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|
State space model for a semi-local linear trend.
Inherits From: LinearGaussianStateSpaceModel, AutoCompositeTensorDistribution, Distribution
tfp.substrates.jax.sts.SemiLocalLinearTrendStateSpaceModel(
num_timesteps,
level_scale,
slope_mean,
slope_scale,
autoregressive_coef,
initial_state_prior,
observation_noise_scale=0.0,
name=None,
**linear_gaussian_ssm_kwargs
)
A state space model (SSM) posits a set of latent (unobserved) variables that
evolve over time with dynamics specified by a probabilistic transition model
p(z[t+1] | z[t]). At each timestep, we observe a value sampled from an
observation model conditioned on the current state, p(x[t] | z[t]). The
special case where both the transition and observation models are Gaussians
with mean specified as a linear function of the inputs, is known as a linear
Gaussian state space model and supports tractable exact probabilistic
calculations; see tfp.distributions.LinearGaussianStateSpaceModel for
details.
The semi-local linear trend model is a special case of a linear Gaussian
SSM, in which the latent state posits a level and slope. The level
evolves via a Gaussian random walk centered at the current slope, while
the slope follows a first-order autoregressive (AR1) process with
mean slope_mean:
level[t] = level[t-1] + slope[t-1] + Normal(0., level_scale)
slope[t] = (slope_mean +
autoregressive_coef * (slope[t-1] - slope_mean) +
Normal(0., slope_scale))
The latent state is the two-dimensional tuple [level, slope]. The
level is observed at each timestep.
The parameters level_scale, slope_mean, slope_scale,
autoregressive_coef, and observation_noise_scale are each (a batch of)
scalars. The batch shape of this Distribution is the broadcast batch shape
of these parameters and of the initial_state_prior.
Mathematical Details
The semi-local linear trend model implements a
tfp.distributions.LinearGaussianStateSpaceModel with latent_size = 2
and observation_size = 1, following the transition model:
transition_matrix = [[1., 1.]
[0., autoregressive_coef]]
transition_noise ~ N(loc=slope_mean - autoregressive_coef * slope_mean,
scale=diag([level_scale, slope_scale]))
which implements the evolution of [level, slope] described above, and
the observation model:
observation_matrix = [[1., 0.]]
observation_noise ~ N(loc=0, scale=observation_noise_scale)
which picks out the first latent component, i.e., the level, as the
observation at each timestep.
Examples
A simple model definition:
semilocal_trend_model = SemiLocalLinearTrendStateSpaceModel(
num_timesteps=50,
level_scale=0.5,
slope_mean=0.2,
slope_scale=0.5,
autoregressive_coef=0.9,
initial_state_prior=tfd.MultivariateNormalDiag(scale_diag=[1., 1.]))
y = semilocal_trend_model.sample() # y has shape [50, 1]
lp = semilocal_trend_model.log_prob(y) # log_prob is scalar
Passing additional parameter dimensions constructs a batch of models. The overall batch shape is the broadcast batch shape of the parameters:
semilocal_trend_model = SemiLocalLinearTrendStateSpaceModel(
num_timesteps=50,
level_scale=tf.ones([10]),
slope_mean=0.2,
slope_scale=0.5,
autoregressive_coef=0.9,
initial_state_prior=tfd.MultivariateNormalDiag(
scale_diag=tf.ones([10, 10, 2])))
y = semilocal_trend_model.sample(5) # y has shape [5, 10, 10, 50, 1]
lp = semilocal_trend_model.log_prob(y) # lp has shape [5, 10, 10]
Methods
backward_smoothing_pass
backward_smoothing_pass(
filtered_means, filtered_covs, predicted_means, predicted_covs
)
Run the backward pass in Kalman smoother.
The backward smoothing is using Rauch, Tung and Striebel smoother as
as discussed in section 18.3.2 of Kevin P. Murphy, 2012, Machine Learning:
A Probabilistic Perspective, The MIT Press. The inputs are returned by
forward_filter function.
| Args | |
|---|---|
filtered_means
|
Means of the per-timestep filtered marginal
distributions p(z[t] | x[:t]), as a Tensor of shape
sample_shape(x) + batch_shape + [num_timesteps, latent_size].
|
filtered_covs
|
Covariances of the per-timestep filtered marginal
distributions p(z[t] | x[:t]), as a Tensor of shape
sample_shape(x) + batch_shape + [num_timesteps, latent_size,
latent_size].
|
predicted_means
|
Means of the per-timestep predictive
distributions over latent states, p(z[t+1] | x[:t]), as a
Tensor of shape sample_shape(x) + batch_shape +
[num_timesteps, latent_size].
|
predicted_covs
|
Covariances of the per-timestep predictive
distributions over latent states, p(z[t+1] | x[:t]), as a
Tensor of shape sample_shape(x) + batch_shape +
[num_timesteps, latent_size, latent_size].
|
| Returns | |
|---|---|
posterior_means
|
Means of the smoothed marginal distributions
p(z[t] | x[1:T]), as a Tensor of shape
sample_shape(x) + batch_shape + [num_timesteps, latent_size],
which is of the same shape as filtered_means.
|
posterior_covs
|
Covariances of the smoothed marginal distributions
p(z[t] | x[1:T]), as a Tensor of shape
sample_shape(x) + batch_shape + [num_timesteps, latent_size,
latent_size]. which is of the same shape as filtered_covs.
|
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
@classmethodexperimental_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 Tensors, with prepended dimensions
sample_shape.
|
log_prob
|
a Tensor of shape sample_shape(x) + self.batch_shape with
values of type self.dtype.
|
forward_filter
forward_filter(
x, mask=None, final_step_only=False
)
Run a Kalman filter over a provided sequence of outputs.
