Dynamic Bayesian Network (DBN)

class pgmpy.models.DynamicBayesianNetwork.DynamicBayesianNetwork(ebunch=None)[source]

Bases: DAG

Base class for Dynamic Bayesian Network

This is a time variant model of the static Bayesian model, where each time-slice has some static nodes and is then replicated over a certain time period.

The nodes can be any hashable python objects.

Parameters:

ebunch (Data to initialize graph. If data=None (default) an empty) – graph is created. The data can be an edge list, or any NetworkX graph object

Examples

Create an empty Dynamic Bayesian Network with no nodes and no edges: >>> from pgmpy.models import DynamicBayesianNetwork as DBN >>> dbn = DBN()

Adding nodes and edges inside the Dynamic Bayesian Network. A single node can be added using the method below. For adding edges we need to specify the time slice since edges can be across different time slices.

For example for a network as [image](http://s8.postimg.org/aaybw4x2t/Blank_Flowchart_New_Page_1.png), we will need to add all the edges in the 2-TBN as:

>>> dbn.add_edges_from([(('D', 0), ('G', 0)), (('I', 0), ('G', 0)),
...                     (('G', 0), ('L', 0)), (('D', 0), ('D', 1)),
...                     (('I', 0), ('I', 1)), (('G', 0), ('G', 1)),
...                     (('G', 0), ('L', 1)), (('L', 0), ('L', 1))])

We can query the edges and nodes in the network as: >>> dbn.nodes() [‘G’, ‘D’, ‘I’, ‘L’] >>> dbn.edges() [((‘D’, 1), (‘G’, 1)), ((‘I’, 0), (‘G’, 0)), ((‘I’, 0), (‘I’, 1)),

((‘I’, 1), (‘G’, 1)), ((‘G’, 0), (‘L’, 0)), ((‘G’, 0), (‘G’, 1)), ((‘G’, 0), (‘L’, 1)), ((‘D’, 0), (‘G’, 0)), ((‘D’, 0), (‘D’, 1)), ((‘L’, 0), (‘L’, 1)), ((‘G’, 1), (‘L’, 1))]

If any variable is not present in the network while adding an edge, pgmpy will automatically add that variable to the network.

But for adding nodes to the model we don’t need to specify the time slice as it is common in all the time slices. And therefore pgmpy automatically replicated it all the time slices. For example, for adding a new variable S in the above network we can simply do: >>> dbn.add_node(‘S’) >>> dbn.nodes() [‘S’, ‘G’, ‘D’, ‘I’, ‘L’]

Public Methods

add_node add_nodes_from add_edges add_edges_from add_cpds initialize_initial_state inter_slice intra_slice copy

active_trail_nodes(variables, observed=None, include_latents=False)[source]

Returns a dictionary with the given variables as keys and all the nodes reachable from that respective variable as values.

Parameters:

  • variables (str or array like) – variables whose active trails are to be found.

  • observed (List of nodes (optional)) – If given the active trails would be computed assuming these nodes to be observed.

  • include_latents (boolean (default: False)) – Whether to include the latent variables in the returned active trail nodes.

Examples

>>> from pgmpy.base import DAG
>>> student = DAG()
>>> student.add_nodes_from(['diff', 'intel', 'grades'])
>>> student.add_edges_from([('diff', 'grades'), ('intel', 'grades')])
>>> student.active_trail_nodes('diff')
{'diff': {'diff', 'grades'}}
>>> student.active_trail_nodes(['diff', 'intel'], observed='grades')
{'diff': {'diff', 'intel'}, 'intel': {'diff', 'intel'}}

References

Details of the algorithm can be found in ‘Probabilistic Graphical Model Principles and Techniques’ - Koller and Friedman Page 75 Algorithm 3.1

add_cpds(*cpds)[source]

This method adds the cpds to the Dynamic Bayesian Network. Note that while adding variables and the evidence in cpd, they have to be of the following form (node_name, time_slice) Here, node_name is the node that is inserted while the time_slice is an integer value, which denotes the index of the time_slice that the node belongs to.

Parameters:

cpds (list, set, tuple (array-like)) – List of CPDs which are to be associated with the model. Each CPD should be an instance of TabularCPD.

