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|
Joint distribution parameterized by distribution-making functions.
Inherits From: JointDistribution
tfp.substrates.jax.distributions.JointDistributionSequential(
model, validate_args=False, name=None
)
This distribution enables both sampling and joint probability computation from a single model specification.
A joint distribution is a collection of possibly interdependent distributions.
Like tf.keras.Sequential, the JointDistributionSequential can be specified
via a list of functions (each responsible for making a
tfp.distributions.Distribution-like instance). Unlike
tf.keras.Sequential, each function can depend on the output of all previous
elements rather than only the immediately previous.
Mathematical Details
The JointDistributionSequential implements the chain rule of probability.
That is, the probability function of a length-d vector x is,
p(x) = prod{ p(x[i] | x[:i]) : i = 0, ..., (d - 1) }
The JointDistributionSequential is parameterized by a list comprised of
either:
tfp.distributions.Distribution-like instances or,callables which return atfp.distributions.Distribution-like instance.
Each list element implements the i-th full conditional distribution,
p(x[i] | x[:i]). The "conditioned on" elements are represented by the
callable's required arguments. Directly providing a Distribution-like
instance is a convenience and is semantically identical a zero argument
callable.
Denote the i-th callables non-default arguments as args[i]. Since the
callable is the conditional manifest, 0 <= len(args[i]) <= i - 1. When
len(args[i]) < i - 1, the callable only depends on a subset of the
previous distributions, specifically those at indexes:
range(i - 1, i - 1 - num_args[i], -1).
(See "Examples" and "Discussion" for why the order is reversed.)
Name resolution: The names ofJointDistributionSequentialcomponents
are defined by explicitnamearguments passed to distributions
(tfd.Normal(0., 1., name='x')) and/or by the argument names in
distribution-making functions (lambda x: tfd.Normal(x., 1.)). Both
approaches may be used in the same distribution, as long as they are
consistent; referring to a single component by multiple names will raise aValueError`. Unnamed components will be assigned a dummy name.
Examples
tfd = tfp.distributions
# Consider the following generative model:
# e ~ Exponential(rate=[100,120])
# g ~ Gamma(concentration=e[0], rate=e[1])
# n ~ Normal(loc=0, scale=2.)
# m ~ Normal(loc=n, scale=g)
# for i = 1, ..., 12:
# x[i] ~ Bernoulli(logits=m)
# In TFP, we can write this as:
joint = tfd.JointDistributionSequential([
tfd.Independent(tfd.Exponential(rate=[100, 120]), 1), # e
lambda e: tfd.Gamma(concentration=e[..., 0], rate=e[..., 1]), # g
tfd.Normal(loc=0, scale=2.), # n
lambda n, g: tfd.Normal(loc=n, scale=g), # m
lambda m: tfd.Sample(tfd.Bernoulli(logits=m), 12) # x
])
# (Notice the 1:1 correspondence between "math" and "code".)
x = joint.sample()
# ==> A length-5 list of Tensors representing a draw/realization from each
# distribution.
joint.log_prob(x)
# ==> A scalar `Tensor` representing the total log prob under all five
# distributions.
joint.resolve_graph()
# ==> (('e', ()),
# ('g', ('e',)),
# ('n', ()),
# ('m', ('n', 'g')),
# ('x', ('m',)))
Discussion
JointDistributionSequential builds each distribution in list order; list
items must be either a:
tfd.Distribution-like instance (e.g.,eandn), or a- Python
callable(e.g.,g,m,x).
Regarding #1, an object is deemed "tfd.Distribution-like" if it has a
sample, log_prob, and distribution properties, e.g., batch_shape,
event_shape, dtype.
Regarding #2, in addition to using a function (or lambda), supplying a TFD
"class" is also permissible, this also being a "Python callable." For
example, instead of writing:
lambda loc, scale: tfd.Normal(loc=loc, scale=scale)
one could have simply written tfd.Normal.
