shape [B1, ..., Bn] representing n different calculations of the Kullback-Leibler divergence.    log_cdf View source
log_cdf(
    value, name='log_cdf'
)
 Log cumulative distribution function. Given random variable X, the cumulative distribution function cdf is: log_cdf(x) := Log[ P[X <= x] ]
 Often, a numerical approximation can be used for log_cdf(x) that yields a more accurate answer than simply taking the logarithm of the cdf when x << -1.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  logcdf   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    log_prob View source
log_prob(
    value, name='log_prob'
)
 Log probability density/mass function.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  log_prob   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    log_survival_function View source
log_survival_function(
    value, name='log_survival_function'
)
 Log survival function. Given random variable X, the survival function is defined: log_survival_function(x) = Log[ P[X > x] ]
                         = Log[ 1 - P[X <= x] ]
                         = Log[ 1 - cdf(x) ]
 Typically, different numerical approximations can be used for the log survival function, which are more accurate than 1 - cdf(x) when x >> 1.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns   Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.
 mean View source
mean(
    name='mean'
)
 Mean. mode View source
mode(
    name='mode'
)
 Mode. Additional documentation from Gamma: The mode of a gamma distribution is (shape - 1) / rate when shape > 1, and NaN otherwise. If self.allow_nan_stats is False, an exception will be raised rather than returning NaN. param_shapes View source
@classmethod
param_shapes(
    sample_shape, name='DistributionParamShapes'
)
 Shapes of parameters given the desired shape of a call to sample(). This is a class method that describes what key/value arguments are required to instantiate the given Distribution so that a particular shape is returned for that instance's call to sample(). Subclasses should override class method _param_shapes.

 Args
  sample_shape   Tensor or python list/tuple. Desired shape of a call to sample().
  name   name to prepend ops with.

 Returns   dict of parameter name to Tensor shapes.
 param_static_shapes View source
@classmethod
param_static_shapes(
    sample_shape
)
 param_shapes with static (i.e. TensorShape) shapes. This is a class method that describes what key/value arguments are required to instantiate the given Distribution so that a particular shape is returned for that instance's call to sample(). Assumes that the sample's shape is known statically. Subclasses should override class method _param_shapes to return constant-valued tensors when constant values are fed.

 Args
  sample_shape   TensorShape or python list/tuple. Desired shape of a call to sample().

 Returns   dict of parameter name to TensorShape.

 Raises
  ValueError   if sample_shape is a TensorShape and is not fully defined.    prob View source
prob(
    value, name='prob'
)
 Probability density/mass function.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  prob   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    quantile View source
quantile(
    value, name='quantile'
)
 Quantile function. Aka "inverse cdf" or "percent point function". Given random variable X and p in [0, 1], the quantile is: quantile(p) := x such that P[X <= x] == p

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  quantile   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    sample View source
sample(
    sample_shape=(), seed=None, name='sample'
)
 Generate samples of the specified shape. Note that a call to sample() without arguments will generate a single sample.

 Args
  sample_shape   0D or 1D int32 Tensor. Shape of the generated samples.
  seed   Python integer seed for RNG
  name   name to give to the op.

 Returns
  samples   a Tensor with prepended dimensions sample_shape.    stddev View source
stddev(
    name='stddev'
)
 Standard deviation. Standard deviation is defined as, stddev = E[(X - E[X])**2]**0.5
 where X is the random variable associated with this distribution, E denotes expectation, and stddev.shape = batch_shape + event_shape.

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  stddev   Floating-point Tensor with shape identical to batch_shape + event_shape, i.e., the same shape as self.mean().    survival_function View source
survival_function(
    value, name='survival_function'
)
 Survival function. Given random variable X, the survival function is defined: survival_function(x) = P[X > x]
                     = 1 - P[X <= x]
                     = 1 - cdf(x).

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns   Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.
 variance View source
variance(
    name='variance'
)
 Variance. Variance is defined as, Var = E[(X - E[X])**2]
 where X is the random variable associated with this distribution, E denotes expectation, and Var.shape = batch_shape + event_shape.

