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Determinantal point process (DPP) distribution.
Inherits From: AutoCompositeTensorDistribution
, Distribution
, AutoCompositeTensor
tfp.distributions.DeterminantalPointProcess(
eigenvalues,
eigenvectors,
validate_args=False,
allow_nan_stats=False,
name='DeterminantalPointProcess'
)
The DPP disribution parameterized by the eigenvalues and eigenvectors of the L-ensemble matrix. The L-ensemble matrix indicates the degree of "repulsion" between pairs of items.
Mathematical details
A Determinantal Point Process is a distribution over subsets of n
items,
called the ground set. The DPP is parameterized by a positive definite
matrix of shape n x n
, the L-ensemble matrix. It assigns to any subset S
of {1, ..., n}
the probability:
Pr(S) = det(L_S) / det(I + L)
where:
L
is the L-ensemble matrix parameterized byeigenvalues
andeigenvectors
, i.e.L = U D U^T
forU = eigenvectors
andD = eigenvalues
.L_S
is the principal submatrix ofL
indexed by items inS
. In Numpy slicing notation,L_S = L[S, :][:, S]
.det
is the matrix determinant.
Marginal probabilities, i.e. the probability that a sample from the DPP contains the subset S, are obtained by way of the marginal kernel:
K = L / (I + L)
where /
is the matrix inverse.
When sampling a random set A
from the DPP, the marginal probability of S
,
given by exp(dpp.marginal_log_prob(S))
, is:
Pr(A is a superset of S) = det(K_S)
This is a marginal probability in the following sense. If we think of the
DPP as a joint distribution over n
binary indicator variables, each telling
whether a given element is in a given subset S
, then we can consider the
marginal distribution obtained by "summing" out some of these binary
indicators. The resulting marginal distribution happens also to be a DPP. What
is referred to as the marginal_log_prob
of S
(under the original DPP) is
just the log_prob
of S
under the marginal DPP, obtained by summing out the
indicators of the complement of S. This tells us the (log) probability that
a sample from the full DPP includes S
as a subset.
Written in terms of sets, with each S'
a subset of the complement of S
:
det(K_S) = sum_{S' s.t. S' intersect S is empty} [ Pr(S union S') ]
where Pr(S union S')
is the probability of sampling exactly S union S'
from the DPP.
For further detail, see Theorem 2.2 of [3].
Repulsion
Rewriting L = B B^T
(which in particular can be done using B = U sqrt(D)
,
where D
are the eigenvalues and U
the eigenvectors), we have
Pr(S) = Vol^2(b_s1, b_s2, ..., b_sk)
where b_s1, ...
is the s1
th column of B
. Hence, the probability of
sampling two points simultaneously decreases as a function of how colinear
their corresponding eigenvectors are.
Sampling
Sampling is implemented following the algorithm introduced in 2, and proceeds in two phases.
Given an orthonormalization L = U D U^T
:
First, an elementary DPP (E-DPP) is built by sampling a subset of eigenvectors
S
from a Bernoulli distribution with probs equal toD / (D + 1)
. This E-DPP has the same eigenvectorsU
asL
, but its eigenvalues are1
iff the corresponding Bernoulli trial was succesful,0
otherwise.Then, a number of points
k
equal to the number of selected eigenvalues is selected iteratively from the elementary DPP. After sampling a pointi
, the kernel is updated by projecting it onto the subspace of eigenvectors orthogonal to thei
th basis vector.