Examples

>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> from pgmpy.factors.discrete import TabularCPD
>>> dbn = DBN()
>>> dbn.add_edges_from([(('D', 0),('G', 0)),(('I', 0),('G', 0)),(('D', 0),('D', 1)),(('I', 0),('I', 1))])
>>> grade_cpd = TabularCPD(('G', 0), 3, [[0.3, 0.05, 0.9, 0.5],
...                                      [0.4, 0.25, 0.08, 0.3],
...                                      [0.3, 0.7, 0.02, 0.2]],
...                        evidence=[('I', 0),('D', 0)],
...                        evidence_card=[2, 2])
>>> d_i_cpd = TabularCPD(('D',1), 2, [[0.6, 0.3],
...                                   [0.4, 0.7]],
...                      evidence=[('D',0)],
...                      evidence_card=[2])
>>> diff_cpd = TabularCPD(('D', 0), 2, [[0.6, 0.4]])
>>> intel_cpd = TabularCPD(('I', 0), 2, [[0.7, 0.3]])
>>> i_i_cpd = TabularCPD(('I', 1), 2, [[0.5, 0.4],
...                                    [0.5, 0.6]],
...                      evidence=[('I', 0)],
...                      evidence_card=[2])
>>> dbn.add_cpds(grade_cpd, d_i_cpd, diff_cpd, intel_cpd, i_i_cpd)
>>> dbn.get_cpds()
[<TabularCPD representing P(('G', 0):3 | ('I', 0):2, ('D', 0):2) at 0x7ff7f27b0cf8>,
 <TabularCPD representing P(('D', 1):2 | ('D', 0):2) at 0x7ff810b9c2e8>,
 <TabularCPD representing P(('D', 0):2) at 0x7ff7f27e6f98>,
 <TabularCPD representing P(('I', 0):2) at 0x7ff7f27e6ba8>,
 <TabularCPD representing P(('I', 1):2 | ('I', 0):2) at 0x7ff7f27e6668>]
add_edge(start, end, **kwargs)[source]

Add an edge between two nodes.

The nodes will be automatically added if they are not present in the network.

Parameters:

  • start (tuple) – Both the start and end nodes should specify the time slice as (node_name, time_slice). Here, node_name can be any hashable python object while the time_slice is an integer value, which denotes the time slice that the node belongs to.

  • end (tuple) – Both the start and end nodes should specify the time slice as (node_name, time_slice). Here, node_name can be any hashable python object while the time_slice is an integer value, which denotes the time slice that the node belongs to.

Examples

>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> model = DBN()
>>> model.add_nodes_from(['D', 'I'])
>>> model.add_edge(('D',0), ('I',0))
>>> sorted(model.edges())
[(('D', 0), ('I', 0)), (('D', 1), ('I', 1))]
add_edges_from(ebunch, **kwargs)[source]

Add all the edges in ebunch.

If nodes referred in the ebunch are not already present, they will be automatically added. Node names can be any hashable python object.

Parameters:

ebunch (list, array-like) – List of edges to add. Each edge must be of the form of ((start, time_slice), (end, time_slice)).

Examples

>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> dbn = DBN()
>>> dbn.add_edges_from([(('D', 0), ('G', 0)), (('I', 0), ('G', 0))])
>>> dbn.nodes()
['G', 'I', 'D']
>>> dbn.edges()
[(('D', 1), ('G', 1)),
 (('I', 1), ('G', 1)),
 (('D', 0), ('G', 0)),
 (('I', 0), ('G', 0))]
add_node(node, **attr)[source]

Adds a single node to the Network

Parameters:

node (node) – A node can be any hashable Python object.

Examples

>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> dbn = DBN()
>>> dbn.add_node('A')
['A']
add_nodes_from(nodes, **attr)[source]

Add multiple nodes to the Network.

Parameters:

nodes (iterable container) – A container of nodes (list, dict, set, etc.).

Examples

>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> dbn = DBN()
>>> dbn.add_nodes_from(['A', 'B', 'C'])
add_weighted_edges_from(ebunch_to_add, weight='weight', **attr)

Add weighted edges in ebunch_to_add with specified weight attr

Parameters:

  • ebunch_to_add (container of edges) – Each edge given in the list or container will be added to the graph. The edges must be given as 3-tuples (u, v, w) where w is a number.

  • weight (string, optional (default= 'weight')) – The attribute name for the edge weights to be added.

  • attr (keyword arguments, optional (default= no attributes)) – Edge attributes to add/update for all edges.

See also

add_edge

add a single edge

add_edges_from

add multiple edges

Notes

Adding the same edge twice for Graph/DiGraph simply updates the edge data. For MultiGraph/MultiDiGraph, duplicate edges are stored.

When adding edges from an iterator over the graph you are changing, a RuntimeError can be raised with message: RuntimeError: dictionary changed size during iteration. This happens when the graph’s underlying dictionary is modified during iteration. To avoid this error, evaluate the iterator into a separate object, e.g. by using list(iterator_of_edges), and pass this object to G.add_weighted_edges_from.