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  variance   Floating-point Tensor with shape identical to batch_shape + event_shape, i.e., the same shape as self.mean().


tf.compat.v1.distributions.Gamma Gamma distribution. Inherits From: Distribution
tf.compat.v1.distributions.Gamma(
    concentration, rate, validate_args=False, allow_nan_stats=True,
    name='Gamma'
)
 The Gamma distribution is defined over positive real numbers using parameters concentration (aka "alpha") and rate (aka "beta"). Mathematical Details The probability density function (pdf) is, pdf(x; alpha, beta, x > 0) = x**(alpha - 1) exp(-x beta) / Z
Z = Gamma(alpha) beta**(-alpha)
 where:
concentration = alpha, alpha > 0,
rate = beta, beta > 0,
Z is the normalizing constant, and,
Gamma is the gamma function.  The cumulative density function (cdf) is, cdf(x; alpha, beta, x > 0) = GammaInc(alpha, beta x) / Gamma(alpha)
 where GammaInc is the lower incomplete Gamma function. The parameters can be intuited via their relationship to mean and stddev, concentration = alpha = (mean / stddev)**2
rate = beta = mean / stddev**2 = concentration / mean
 Distribution parameters are automatically broadcast in all functions; see examples for details. Warning: The samples of this distribution are always non-negative. However, the samples that are smaller than np.finfo(dtype).tiny are rounded to this value, so it appears more often than it should. This should only be noticeable when the concentration is very small, or the rate is very large. See note in tf.random.gamma docstring. Samples of this distribution are reparameterized (pathwise differentiable). The derivatives are computed using the approach described in (Figurnov et al., 2018). Examples import tensorflow_probability as tfp
tfd = tfp.distributions

dist = tfd.Gamma(concentration=3.0, rate=2.0)
dist2 = tfd.Gamma(concentration=[3.0, 4.0], rate=[2.0, 3.0])
 Compute the gradients of samples w.r.t. the parameters: concentration = tf.constant(3.0)
rate = tf.constant(2.0)
dist = tfd.Gamma(concentration, rate)
samples = dist.sample(5)  # Shape [5]
loss = tf.reduce_mean(tf.square(samples))  # Arbitrary loss function
# Unbiased stochastic gradients of the loss function
grads = tf.gradients(loss, [concentration, rate])
 References: Implicit Reparameterization Gradients: Figurnov et al., 2018 (pdf)

 Args
  concentration   Floating point tensor, the concentration params of the distribution(s). Must contain only positive values.
  rate   Floating point tensor, the inverse scale params of the distribution(s). Must contain only positive values.
  validate_args   Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
  allow_nan_stats   Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value "NaN" to indicate the result is undefined. When False, an exception is raised if one or more of the statistic's batch members are undefined.
  name   Python str name prefixed to Ops created by this class.

 Raises
  TypeError   if concentration and rate are different dtypes.

 Attributes
  allow_nan_stats   Python bool describing behavior when a stat is undefined. Stats return +/- infinity when it makes sense. E.g., the variance of a Cauchy distribution is infinity. However, sometimes the statistic is undefined, e.g., if a distribution's pdf does not achieve a maximum within the support of the distribution, the mode is undefined. If the mean is undefined, then by definition the variance is undefined. E.g. the mean for Student's T for df = 1 is undefined (no clear way to say it is either + or - infinity), so the variance = E[(X - mean)**2] is also undefined.

  batch_shape   Shape of a single sample from a single event index as a TensorShape. May be partially defined or unknown. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.

  concentration   Concentration parameter.
  dtype   The DType of Tensors handled by this Distribution.
  event_shape   Shape of a single sample from a single batch as a TensorShape. May be partially defined or unknown.

  name   Name prepended to all ops created by this Distribution.
  parameters   Dictionary of parameters used to instantiate this Distribution.
  rate   Rate parameter.
  reparameterization_type   Describes how samples from the distribution are reparameterized. Currently this is one of the static instances distributions.FULLY_REPARAMETERIZED or distributions.NOT_REPARAMETERIZED.

  validate_args   Python bool indicating possibly expensive checks are enabled.    Methods batch_shape_tensor View source
batch_shape_tensor(
    name='batch_shape_tensor'
)
 Shape of a single sample from a single event index as a 1-D Tensor. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.