Notice that directly providing a tfd.Distribution-like instance means there
cannot exist a (dynamic) dependency on other distributions; it is
"independent" both "computationally" and "statistically." The same is
self-evidently true of zero-argument callables.
A distribution instance depends on other distribution instances through the
distribution making function's required arguments. If the distribution maker
has k required arguments then the JointDistributionSequential calls the
maker with samples produced by the previous k distributions.
Args | |
|---|---|
model
|
Python list of either tfd.Distribution instances and/or
lambda functions which take the k previous distributions and returns a
new tfd.Distribution instance.
|
validate_args
|
Python bool. Whether to validate input with asserts.
If validate_args is False, and the inputs are invalid,
correct behavior is not guaranteed.
Default value: False.
|
name
|
The name for ops managed by the distribution.
Default value: None (i.e., "JointDistributionSequential").
|
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. |
model
|
|
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
|
trainable_variables
|
|
validate_args
|
Python bool indicating possibly expensive checks are enabled.
|
variables
|
|
Methods
batch_shape_tensor
batch_shape_tensor(
sample_shape=(), 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 | |
|---|---|
sample_shape
|
The sample shape under which to evaluate the joint distribution. Sample shape at root (toplevel) nodes may affect the batch or event shapes of child nodes. |
name
|
name to give to the op |
| Returns | |
|---|---|
batch_shape
|
Tensor representing batch shape of each distribution in
model.
|
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.
other types with built-in registrations: JointDistributionNamed, JointDistributionNamedAutoBatched, JointDistributionSequential, JointDistributionSequentialAutoBatched
| 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.
Additional documentation from JointDistributionSequential:
Shannon entropy in nats.
event_shape_tensor
event_shape_tensor(
sample_shape=(), name='event_shape_tensor'
)
Shape of a single sample from a single batch as a 1-D int32 Tensor.
| Args | |
|---|---|
sample_shape
|
The sample shape under which to evaluate the joint distribution. Sample shape at root (toplevel) nodes may affect the batch or event shapes of child nodes. |
name
|
name to give to the op |
| Returns | |
|---|---|
event_shape
|
tuple of Tensors representing the event_shape for each
distribution in model.
|
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 for each distribution in model.
|
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 for each distribution in model.
|
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.
other types with built-in registrations: JointDistributionNamed, JointDistributionNamedAutoBatched, JointDistributionSequential, JointDistributionSequentialAutoBatched
| 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
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(
*args, **kwargs
)
Log probability density/mass function.
The measure methods of `JointDistribution` (`log_prob`, `prob`, etc.)
can be called either by passing a single structure of tensors or by using
named args for each part of the joint distribution state. For example,
jd = tfd.JointDistributionSequential([ tfd.Normal(0., 1.), lambda z: tfd.Normal(z, 1.) ], validate_args=True) jd.dtype # ==> [tf.float32, tf.float32] z, x = sample = jd.sample() # The following calling styles are all permissable and produce the exactly # the same output. assert (jd.log_prob(sample) == jd.log_prob(value=sample) == jd.log_prob(z, x) == jd.log_prob(z=z, x=x) == jd.log_prob(z, x=x)) # These calling possibilities also imply that one can also use `*` # expansion, if `sample` is a sequence: jd.log_prob(*sample) # and similarly, if `sample` is a map, one can use `**` expansion: jd.log_prob(**sample)
`JointDistribution` component distributions names are resolved via
`jd._flat_resolve_names()`, which is implemented by each `JointDistribution`
subclass (see subclass documentation for details). Generally, for components
where a name was provided---
either explicitly as the `name` argument to a distribution or as a key in a
dict-valued JointDistribution, or implicitly, e.g., by the argument name of
a `JointDistributionSequential` distribution-making function---the provided
name will be used. Otherwise the component will receive a dummy name; these
may change without warning and should not be relied upon.