Examples
Sample points on the unit square grid:
import itertools
import tensorflow as tf
import tensorflow_probability as tfp
import matplotlib.pyplot as plt
tfd = tfp.distributions
tfpk = tfp.math.psd_kernels
grid_size = 16
# Generate grid_size**2 pts on the unit square.
grid = np.arange(0, 1, 1./grid_size)
points = np.array(list(itertools.product(grid, grid)))
# Create the kernel L that parameterizes the DPP.
kernel_amplitude = 2.
kernel_lengthscale = 2. / grid_size
kernel = tfpk.ExponentiatedQuadratic(kernel_amplitude, kernel_lengthscale)
kernel_matrix = kernel.matrix(points, points)
eigenvalues, eigenvectors = tf.linalg.eigh(kernel_matrix)
dpp = tfd.DeterminantalPointProcess(eigenvalues, eigenvectors)
# The inner-most dimension of the result of `dpp.sample` is a multi-hot
# encoding of a subset of {1, ..., ground_set_size}.
plt.figure(figsize=(6, 6))
for i, samp in enumerate(dpp.sample(4, seed=(1, 2))): # 4 x grid_size**2
plt.subplot(221 + i)
plt.scatter(*points[np.where(samp)].T)
plt.xticks([])
plt.yticks([])
plt.tight_layout()
plt.show()
# Like any TFP distribution, the DPP supports batching and shaped samples.
kernel_amplitude = [2., 3, 4] # Build a batch of 3 PSD kernels.
kernel_lengthscale = 2. / grid_size
kernel = tfpk.ExponentiatedQuadratic(kernel_amplitude, kernel_lengthscale)
kernel_matrix = kernel.matrix(points, points) # 3 x 256 x 256
eigenvalues, eigenvectors = tf.linalg.eigh(kernel_matrix)
dpp = tfd.DeterminantalPointProcess(eigenvalues, eigenvectors)
print(dpp) # batch shape: [3], event shape: [256]
samps = dpp.sample(2, seed=(10, 20))
print(samps.shape) # shape: [2, 3, 256]
print(dpp.log_prob(samps)) # tensor with shape [2, 3]
References
[1]: Odile Macchi. The coincidence approach to stochastic point processes. Advances in Applied Probability, 1975.
[2]: J. Ben Hough, Manjunath Krishnapur, Yuval Peres, Balint Virag. Determinantal point processes and independence. Probability Surveys, 2006. https://arxiv.org/abs/math/0503110
[3]: Alex Kulesza, Ben Taskar. Determinantal point processes for machine learning. Foundations and Trends in Machine Learning, 2012. https://arxiv.org/abs/1207.6083
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 Tensor s handled by this Distribution .
|
eigenvalues
|
|
eigenvectors
|
|
event_shape
|
Shape of a single sample from a single batch as a TensorShape .
May be partially defined or unknown. |
experimental_shard_axis_names
|
The list or structure of lists of active shard axis names. |
name
|
Name prepended to all ops created by this Distribution .
|
name_scope
|
Returns a tf.name_scope instance for this class.
|
non_trainable_variables
|
Sequence of non-trainable variables owned by this module and its submodules. |
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
|
submodules
|
Sequence of all sub-modules.
Submodules are modules which are properties of this module, or found as properties of modules which are properties of this module (and so on).
|
trainable_variables
|
Sequence of trainable variables owned by this module and its submodules. |
validate_args
|
Python bool indicating possibly expensive checks are enabled.
|
variables
|
Sequence of variables owned by this module and its submodules. |
Methods
batch_shape_tensor
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
cdf(
value, name='cdf', **kwargs
)
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.
|
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
cdf
|
a Tensor of shape sample_shape(x) + self.batch_shape with
values of type self.dtype .
|
copy
copy(
**override_parameters_kwargs
)
Creates a deep copy of the distribution.
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
covariance(
name='covariance', **kwargs
)
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.
|
**kwargs
|
Named arguments forwarded to subclass implementation. |
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
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)
, (Shannon)
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 (Shannon) cross entropy.
|
entropy
entropy(
name='entropy', **kwargs
)
Shannon entropy in nats.
event_shape_tensor
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 .
|
experimental_default_event_space_bijector
experimental_default_event_space_bijector(
*args, **kwargs
)
Bijector mapping the reals (R**n) to the event space of the distribution.
Distributions with continuous support may implement
_default_event_space_bijector
which returns a subclass of
tfp.bijectors.Bijector
that maps R**n to the distribution's event space.