 Args
  name   name to give to the op

 Returns
  batch_shape   Tensor.    cdf View source
cdf(
    value, name='cdf'
)
 Cumulative distribution function. Given random variable X, the cumulative distribution function cdf is: cdf(x) := P[X <= x]

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  cdf   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    copy View source
copy(
    **override_parameters_kwargs
)
 Creates a deep copy of the distribution.
Note: the copy distribution may continue to depend on the original initialization arguments.

 Args
  **override_parameters_kwargs   String/value dictionary of initialization arguments to override with new values.

 Returns
  distribution   A new instance of type(self) initialized from the union of self.parameters and override_parameters_kwargs, i.e., dict(self.parameters, **override_parameters_kwargs).    covariance View source
covariance(
    name='covariance'
)
 Covariance. Covariance is (possibly) defined only for non-scalar-event distributions. For example, for a length-k, vector-valued distribution, it is calculated as, Cov[i, j] = Covariance(X_i, X_j) = E[(X_i - E[X_i]) (X_j - E[X_j])]
 where Cov is a (batch of) k x k matrix, 0 <= (i, j) < k, and E denotes expectation. Alternatively, for non-vector, multivariate distributions (e.g., matrix-valued, Wishart), Covariance shall return a (batch of) matrices under some vectorization of the events, i.e., Cov[i, j] = Covariance(Vec(X)_i, Vec(X)_j) = [as above]
 where Cov is a (batch of) k' x k' matrices, 0 <= (i, j) < k' = reduce_prod(event_shape), and Vec is some function mapping indices of this distribution's event dimensions to indices of a length-k' vector.

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  covariance   Floating-point Tensor with shape [B1, ..., Bn, k', k'] where the first n dimensions are batch coordinates and k' = reduce_prod(self.event_shape).    cross_entropy View source
cross_entropy(
    other, name='cross_entropy'
)
 Computes the (Shannon) cross entropy. Denote this distribution (self) by P and the other distribution by Q. Assuming P, Q are absolutely continuous with respect to one another and permit densities p(x) dr(x) and q(x) dr(x), (Shanon) cross entropy is defined as: H[P, Q] = E_p[-log q(X)] = -int_F p(x) log q(x) dr(x)
 where F denotes the support of the random variable X ~ P.

 Args
  other   tfp.distributions.Distribution instance.
  name   Python str prepended to names of ops created by this function.

 Returns
  cross_entropy   self.dtype Tensor with shape [B1, ..., Bn] representing n different calculations of (Shanon) cross entropy.    entropy View source
entropy(
    name='entropy'
)
 Shannon entropy in nats. event_shape_tensor View source
event_shape_tensor(
    name='event_shape_tensor'
)
 Shape of a single sample from a single batch as a 1-D int32 Tensor.

 Args
  name   name to give to the op

 Returns
  event_shape   Tensor.    is_scalar_batch View source
is_scalar_batch(
    name='is_scalar_batch'
)
 Indicates that batch_shape == [].

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  is_scalar_batch   bool scalar Tensor.    is_scalar_event View source
is_scalar_event(
    name='is_scalar_event'
)
 Indicates that event_shape == [].

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  is_scalar_event   bool scalar Tensor.    kl_divergence View source
kl_divergence(
    other, name='kl_divergence'
)
 Computes the Kullback--Leibler divergence. Denote this distribution (self) by p and the other distribution by q. Assuming p, q are absolutely continuous with respect to reference measure r, the KL divergence is defined as: KL[p, q] = E_p[log(p(X)/q(X))]
         = -int_F p(x) log q(x) dr(x) + int_F p(x) log p(x) dr(x)
         = H[p, q] - H[p]
 where F denotes the support of the random variable X ~ p, H[., .] denotes (Shanon) cross entropy, and H[.] denotes (Shanon) entropy.

 Args
  other   tfp.distributions.Distribution instance.
  name   Python str prepended to names of ops created by this function.