Note that the returned values filtered_means, predicted_means, and
observation_means depend on the observed time series x, while the
corresponding covariances are independent of the observed series; i.e., they
depend only on the model itself. This means that the mean values have shape
concat([sample_shape(x), batch_shape, [num_timesteps,
{latent/observation}_size]]), while the covariances have shape
concat[(batch_shape, [num_timesteps, {latent/observation}_size,
{latent/observation}_size]]), which does not depend on the sample shape.
| Args | |
|---|---|
x
|
a float-type Tensor with rightmost dimensions
[num_timesteps, observation_size] matching
self.event_shape. Additional dimensions must match or be
broadcastable to self.batch_shape; any further dimensions
are interpreted as a sample shape.
|
mask
|
optional bool-type Tensor with rightmost dimension
[num_timesteps]; True values specify that the value of x
at that timestep is masked, i.e., not conditioned on. Additional
dimensions must match or be broadcastable to self.batch_shape; any
further dimensions must match or be broadcastable to the sample
shape of x.
Default value: None (falls back to self.mask).
|
final_step_only
|
optional Python bool. If True, the num_timesteps
dimension is omitted from all return values and only the value from the
final timestep is returned (in this case, log_likelihoods will
be the cumulative log marginal likelihood). This may be significantly
more efficient than returning all values (although note that no
efficiency gain is expected when self.experimental_parallelize=True).
Default value: False.
|
| Returns | |
|---|---|
log_likelihoods
|
Per-timestep log marginal likelihoods log
p(x[t] | x[:t-1]) evaluated at the input x, as a Tensor
of shape sample_shape(x) + batch_shape + [num_timesteps].
If final_step_only is True, this will instead be the
cumulative log marginal likelihood at the final step.
|
filtered_means
|
Means of the per-timestep filtered marginal
distributions p(z[t] | x[:t]), as a Tensor of shape
sample_shape(x) + batch_shape + [num_timesteps, latent_size].
|
filtered_covs
|
Covariances of the per-timestep filtered marginal
distributions p(z[t] | x[:t]), as a Tensor of shape
sample_shape(x) + batch_shape + [num_timesteps, latent_size,
latent_size]. Since posterior covariances do not depend on observed
data, some implementations may return a Tensor whose shape omits the
initial sample_shape(x).
|
predicted_means
|
Means of the per-timestep predictive
distributions over latent states, p(z[t+1] | x[:t]), as a
Tensor of shape sample_shape(x) + batch_shape +
[num_timesteps, latent_size].
|
predicted_covs
|
Covariances of the per-timestep predictive
distributions over latent states, p(z[t+1] | x[:t]), as a
Tensor of shape sample_shape(x) + batch_shape +
[num_timesteps, latent_size, latent_size]. Since posterior covariances
do not depend on observed data, some implementations may return a
Tensor whose shape omits the initial sample_shape(x).
|
observation_means
|
Means of the per-timestep predictive
distributions over observations, p(x[t] | x[:t-1]), as a
Tensor of shape sample_shape(x) + batch_shape +
[num_timesteps, observation_size].
|
observation_covs
|
Covariances of the per-timestep predictive
distributions over observations, p(x[t] | x[:t-1]), as a
Tensor of shape sample_shape(x) + batch_shape + [num_timesteps,
observation_size, observation_size]. Since posterior covariances
do not depend on observed data, some implementations may return a
Tensor whose shape omits the initial sample_shape(x).
|
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.
|
latent_size_tensor
latent_size_tensor()
latents_to_observations
latents_to_observations(
latent_means, latent_covs
)
Push latent means and covariances forward through the observation model.
| Args | |
|---|---|
latent_means
|
float Tensor of shape [..., num_timesteps, latent_size]
|
latent_covs
|
float Tensor of shape
[..., num_timesteps, latent_size, latent_size].
|
| Returns | |
|---|---|
observation_means
|
float Tensor of shape
[..., num_timesteps, observation_size]
|
observation_covs
|
float Tensor of shape
[..., num_timesteps, observation_size, observation_size]
|
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.