For example, the default bijector for the Beta
distribution
is tfp.bijectors.Sigmoid()
, which maps the real line to [0, 1]
, the
support of the Beta
distribution. The default bijector for the
CholeskyLKJ
distribution is tfp.bijectors.CorrelationCholesky
, which
maps R^(k * (k-1) // 2) to the submanifold of k x k lower triangular
matrices with ones along the diagonal.
The purpose of experimental_default_event_space_bijector
is
to enable gradient descent in an unconstrained space for Variational
Inference and Hamiltonian Monte Carlo methods. Some effort has been made to
choose bijectors such that the tails of the distribution in the
unconstrained space are between Gaussian and Exponential.
For distributions with discrete event space, or for which TFP currently
lacks a suitable bijector, this function returns None
.
Args | |
---|---|
*args
|
Passed to implementation _default_event_space_bijector .
|
**kwargs
|
Passed to implementation _default_event_space_bijector .
|
Returns | |
---|---|
event_space_bijector
|
Bijector instance or None .
|
experimental_fit
@classmethod
experimental_fit( value, sample_ndims=1, validate_args=False, **init_kwargs )
Instantiates a distribution that maximizes the likelihood of x
.
Args | |
---|---|
value
|
a Tensor valid sample from this distribution family.
|
sample_ndims
|
Positive int Tensor number of leftmost dimensions of
value that index i.i.d. samples.
Default value: 1 .
|
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.
Default value: False .
|
**init_kwargs
|
Additional keyword arguments passed through to
cls.__init__ . These take precedence in case of collision with the
fitted parameters; for example,
tfd.Normal.experimental_fit([1., 1.], scale=20.) returns a Normal
distribution with scale=20. rather than the maximum likelihood
parameter scale=0. .
|
Returns | |
---|---|
maximum_likelihood_instance
|
instance of cls with parameters that
maximize the likelihood of value .
|
experimental_local_measure
experimental_local_measure(
value, backward_compat=False, **kwargs
)
Returns a log probability density together with a TangentSpace
.
A TangentSpace
allows us to calculate the correct push-forward
density when we apply a transformation to a Distribution
on
a strict submanifold of R^n (typically via a Bijector
in the
TransformedDistribution
subclass). The density correction uses
the basis of the tangent space.
Args | |
---|---|
value
|
float or double Tensor .
|
backward_compat
|
bool specifying whether to fall back to returning
FullSpace as the tangent space, and representing R^n with the standard
basis.
|
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
log_prob
|
a Tensor representing the log probability density, of shape
sample_shape(x) + self.batch_shape with values of type self.dtype .
|
tangent_space
|
a TangentSpace object (by default FullSpace )
representing the tangent space to the manifold at value .
|
Raises | |
---|---|
UnspecifiedTangentSpaceError if backward_compat is False and
the _experimental_tangent_space attribute has not been defined.
|
experimental_sample_and_log_prob
experimental_sample_and_log_prob(
sample_shape=(), seed=None, name='sample_and_log_prob', **kwargs
)
Samples from this distribution and returns the log density of the sample.
The default implementation simply calls sample
and log_prob
:
def _sample_and_log_prob(self, sample_shape, seed, **kwargs):
x = self.sample(sample_shape=sample_shape, seed=seed, **kwargs)
return x, self.log_prob(x, **kwargs)
However, some subclasses may provide more efficient and/or numerically stable implementations.
Args | |
---|---|
sample_shape
|
integer Tensor desired shape of samples to draw.
Default value: () .
|
seed
|
PRNG seed; see tfp.random.sanitize_seed for details.
Default value: None .
|
name
|
name to give to the op.