 Returns
  kl_divergence   self.dtype Tensor with shape [B1, ..., Bn] representing n different calculations of the Kullback-Leibler divergence.    log_cdf View source
log_cdf(
    value, name='log_cdf'
)
 Log cumulative distribution function. Given random variable X, the cumulative distribution function cdf is: log_cdf(x) := Log[ P[X <= x] ]
 Often, a numerical approximation can be used for log_cdf(x) that yields a more accurate answer than simply taking the logarithm of the cdf when x << -1.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  logcdf   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    log_prob View source
log_prob(
    value, name='log_prob'
)
 Log probability density/mass function.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  log_prob   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    log_survival_function View source
log_survival_function(
    value, name='log_survival_function'
)
 Log survival function. Given random variable X, the survival function is defined: log_survival_function(x) = Log[ P[X > x] ]
                         = Log[ 1 - P[X <= x] ]
                         = Log[ 1 - cdf(x) ]
 Typically, different numerical approximations can be used for the log survival function, which are more accurate than 1 - cdf(x) when x >> 1.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns   Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.
 mean View source
mean(
    name='mean'
)
 Mean. mode View source
mode(
    name='mode'
)
 Mode. Additional documentation from Gamma: The mode of a gamma distribution is (shape - 1) / rate when shape > 1, and NaN otherwise. If self.allow_nan_stats is False, an exception will be raised rather than returning NaN. param_shapes View source
@classmethod
param_shapes(
    sample_shape, name='DistributionParamShapes'
)
 Shapes of parameters given the desired shape of a call to sample(). This is a class method that describes what key/value arguments are required to instantiate the given Distribution so that a particular shape is returned for that instance's call to sample(). Subclasses should override class method _param_shapes.

 Args
  sample_shape   Tensor or python list/tuple. Desired shape of a call to sample().
  name   name to prepend ops with.

 Returns   dict of parameter name to Tensor shapes.
 param_static_shapes View source
@classmethod
param_static_shapes(
    sample_shape
)
 param_shapes with static (i.e. TensorShape) shapes. This is a class method that describes what key/value arguments are required to instantiate the given Distribution so that a particular shape is returned for that instance's call to sample(). Assumes that the sample's shape is known statically. Subclasses should override class method _param_shapes to return constant-valued tensors when constant values are fed.

 Args
  sample_shape   TensorShape or python list/tuple. Desired shape of a call to sample().

 Returns   dict of parameter name to TensorShape.

 Raises
  ValueError   if sample_shape is a TensorShape and is not fully defined.    prob View source
prob(
    value, name='prob'
)
 Probability density/mass function.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  prob   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    quantile View source
quantile(
    value, name='quantile'
)
 Quantile function. Aka "inverse cdf" or "percent point function". Given random variable X and p in [0, 1], the quantile is: quantile(p) := x such that P[X <= x] == p

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  quantile   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    sample View source
sample(
    sample_shape=(), seed=None, name='sample'
)
 Generate samples of the specified shape. Note that a call to sample() without arguments will generate a single sample.

 Args
  sample_shape   0D or 1D int32 Tensor. Shape of the generated samples.
  seed   Python integer seed for RNG
  name   name to give to the op.

 Returns
  samples   a Tensor with prepended dimensions sample_shape.    stddev View source
stddev(
    name='stddev'
)
 Standard deviation. Standard deviation is defined as, stddev = E[(X - E[X])**2]**0.5
 where X is the random variable associated with this distribution, E denotes expectation, and stddev.shape = batch_shape + event_shape.

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  stddev   Floating-point Tensor with shape identical to batch_shape + event_shape, i.e., the same shape as self.mean().    survival_function View source
survival_function(
    value, name='survival_function'
)
 Survival function. Given random variable X, the survival function is defined: survival_function(x) = P[X > x]
                     = 1 - P[X <= x]
                     = 1 - cdf(x).

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns   Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.
 variance View source
variance(
    name='variance'
)
 Variance. Variance is defined as, Var = E[(X - E[X])**2]
 where X is the random variable associated with this distribution, E denotes expectation, and Var.shape = batch_shape + event_shape.

