tfsnippet.bayes¶

class tfsnippet.bayes.BayesianNet(observed=None)¶

Bases: object

Bayesian networks.

BayesianNet is a class which helps to construct Bayesian networks and to derive the variational lower-bounds. It is inspired by zhusuan.BayesianNet.

Due to the expressive limitations of TensorFlow, it is hard to build BayesianNet with the concept of random variables. Instead, we only collect StochasticTensor objects, i.e., tensors sampled from the distributions of these random variables. Thus BayesianNet is actually a collection of (multiple) ancestral samples from the random variables. Fortunately, we can approximate most interested statistics of the desired random variables with these samples, by using Monte Carlo methods. For example, obtaining the expectation of a random variable by averaging over multiple samples from it. The StochasticTensor objects are called stochastic nodes within the context of BayesianNet.

To build a Bayesian network, first obtain a BayesianNet:

net = tfsnippet.bayes.BayesianNet()

Then add stochastic nodes into the network:

A Bayesian Linear Regression example, as of zhusuan.BayesianNet:

\[ \begin{align}\begin{aligned}w \sim N(0, \alpha^2 I)\\y \sim N(w^Tx, \beta^2)\end{aligned}\end{align} \]

from tfsnippet.bayes import BayesianNet()
from tfsnippet.distributions import Normal

def bayesian_linear_regression(x, alpha, beta, observed=None):
    net = BayesianNet(observed)
    w = net.add('w', Normal(mean=0., logstd=tf.log(alpha)))
    y_mean = tf.reduce_sum(tf.expand_dims(w, 0) * x, 1)
    y = net.add('y', Normal(mean=y_mean, logstd=tf.log(beta)))
    return net

To observe any stochastic nodes in the network, pass a dictionary mapping of (name, Tensor) as observed when constructing BayesianNet. For example:

model = bayesian_linear_regression(..., observed={'w': w_obs})

After construction, BayesianNet supports queries on the network.

# get samples of random variable y following generative process
# in the network
model.output('y')

# because w is observed in this case, its observed value will be
# returned
model.output('w')

# also multiple outputs can be fetched together
model.outputs(['y', 'w'])

# get local log probability values of w and y, which returns
# log p(w) and log p(y|w, x)
model.local_log_probs(['w', 'y'])

# query many quantities at the same time
model.query(['w', 'y'])

See also

zhusuan.BayesianNet

__contains__(name)¶: Test whether or not a stochastic node with name exists.

__getitem__(name)¶

Get StochasticTensor of a stochastic node.

Parameters:	name (str) – Name of the queried stochastic node.
Returns:	`StochasticTensor` of the queried node.
Return type:	StochasticTensor
Raises:	`KeyError` – If non-exist name is queried.

__init__(observed=None)¶

Construct the BayesianNet.

Parameters:	observed – Dict of `(str, tf.Tensor)`, the names of stochastic nodes and their observations.

__iter__()¶: Get an iterator of the stochastic node names.

add(name, distribution, n_samples=None, group_ndims=0, is_reparameterized=None, flow=None)¶

Add a stochastic node to the network.

A StochasticTensor will be created for this node. If name exists in observed dict, its value will be used as the observation of this node. Otherwise samples will be taken from distribution.

Parameters:	name (str) – Name of the stochastic node. distribution (Distribution or zhusuan.distributions.Distribution) – Distribution where the samples should be taken from. n_samples (int or tf.Tensor) – Number of samples to take. If specified, n_samples will be taken, with a dedicated sampling dimension `[n_samples]` at the front. If not specified, just one sample will be taken, without the dedicated dimension. group_ndims (int or tf.Tensor) – Number of dimensions at the end of `[n_samples] + batch_shape` to be considered as events group. (default 0) is_reparameterized – Whether or not the re-parameterization trick should be applied? (default `None`, following the setting of distribution) flow (Flow) – If specified, transform distribution by the flow.
Returns:	The sampled stochastic tensor.
Return type:	StochasticTensor
Raises:	`TypeError` – If name is not a str, or distribution is a `TransformedDistribution`. `KeyError` – If `StochasticTensor` with name already exists. `ValueError` – If transform cannot be applied.

chain(model_builder, latent_names=None, latent_axis=None, observed=None, **kwargs)¶: Alias for variational_chain().

get(name)¶

Get StochasticTensor of a stochastic node.

Parameters:	name (str) – Name of the queried stochastic node.
Returns:	`StochasticTensor` of the queried node, or `None` if no node exists with name.
Return type:	StochasticTensor

local_log_prob(name)¶

Get the log-density of a stochastic node.

Parameters:	name (str) – Name of the queried stochastic node.
Returns:	Log-density of the queried stochastic node.
Return type:	tf.Tensor
Raises:	`KeyError` – If non-exist name is queried.

local_log_probs(names)¶

Get the log-densities of stochastic nodes.

Parameters:	names (Iterable[str]) – Names of the queried stochastic nodes.
Returns:	Log-densities of the queried stochastic nodes.
Return type:	list[tf.Tensor]
Raises:	`KeyError` – If non-exist name is queried.

observed¶

Get the read-only dict of observations.

Returns:	The read-only dict of observations.
Return type:	collections.Mapping[str, tf.Tensor]

output(name)¶

Get the output of a stochastic node. The output of a stochastic node is its StochasticTensor.tensor.

Parameters:	name (str) – Name of the queried stochastic node.
Returns:	Output of the queried stochastic node.
Return type:	tf.Tensor
Raises:	`KeyError` – If non-exist name is queried.

outputs(names)¶

Get the outputs of stochastic nodes. The output of a stochastic node is its StochasticTensor.tensor.

Parameters:	names (Iterable[str]) – Names of the queried stochastic nodes.
Returns:	Outputs of the queried stochastic nodes.
Return type:	list[tf.Tensor]
Raises:	`KeyError` – If non-exist name is queried.

query(names)¶

Get the outputs and log-densities of stochastic node(s).

Parameters:	names (Iterable[str]) – Names of the queried stochastic nodes.
Returns:	Tuples of (output, log-prob) of the queried stochastic nodes.
Return type:	list[(tf.Tensor, tf.Tensor)]
Raises:	`KeyError` – If non-exist name is queried.

variational_chain(model_builder, latent_names=None, latent_axis=None, observed=None, **kwargs)¶

Treat this BayesianNet as variational, and build the model net chained after this variational net.

Parameters:

model_builder – Function which receives the observed dict, and produce the model BayesianNet or a tuple of the model BayesianNet and the log-joint of the model.
latent_names (Iterable[str]) – Names of the nodes to be considered as latent variables in this BayesianNet. All these variables will be fed into model_builder as observed variables, overriding the observations in observed. (default all the variables in this BayesianNet)
latent_axis – The axis or axes to be considered as the sampling dimensions of latent variables. The specified axes will be summed up in the variational lower-bounds or training objectives. (default None)
observed – Dict of (name, observation) fed into model_builder. (default None)
**kwargs – Additional named arguments passed to model_builder.

Returns:

The object that holds this: BayesianNet as the variational net, the constructed model net, and the VariationalInference object for obtaining the variational lower-bounds and training objectives.

Return type:

tfsnippet.variational.VariationalChain

tfsnippet.bayes¶

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