Default value: 'sample_and_log_prob' .
|
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
samples
|
a Tensor , or structure of Tensor s, with prepended dimensions
sample_shape .
|
log_prob
|
a Tensor of shape sample_shape(x) + self.batch_shape with
values of type self.dtype .
|
is_scalar_batch
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
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
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 (Shannon) cross entropy, and H[.]
denotes (Shannon) 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.
|
l_ensemble_matrix
l_ensemble_matrix()
Returns the L-ensemble parameterization of the DPP.
log_cdf
log_cdf(
value, name='log_cdf', **kwargs
)
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.
|
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
logcdf
|
a Tensor of shape sample_shape(x) + self.batch_shape with
values of type self.dtype .
|
log_prob
log_prob(
value, name='log_prob', **kwargs
)
Log probability density/mass function.
Args | |
---|---|
value
|
float or double Tensor .
|
name
|
Python str prepended to names of ops created by this function.
|
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
log_prob
|
a Tensor of shape sample_shape(x) + self.batch_shape with
values of type self.dtype .
|
log_survival_function
log_survival_function(
value, name='log_survival_function', **kwargs
)
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.
|
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
Tensor of shape sample_shape(x) + self.batch_shape with values of type
self.dtype .
|
marginal_kernel
marginal_kernel()
Returns the marginal kernel that defines the DPP.
marginal_log_prob
marginal_log_prob(
value
)
Computes the marginal log probability of an event.
The marginal log probability is the log-probability that a set sampled from
the DPP will include value
as a subset. By contrast, log_prob
returns
the log-probability of sampling exactly value
.
Args | |
---|---|
value
|
Tensor broadcastable to [batch_shape, n_points] corresponding
to the one-hot encoding of a subset of points.
|
Returns | |
---|---|
The log marginal probability of value according to the DPP.
|
mean
mean(
name='mean', **kwargs
)
Mean.
mode
mode(
name='mode', **kwargs
)
Mode.
param_shapes
@classmethod
param_shapes( sample_shape, name='DistributionParamShapes' )
Shapes of parameters given the desired shape of a call to sample()
. (deprecated)
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
@classmethod
param_static_shapes( sample_shape )
param_shapes with static (i.e. TensorShape
) shapes. (deprecated)
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.
|
parameter_properties
@classmethod
parameter_properties( dtype=tf.float32, num_classes=None )
Returns a dict mapping constructor arg names to property annotations.
This dict should include an entry for each of the distribution's
Tensor
-valued constructor arguments.
Distribution subclasses are not required to implement
_parameter_properties
, so this method may raise NotImplementedError
.
Providing a _parameter_properties
implementation enables several advanced
features, including:
- Distribution batch slicing (
sliced_distribution = distribution[i:j]
). - Automatic inference of
_batch_shape
and_batch_shape_tensor
, which must otherwise be computed explicitly. - Automatic instantiation of the distribution within TFP's internal property tests.
- Automatic construction of 'trainable' instances of the distribution using appropriate bijectors to avoid violating parameter constraints. This enables the distribution family to be used easily as a surrogate posterior in variational inference.
In the future, parameter property annotations may enable additional
functionality; for example, returning Distribution instances from
tf.vectorized_map
.
Args | |
---|---|
dtype
|
Optional float dtype to assume for continuous-valued parameters.
Some constraining bijectors require advance knowledge of the dtype
because certain constants (e.g., tfb.Softplus.low ) must be
instantiated with the same dtype as the values to be transformed.
|
num_classes
|
Optional int Tensor number of classes to assume when
inferring the shape of parameters for categorical-like distributions.
Otherwise ignored.
|
Returns | |
---|---|
parameter_properties
|
A
str -> tfp.python.internal.parameter_properties.ParameterPropertiesdict mapping constructor argument names to ParameterProperties`
instances.
|
Raises | |
---|---|
NotImplementedError
|
if the distribution class does not implement
_parameter_properties .
|
prob
prob(
value, name='prob', **kwargs
)
Probability density/mass function.