Note: not all `JointDistribution` subclasses support all calling styles;
for example, `JointDistributionNamed` does not support positional arguments
(aka "unnamed arguments") unless the provided model specifies an ordering of
variables (i.e., is an `collections.OrderedDict` or `collections.namedtuple`
rather than a plain `dict`).
Note: care is taken to resolve any potential ambiguity---this is generally
possible by inspecting the structure of the provided argument and "aligning"
it to the joint distribution output structure (defined by `jd.dtype`). For
example,
trivial_jd = tfd.JointDistributionSequential([tfd.Exponential(1.)]) trivial_jd.dtype # => [tf.float32] trivial_jd.log_prob([4.]) # ==> Tensor with shape `[]`. lp = trivial_jd.log_prob(4.) # ==> Tensor with shape `[]`.
Notice that in the first call, `[4.]` is interpreted as a list of one
scalar while in the second call the input is a scalar. Hence both inputs
result in identical scalar outputs. If we wanted to pass an explicit
vector to the `Exponential` component---creating a vector-shaped batch
of `log_prob`s---we could instead write
`trivial_jd.log_prob(np.array([4]))`.
Args:
*args: Positional arguments: a `value` structure or component values
(see above).
**kwargs: Keyword arguments: a `value` structure or component values
(see above). May also include `name`, specifying a Python string name
for ops generated by this method.
| Returns | |
|---|---|
log_prob
|
a Tensor of shape sample_shape(x) + self.batch_shape with
values of type self.dtype.
|
log_prob_parts
log_prob_parts(
value, name='log_prob_parts'
)
Log probability density/mass function.
| Args | |
|---|---|
value
|
list of Tensors in distribution_fn order for which we compute
the log_prob_parts and to parameterize other ("downstream")
distributions.
|
name
|
name prepended to ops created by this function.
Default value: "log_prob_parts".
|
| Returns | |
|---|---|
log_prob_parts
|
a tuple of Tensors representing the log_prob for
each distribution_fn evaluated at each corresponding value.
|
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.
|
mean
mean(
name='mean', **kwargs
)
Mean.
mode
mode(
name='mode', **kwargs
)
Mode.
param_shapes
@classmethodparam_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
@classmethodparam_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
prob(
*args, **kwargs
)
Probability density/mass function.
The measure methods of `JointDistribution` (`log_prob`, `prob`, etc.)
can be called either by passing a single structure of tensors or by using
named args for each part of the joint distribution state. For example,
jd = tfd.JointDistributionSequential([ tfd.Normal(0., 1.), lambda z: tfd.Normal(z, 1.) ], validate_args=True) jd.dtype # ==> [tf.float32, tf.float32] z, x = sample = jd.sample() # The following calling styles are all permissable and produce the exactly # the same output. assert (jd.prob(sample) == jd.prob(value=sample) == jd.prob(z, x) == jd.prob(z=z, x=x) == jd.prob(z, x=x)) # These calling possibilities also imply that one can also use `*` # expansion, if `sample` is a sequence: jd.prob(*sample) # and similarly, if `sample` is a map, one can use `**` expansion: jd.prob(**sample)
`JointDistribution` component distributions names are resolved via
`jd._flat_resolve_names()`, which is implemented by each `JointDistribution`
subclass (see subclass documentation for details). Generally, for components
where a name was provided---
either explicitly as the `name` argument to a distribution or as a key in a
dict-valued JointDistribution, or implicitly, e.g., by the argument name of
a `JointDistributionSequential` distribution-making function---the provided
name will be used. Otherwise the component will receive a dummy name; these
may change without warning and should not be relied upon.
Note: not all `JointDistribution` subclasses support all calling styles;
for example, `JointDistributionNamed` does not support positional arguments
(aka "unnamed arguments") unless the provided model specifies an ordering of
variables (i.e., is an `collections.OrderedDict` or `collections.namedtuple`
rather than a plain `dict`).
