Models

class lgbn.models.BayesianNetwork

A Bayesian Network.

A Bayesian network is a directed acyclic graph where each node is a random variable with a distribution conditional on the parent nodes.

add_cpd(cpd: CPD) → None

Add a conditional probability distribution to the network.

Note

Also adds the node and edges to the underlying networkx.DiGraph. If there already is a conditional probability distribution it is replaced and new edges are added, but previous edges not present in the new distribution will not be removed.

Parameters

cpd (CPD) – A conditional probability distribution

apply_op(op)

Modify the network according to the given operation.

An operation is an edge together with an action (add edge, remove edge, flip edge).

Parameters

op – A tuple (action, (u, v)) where action is one of +, - or F and (u, v) is an edge.

Raises

  • NotImplementedError – If the given action is not supported.

  • ValueError – If the edge is not in the network and operation requires editing it. (This is actually raised by networkx.DiGraph.remove_edge.)

cpd_class

The class used to instantiated CPDs when loading from a dict via .from_dict(data).

alias of CPD

cpds

A dictionary mapping node identifiers to Conditional Probability Distributions.

alias of Dict[Any, CPD]

classmethod from_dict(data)

Load Bayesian network from a dict.

Parameters

data (Sequence[Dict[str, Any]]) – A list of dictionaries corresponding to CPDs. See CPD.to_dict for more information on the format.

See also

to_dict, CPD.from_dict

Notes

This method expects the data to be sorted by node in topological order, so that a node always comes before its children. This is the way to_dict generates dictionaries.

to_dict()

Serializes the Bayesian network into a list of dictionaries.

Each dictionary is the result of serializing a CPD via CPD.to_dict.

update_cpds_from_structure() → None

Updates the parents attribute in each CPD to match the current graph structure.

Tip

Use this method after updating the network structure (e.g. via learning).

class lgbn.models.CPD(node: Any, parents: Optional[tuple[Any]] = None)

A conditional probability distribution for a node.which also references the node’s parents.s

In a BayesianNetwork the probability distributions of the nodes are specified via CPDs or Conditional Probability distributions. These classes represent the probability distributions of the random variables in the nodes of a Bayesian network, which in general are conditioned on the parent nodes.

Note

This is a base class which cannot actually be used.

See also

LinearGaussianCPD

A conditional probability distribution for linear Gaussian Bayesian networks.

classmethod from_dict(data: Dict[str, Any])

Loads this conditional probability distribution from a dict.

to_dict() → Dict[str, Any]

Serializes this conditional probability distribution into a dict.

class lgbn.models.LinearGaussianBayesianNetwork

A Bayesian network where every node has a Gaussian distribution, where the mean of each node is a linear combination of its parents plus a bias factor and the standard deviations of the nodes are independent.

The joint distribution of these networks also a Gaussian distribution, the parameters of which can be obtained via the to_joint_gaussian method.

cpd_class

alias of LinearGaussianCPD

to_joint_gaussian()

Get the equivalent multivariate Gaussian distribution to this Bayesian network.

Returns a scipy.stats.multivariate_normal frozen random variable which has attributes mean (vector of means) and cov (covariance matrix).

Returns

A frozen random variable.

Return type

scipy.stats.multivariate_normal

Notes

Linear Gaussian Bayesian networks have a joint probability distribution that is also normal, and thus this method is well defined. See p. 252 of 1 and pp. 370-371 of 2.

References

2

C. M. Bishop, Pattern recognition and machine learning. New York: Springer, 2006.

class lgbn.models.LinearGaussianCPD(node: Any, mean: Optional[float] = 0, var: Optional[float] = 1, parents: Optional[tuple[Any]] = None, weights: Optional[tuple[float]] = None)

A linear Gaussian conditional probability distribution.

A linear Gaussian conditional probability distribution is normal distribution where the mean is a linear combination of the means of the parent nodes plus a bias term, i.e. if this node (X) has parents \(U_1, \ldots, U_k\) then

\[p(X) = N(X \mid \mu + w_1 \mu_{U_1} + \ldots + w_k \mu_{U_k}, \sigma^2),\]

where \(\mu\) is specified via the mean parameter, \(\sigma^2\) via the var parameter and \(w_1, \ldots, w_k\) via the weights parameter.

mle(data: DataFrame)

Find maximum likelihood estimate for mean, variance and weights given the data and the dependencies on the parents.

Parameters

data (pandas.DataFrame) – A DataFrame with one row per observation and one column per variable.

Returns

A new conditional probability distribution where the parameters are set to the ML estimates.

Return type

LinearGaussianCPD

Notes

Maximum likelihood estimation of parameters is computed using the sufficient statistics approach described in section 17.2.4 of 1.

References

1(1,2)

D. Koller and N. Friedman, Probabilistic graphical models: principles and techniques. Cambridge, MA: MIT Press, 2009.

to_dict()

Serializes this conditional probability distribution into a dict.