Args | |
---|---|
value
|
float or double Tensor .
|
name
|
Python str prepended to names of ops created by this function.
|
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
prob
|
a Tensor of shape sample_shape(x) + self.batch_shape with
values of type self.dtype .
|
quantile
quantile(
value, name='quantile', **kwargs
)
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.
|
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
quantile
|
a Tensor of shape sample_shape(x) + self.batch_shape with
values of type self.dtype .
|
sample
sample(
sample_shape=(), seed=None, name='sample', **kwargs
)
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
|
PRNG seed; see tfp.random.sanitize_seed for details.
|
name
|
name to give to the op. |
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
samples
|
a Tensor with prepended dimensions sample_shape .
|
stddev
stddev(
name='stddev', **kwargs
)
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.
|
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
stddev
|
Floating-point Tensor with shape identical to
batch_shape + event_shape , i.e., the same shape as self.mean() .
|
survival_function
survival_function(
value, name='survival_function', **kwargs
)
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.
|
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
Tensor of shape sample_shape(x) + self.batch_shape with values of type
self.dtype .
|
unnormalized_log_prob
unnormalized_log_prob(
value, name='unnormalized_log_prob', **kwargs
)
Potentially unnormalized log probability density/mass function.
This function is similar to log_prob
, but does not require that the
return value be normalized. (Normalization here refers to the total
integral of probability being one, as it should be by definition for any
probability distribution.) This is useful, for example, for distributions
where the normalization constant is difficult or expensive to compute. By
default, this simply calls log_prob
.
Args | |
---|---|
value
|
float or double Tensor .
|
name
|
Python str prepended to names of ops created by this function.
|
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
unnormalized_log_prob
|
a Tensor of shape
sample_shape(x) + self.batch_shape with values of type self.dtype .
|
variance
variance(
name='variance', **kwargs
)
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.
|
**kwargs
|
Named arguments forwarded to subclass implementation. |
Returns | |
---|---|
variance
|
Floating-point Tensor with shape identical to
batch_shape + event_shape , i.e., the same shape as self.mean() .
|
with_name_scope
@classmethod
with_name_scope( method )
Decorator to automatically enter the module name scope.
class MyModule(tf.Module):
@tf.Module.with_name_scope
def __call__(self, x):
if not hasattr(self, 'w'):
self.w = tf.Variable(tf.random.normal([x.shape[1], 3]))
return tf.matmul(x, self.w)
Using the above module would produce tf.Variable
s and tf.Tensor
s whose
names included the module name:
mod = MyModule()
mod(tf.ones([1, 2]))
<tf.Tensor: shape=(1, 3), dtype=float32, numpy=..., dtype=float32)>
mod.w
<tf.Variable 'my_module/Variable:0' shape=(2, 3) dtype=float32,
numpy=..., dtype=float32)>
Args | |
---|---|
method
|
The method to wrap. |
Returns | |
---|---|
The original method wrapped such that it enters the module's name scope. |
__getitem__
__getitem__(
slices
)
Slices the batch axes of this distribution, returning a new instance.
b = tfd.Bernoulli(logits=tf.zeros([3, 5, 7, 9]))
b.batch_shape # => [3, 5, 7, 9]
b2 = b[:, tf.newaxis, ..., -2:, 1::2]
b2.batch_shape # => [3, 1, 5, 2, 4]
x = tf.random.normal([5, 3, 2, 2])
cov = tf.matmul(x, x, transpose_b=True)
chol = tf.linalg.cholesky(cov)
loc = tf.random.normal([4, 1, 3, 1])
mvn = tfd.MultivariateNormalTriL(loc, chol)
mvn.batch_shape # => [4, 5, 3]
mvn.event_shape # => [2]
mvn2 = mvn[:, 3:, ..., ::-1, tf.newaxis]
mvn2.batch_shape # => [4, 2, 3, 1]
mvn2.event_shape # => [2]
Args | |
---|---|
slices
|
slices from the [] operator |
Returns | |
---|---|
dist
|
A new tfd.Distribution instance with sliced parameters.
|
__iter__
__iter__()