Note: care is taken to resolve any potential ambiguity---this is generally
possible by inspecting the structure of the provided argument and "aligning"
it to the joint distribution output structure (defined by `jd.dtype`). For
example,
trivial_jd = tfd.JointDistributionSequential([tfd.Exponential(1.)]) trivial_jd.dtype # => [tf.float32] trivial_jd.prob([4.]) # ==> Tensor with shape `[]`. prob = trivial_jd.prob(4.) # ==> Tensor with shape `[]`.
Notice that in the first call, `[4.]` is interpreted as a list of one
scalar while in the second call the input is a scalar. Hence both inputs
result in identical scalar outputs. If we wanted to pass an explicit
vector to the `Exponential` component---creating a vector-shaped batch
of `prob`s---we could instead write
`trivial_jd.prob(np.array([4]))`.
Args:
*args: Positional arguments: a `value` structure or component values
(see above).
**kwargs: Keyword arguments: a `value` structure or component values
(see above). May also include `name`, specifying a Python string name
for ops generated by this method.
| Returns | |
|---|---|
prob
|
a Tensor of shape sample_shape(x) + self.batch_shape with
values of type self.dtype.
|
prob_parts
prob_parts(
value, name='prob_parts'
)
Log probability density/mass function.
| Args | |
|---|---|
value
|
list of Tensors in distribution_fn order for which we compute
the prob_parts and to parameterize other ("downstream") distributions.
|
name
|
name prepended to ops created by this function.
Default value: "prob_parts".
|
| Returns | |
|---|---|
prob_parts
|
a tuple of Tensors representing the prob for
each distribution_fn evaluated at each corresponding value.
|
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.
|
resolve_graph
resolve_graph(
distribution_names=None, leaf_name='x'
)
Creates a tuple of tuples of dependencies.
This function is experimental. That said, we encourage its use
and ask that you report problems to tfprobability@tensorflow.org.
| Args | |
|---|---|
distribution_names
|
list of str or None names corresponding to each
of model elements. (Nones are expanding into the
appropriate str.)
|
leaf_name
|
str used when no maker depends on a particular
model element.
|
| Returns | |
|---|---|
graph
|
tuple of (str tuple) pairs representing the name of each
distribution (maker) and the names of its dependencies.
|
Example
d = tfd.JointDistributionSequential([
tfd.Independent(tfd.Exponential(rate=[100, 120]), 1),
lambda e: tfd.Gamma(concentration=e[..., 0], rate=e[..., 1]),
tfd.Normal(loc=0, scale=2.),
lambda n, g: tfd.Normal(loc=n, scale=g),
])
d.resolve_graph()
# ==> (
# ('e', ()),
# ('g', ('e',)),
# ('n', ()),
# ('x', ('n', 'g')),
# )
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
|
Python integer or tfp.util.SeedStream instance, for seeding PRNG.
|
name
|
name to give to the op. |
**kwargs
|
Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
samples
|
a Tensor with prepended dimensions sample_shape.
|
sample_distributions
sample_distributions(
sample_shape=(), seed=None, value=None, name='sample_distributions', **kwargs
)
Generate samples and the (random) distributions.
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 generating random numbers. |
value
|
list of Tensors in distribution_fn order to use to
parameterize other ("downstream") distribution makers.
Default value: None (i.e., draw a sample from each distribution).
|
name
|
name prepended to ops created by this function.
Default value: "sample_distributions".
|
**kwargs
|
This is an alternative to passing a value, and achieves the
same effect. Named arguments will be used to parameterize other
dependent ("downstream") distribution-making functions. If a value
argument is also provided, raises a ValueError.
|
| Returns | |
|---|---|
distributions
|
a tuple of Distribution instances for each of
distribution_fn.
|
samples
|
a tuple of Tensors with prepended dimensions sample_shape
for each of distribution_fn.
|
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.
|
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().
|
__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.stateless_normal([5, 3, 2, 2])
cov = tf.matmul(x, x, transpose_b=True)
chol = tf.linalg.cholesky(cov)
loc = tf.random.stateless_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__()