Additional documentation from LinearGaussianStateSpaceModel:
kwargs:
mask: optional bool-typeTensorwith rightmost dimension[num_timesteps];Truevalues specify that the value ofxat that timestep is masked, i.e., not conditioned on. Additional dimensions must match or be broadcastable toself.batch_shape; any further dimensions must match or be broadcastable to the sample shape ofx. Default value:None(falls back toself.mask).
| 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.
|
mean
mean(
name='mean', **kwargs
)
Mean.
mode
mode(
name='mode', **kwargs
)
Mode.
observation_size_tensor
observation_size_tensor()
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.
|
parameter_properties
@classmethodparameter_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_shapeand_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 toParameterProperties`
instances.
|
| Raises | |
|---|---|
NotImplementedError
|
if the distribution class does not implement
_parameter_properties.
|
posterior_marginals
posterior_marginals(
x, mask=None
)
Run a Kalman smoother to return posterior mean and cov.
Note that the returned values smoothed_means depend on the observed
time series x, while the smoothed_covs are independent
of the observed series; i.e., they depend only on the model itself.
This means that the mean values have shape concat([sample_shape(x),
batch_shape, [num_timesteps, {latent/observation}_size]]),
while the covariances have shape concat[(batch_shape, [num_timesteps,
{latent/observation}_size, {latent/observation}_size]]), which
does not depend on the sample shape.
This function only performs smoothing. If the user wants the
intermediate values, which are returned by filtering pass forward_filter,
one could get it by:
(log_likelihoods,
filtered_means, filtered_covs,
predicted_means, predicted_covs,
observation_means, observation_covs) = model.forward_filter(x)
smoothed_means, smoothed_covs = model.backward_smoothing_pass(
filtered_means, filtered_covs,
predicted_means, predicted_covs)
where x is an observation sequence.
| Args | |
|---|---|
x
|
a float-type Tensor with rightmost dimensions
[num_timesteps, observation_size] matching
self.event_shape. Additional dimensions must match or be
broadcastable to self.batch_shape; any further dimensions
are interpreted as a sample shape.
|
mask
|
optional bool-type Tensor with rightmost dimension
[num_timesteps]; True values specify that the value of x
at that timestep is masked, i.e., not conditioned on. Additional
dimensions must match or be broadcastable to self.batch_shape; any
further dimensions must match or be broadcastable to the sample
shape of x.
Default value: None (falls back to self.mask).
|
| Returns | |
|---|---|
smoothed_means
|
Means of the per-timestep smoothed
distributions over latent states, p(z[t] | x[:T]), as a
Tensor of shape sample_shape(x) + batch_shape +
[num_timesteps, observation_size].
|
smoothed_covs
|
Covariances of the per-timestep smoothed
distributions over latent states, p(z[t] | x[:T]), as a
Tensor of shape sample_shape(mask) + batch_shape + [num_timesteps,
observation_size, observation_size]. Note that the covariances depend
only on the model and the mask, not on the data, so this may have fewer
dimensions than filtered_means.
|
posterior_sample
posterior_sample(
x, sample_shape=(), mask=None, seed=None, name=None
)
Draws samples from the posterior over latent trajectories.
This method uses Durbin-Koopman sampling [1], an efficient algorithm to
sample from the posterior latents of a linear Gaussian state space model.
The cost of drawing a sample is equal to the cost of drawing a prior
sample (.sample(sample_shape)), plus the cost of Kalman smoothing (
.posterior_marginals(...) on both the observed time series and the
prior sample. This method is significantly more efficient in graph mode,
because it uses only the posterior means and can elide the unneeded
calculation of marginal covariances.
[1] Durbin, J. and Koopman, S.J. A simple and efficient simulation smoother for state space time series analysis. Biometrika 89(3):603-615, 2002. https://www.jstor.org/stable/4140605
| Args | |
|---|---|
x
|
a float-type Tensor with rightmost dimensions
[num_timesteps, observation_size] matching
self.event_shape. Additional dimensions must match or be
broadcastable with self.batch_shape.
|
sample_shape
|
int Tensor shape of samples to draw.
Default value: ().
|
mask
|
optional bool-type Tensor with rightmost dimension
[num_timesteps]; True values specify that the value of x
at that timestep is masked, i.e., not conditioned on. Additional
dimensions must match or be broadcastable with self.batch_shape and
x.shape[:-2].
Default value: None (falls back to self.mask).
|
seed
|
PRNG seed; see tfp.random.sanitize_seed for details.
|
name
|
Python str name for ops generated by this method.
|
| Returns | |
|---|---|
latent_posterior_sample
|
Float Tensor of shape
concat([sample_shape, batch_shape, [num_timesteps, latent_size]]),
where batch_shape is the broadcast shape of self.batch_shape,
x.shape[:-2], and mask.shape[:-1], representing n samples from
the posterior over latent states given the observed value x.
|
prob
prob(
value, name='prob', **kwargs
)
Probability density/mass function.
Additional documentation from LinearGaussianStateSpaceModel:
kwargs:
mask: optional bool-typeTensorwith rightmost dimension[num_timesteps];Truevalues specify that the value ofxat that timestep is masked, i.e., not conditioned on. Additional dimensions must match or be broadcastable toself.batch_shape; any further dimensions must match or be broadcastable to the sample shape ofx. Default value:None(falls back toself.mask).
| 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().
|
__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__()