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  variance   Floating-point Tensor with shape identical to batch_shape + event_shape, i.e., the same shape as self.mean().


tf.compat.v1.distributions.kl_divergence Get the KL-divergence KL(distribution_a || distribution_b). (deprecated)
tf.compat.v1.distributions.kl_divergence(
    distribution_a, distribution_b, allow_nan_stats=True, name=None
)
 Warning: THIS FUNCTION IS DEPRECATED. It will be removed after 2019-01-01. Instructions for updating: The TensorFlow Distributions library has moved to TensorFlow Probability (https://github.com/tensorflow/probability). You should update all references to use tfp.distributions instead of tf.distributions. If there is no KL method registered specifically for type(distribution_a) and type(distribution_b), then the class hierarchies of these types are searched. If one KL method is registered between any pairs of classes in these two parent hierarchies, it is used. If more than one such registered method exists, the method whose registered classes have the shortest sum MRO paths to the input types is used. If more than one such shortest path exists, the first method identified in the search is used (favoring a shorter MRO distance to type(distribution_a)).

 Args
  distribution_a   The first distribution.
  distribution_b   The second distribution.
  allow_nan_stats   Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value "NaN" to indicate the result is undefined. When False, an exception is raised if one or more of the statistic's batch members are undefined.
  name   Python str name prefixed to Ops created by this class.

 Returns   A Tensor with the batchwise KL-divergence between distribution_a and distribution_b.

 Raises
  NotImplementedError   If no KL method is defined for distribution types of distribution_a and distribution_b.


tf.compat.v1.distributions.Laplace The Laplace distribution with location loc and scale parameters. Inherits From: Distribution
tf.compat.v1.distributions.Laplace(
    loc, scale, validate_args=False, allow_nan_stats=True, name='Laplace'
)
 Mathematical details The probability density function (pdf) of this distribution is, pdf(x; mu, sigma) = exp(-|x - mu| / sigma) / Z
Z = 2 sigma
 where loc = mu, scale = sigma, and Z is the normalization constant. Note that the Laplace distribution can be thought of two exponential distributions spliced together "back-to-back." The Lpalce distribution is a member of the location-scale family, i.e., it can be constructed as, X ~ Laplace(loc=0, scale=1)
Y = loc + scale * X

 Args
  loc   Floating point tensor which characterizes the location (center) of the distribution.
  scale   Positive floating point tensor which characterizes the spread of the distribution.
  validate_args   Python bool, default False. When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs.
  allow_nan_stats   Python bool, default True. When True, statistics (e.g., mean, mode, variance) use the value "NaN" to indicate the result is undefined. When False, an exception is raised if one or more of the statistic's batch members are undefined.
  name   Python str name prefixed to Ops created by this class.

 Raises
  TypeError   if loc and scale are of different dtype.

 Attributes
  allow_nan_stats   Python bool describing behavior when a stat is undefined. Stats return +/- infinity when it makes sense. E.g., the variance of a Cauchy distribution is infinity. However, sometimes the statistic is undefined, e.g., if a distribution's pdf does not achieve a maximum within the support of the distribution, the mode is undefined. If the mean is undefined, then by definition the variance is undefined. E.g. the mean for Student's T for df = 1 is undefined (no clear way to say it is either + or - infinity), so the variance = E[(X - mean)**2] is also undefined.

  batch_shape   Shape of a single sample from a single event index as a TensorShape. May be partially defined or unknown. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.

  dtype   The DType of Tensors handled by this Distribution.
  event_shape   Shape of a single sample from a single batch as a TensorShape. May be partially defined or unknown.

  loc   Distribution parameter for the location.
  name   Name prepended to all ops created by this Distribution.
  parameters   Dictionary of parameters used to instantiate this Distribution.
  reparameterization_type   Describes how samples from the distribution are reparameterized. Currently this is one of the static instances distributions.FULLY_REPARAMETERIZED or distributions.NOT_REPARAMETERIZED.

  scale   Distribution parameter for scale.
  validate_args   Python bool indicating possibly expensive checks are enabled.    Methods batch_shape_tensor View source
batch_shape_tensor(
    name='batch_shape_tensor'
)
 Shape of a single sample from a single event index as a 1-D Tensor. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.

 Args
  name   name to give to the op

 Returns
  batch_shape   Tensor.    cdf View source
cdf(
    value, name='cdf'
)
 Cumulative distribution function. Given random variable X, the cumulative distribution function cdf is: cdf(x) := P[X <= x]

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  cdf   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    copy View source
copy(
    **override_parameters_kwargs
)
 Creates a deep copy of the distribution.
Note: the copy distribution may continue to depend on the original initialization arguments.

 Args
  **override_parameters_kwargs   String/value dictionary of initialization arguments to override with new values.

 Returns
  distribution   A new instance of type(self) initialized from the union of self.parameters and override_parameters_kwargs, i.e., dict(self.parameters, **override_parameters_kwargs).    covariance View source
covariance(
    name='covariance'
)
 Covariance. Covariance is (possibly) defined only for non-scalar-event distributions. For example, for a length-k, vector-valued distribution, it is calculated as, Cov[i, j] = Covariance(X_i, X_j) = E[(X_i - E[X_i]) (X_j - E[X_j])]
 where Cov is a (batch of) k x k matrix, 0 <= (i, j) < k, and E denotes expectation. Alternatively, for non-vector, multivariate distributions (e.g., matrix-valued, Wishart), Covariance shall return a (batch of) matrices under some vectorization of the events, i.e., Cov[i, j] = Covariance(Vec(X)_i, Vec(X)_j) = [as above]
 where Cov is a (batch of) k' x k' matrices, 0 <= (i, j) < k' = reduce_prod(event_shape), and Vec is some function mapping indices of this distribution's event dimensions to indices of a length-k' vector.

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  covariance   Floating-point Tensor with shape [B1, ..., Bn, k', k'] where the first n dimensions are batch coordinates and k' = reduce_prod(self.event_shape).    cross_entropy View source
cross_entropy(
    other, name='cross_entropy'
)
 Computes the (Shannon) cross entropy. Denote this distribution (self) by P and the other distribution by Q. Assuming P, Q are absolutely continuous with respect to one another and permit densities p(x) dr(x) and q(x) dr(x), (Shanon) cross entropy is defined as: H[P, Q] = E_p[-log q(X)] = -int_F p(x) log q(x) dr(x)
 where F denotes the support of the random variable X ~ P.

 Args
  other   tfp.distributions.Distribution instance.
  name   Python str prepended to names of ops created by this function.

 Returns
  cross_entropy   self.dtype Tensor with shape [B1, ..., Bn] representing n different calculations of (Shanon) cross entropy.    entropy View source
entropy(
    name='entropy'
)
 Shannon entropy in nats. event_shape_tensor View source
event_shape_tensor(
    name='event_shape_tensor'
)
 Shape of a single sample from a single batch as a 1-D int32 Tensor.

 Args
  name   name to give to the op

 Returns
  event_shape   Tensor.    is_scalar_batch View source
is_scalar_batch(
    name='is_scalar_batch'
)
 Indicates that batch_shape == [].

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  is_scalar_batch   bool scalar Tensor.    is_scalar_event View source
is_scalar_event(
    name='is_scalar_event'
)
 Indicates that event_shape == [].

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  is_scalar_event   bool scalar Tensor.    kl_divergence View source
kl_divergence(
    other, name='kl_divergence'
)
 Computes the Kullback--Leibler divergence. Denote this distribution (self) by p and the other distribution by q. Assuming p, q are absolutely continuous with respect to reference measure r, the KL divergence is defined as: KL[p, q] = E_p[log(p(X)/q(X))]
         = -int_F p(x) log q(x) dr(x) + int_F p(x) log p(x) dr(x)
         = H[p, q] - H[p]
 where F denotes the support of the random variable X ~ p, H[., .] denotes (Shanon) cross entropy, and H[.] denotes (Shanon) entropy.

 Args
  other   tfp.distributions.Distribution instance.
  name   Python str prepended to names of ops created by this function.

 Returns
  kl_divergence   self.dtype Tensor with shape [B1, ..., Bn] representing n different calculations of the Kullback-Leibler divergence.    log_cdf View source
log_cdf(
    value, name='log_cdf'
)
 Log cumulative distribution function. Given random variable X, the cumulative distribution function cdf is: log_cdf(x) := Log[ P[X <= x] ]
 Often, a numerical approximation can be used for log_cdf(x) that yields a more accurate answer than simply taking the logarithm of the cdf when x << -1.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  logcdf   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    log_prob View source
log_prob(
    value, name='log_prob'
)
 Log probability density/mass function.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  log_prob   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    log_survival_function View source
log_survival_function(
    value, name='log_survival_function'
)
 Log survival function. Given random variable X, the survival function is defined: log_survival_function(x) = Log[ P[X > x] ]
                         = Log[ 1 - P[X <= x] ]
                         = Log[ 1 - cdf(x) ]
 Typically, different numerical approximations can be used for the log survival function, which are more accurate than 1 - cdf(x) when x >> 1.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns   Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.
 mean View source
mean(
    name='mean'
)
 Mean. mode View source
mode(
    name='mode'
)
 Mode. param_shapes View source
@classmethod
param_shapes(
    sample_shape, name='DistributionParamShapes'
)
 Shapes of parameters given the desired shape of a call to sample(). This is a class method that describes what key/value arguments are required to instantiate the given Distribution so that a particular shape is returned for that instance's call to sample(). Subclasses should override class method _param_shapes.

 Args
  sample_shape   Tensor or python list/tuple. Desired shape of a call to sample().
  name   name to prepend ops with.

 Returns   dict of parameter name to Tensor shapes.
 param_static_shapes View source
@classmethod
param_static_shapes(
    sample_shape
)
 param_shapes with static (i.e. TensorShape) shapes. This is a class method that describes what key/value arguments are required to instantiate the given Distribution so that a particular shape is returned for that instance's call to sample(). Assumes that the sample's shape is known statically. Subclasses should override class method _param_shapes to return constant-valued tensors when constant values are fed.

 Args
  sample_shape   TensorShape or python list/tuple. Desired shape of a call to sample().

 Returns   dict of parameter name to TensorShape.

 Raises
  ValueError   if sample_shape is a TensorShape and is not fully defined.    prob View source
prob(
    value, name='prob'
)
 Probability density/mass function.

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  prob   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    quantile View source
quantile(
    value, name='quantile'
)
 Quantile function. Aka "inverse cdf" or "percent point function". Given random variable X and p in [0, 1], the quantile is: quantile(p) := x such that P[X <= x] == p

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns
  quantile   a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.    sample View source
sample(
    sample_shape=(), seed=None, name='sample'
)
 Generate samples of the specified shape. Note that a call to sample() without arguments will generate a single sample.

 Args
  sample_shape   0D or 1D int32 Tensor. Shape of the generated samples.
  seed   Python integer seed for RNG
  name   name to give to the op.

 Returns
  samples   a Tensor with prepended dimensions sample_shape.    stddev View source
stddev(
    name='stddev'
)
 Standard deviation. Standard deviation is defined as, stddev = E[(X - E[X])**2]**0.5
 where X is the random variable associated with this distribution, E denotes expectation, and stddev.shape = batch_shape + event_shape.

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  stddev   Floating-point Tensor with shape identical to batch_shape + event_shape, i.e., the same shape as self.mean().    survival_function View source
survival_function(
    value, name='survival_function'
)
 Survival function. Given random variable X, the survival function is defined: survival_function(x) = P[X > x]
                     = 1 - P[X <= x]
                     = 1 - cdf(x).

 Args
  value   float or double Tensor.
  name   Python str prepended to names of ops created by this function.

 Returns   Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype.
 variance View source
variance(
    name='variance'
)
 Variance. Variance is defined as, Var = E[(X - E[X])**2]
 where X is the random variable associated with this distribution, E denotes expectation, and Var.shape = batch_shape + event_shape.

 Args
  name   Python str prepended to names of ops created by this function.

 Returns
  variance   Floating-point Tensor with shape identical to batch_shape + event_shape, i.e., the same shape as self.mean().