Examples

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_weighted_edges_from([(0, 1, 3.0), (1, 2, 7.5)])

Evaluate an iterator over edges before passing it

>>> G = nx.Graph([(1, 2), (2, 3), (3, 4)])
>>> weight = 0.1
>>> # Grow graph by one new node, adding edges to all existing nodes.
>>> # wrong way - will raise RuntimeError
>>> # G.add_weighted_edges_from(((5, n, weight) for n in G.nodes))
>>> # correct way - note that there will be no self-edge for node 5
>>> G.add_weighted_edges_from(list((5, n, weight) for n in G.nodes))
property adj

Graph adjacency object holding the neighbors of each node.

This object is a read-only dict-like structure with node keys and neighbor-dict values. The neighbor-dict is keyed by neighbor to the edge-data-dict. So G.adj[3][2][‘color’] = ‘blue’ sets the color of the edge (3, 2) to “blue”.

Iterating over G.adj behaves like a dict. Useful idioms include for nbr, datadict in G.adj[n].items():.

The neighbor information is also provided by subscripting the graph. So for nbr, foovalue in G[node].data(‘foo’, default=1): works.

For directed graphs, G.adj holds outgoing (successor) info.

adjacency()

Returns an iterator over (node, adjacency dict) tuples for all nodes.

For directed graphs, only outgoing neighbors/adjacencies are included.

Returns:

adj_iter – An iterator over (node, adjacency dictionary) for all nodes in the graph.

Return type:

iterator

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> [(n, nbrdict) for n, nbrdict in G.adjacency()]
[(0, {1: {}}), (1, {0: {}, 2: {}}), (2, {1: {}, 3: {}}), (3, {2: {}})]
adjlist_inner_dict_factory

alias of dict

adjlist_outer_dict_factory

alias of dict

check_model()[source]

Check the model for various errors. This method checks for the following errors.

  • Checks if the sum of the probabilities in each associated CPD for each

    state is equal to 1 (tol=0.01).

  • Checks if the CPDs associated with nodes are consistent with their parents.

Returns:

boolean – according to the problem.

Return type:

True if everything seems to be order. Otherwise raises error

clear()

Remove all nodes and edges from the graph.

This also removes the name, and all graph, node, and edge attributes.

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.clear()
>>> list(G.nodes)
[]
>>> list(G.edges)
[]
clear_edges()

Remove all edges from the graph without altering nodes.

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.clear_edges()
>>> list(G.nodes)
[0, 1, 2, 3]
>>> list(G.edges)
[]
copy()[source]

Returns a copy of the Dynamic Bayesian Network.

Returns:

DynamicBayesianNetwork

Return type:

copy of the Dynamic Bayesian Network

Examples

>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> from pgmpy.factors.discrete import TabularCPD
>>> dbn = DBN()
>>> dbn.add_edges_from([(('D',0),('G',0)),(('I',0),('G',0)),(('D',0),('D',1)),(('I',0),('I',1))])
>>> grade_cpd =  TabularCPD(('G',0), 3, [[0.3, 0.05, 0.9,  0.5 ],
...                                      [0.4, 0.25, 0.08,  0.3],
...                                      [0.3,  0.7, 0.02, 0.2 ]],
...                         [('I', 0), ('D', 0)],[2,2])
>>> dbn.add_cpds(grade_cpd)
>>> dbn_copy = dbn.copy()
>>> dbn_copy.nodes()
['Z', 'G', 'I', 'D']
>>> dbn_copy.edges()
[(('I', 1), ('G', 1)),
(('I', 0), ('I', 1)),
(('I', 0), ('G', 0)),
(('D', 1), ('G', 1)),
(('D', 0), ('G', 0)),
(('D', 0), ('D', 1))]
>>> dbn_copy.get_cpds()
[<TabularCPD representing P(('G', 0):3 | ('I', 0):2, ('D', 0):2) at 0x7f13961a3320>]
property degree

A DegreeView for the Graph as G.degree or G.degree().

The node degree is the number of edges adjacent to the node. The weighted node degree is the sum of the edge weights for edges incident to that node.

This object provides an iterator for (node, degree) as well as lookup for the degree for a single node.

Parameters:

  • nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges incident to these nodes.

  • weight (string or None, optional (default=None)) – The name of an edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. The degree is the sum of the edge weights adjacent to the node.

Returns:

If multiple nodes are requested (the default), returns a DiDegreeView mapping nodes to their degree. If a single node is requested, returns the degree of the node as an integer.

Return type:

DiDegreeView or int

See also

in_degree, out_degree

Examples

>>> G = nx.DiGraph()  # or MultiDiGraph
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.degree(0)  # node 0 with degree 1
1
>>> list(G.degree([0, 1, 2]))
[(0, 1), (1, 2), (2, 2)]
do(nodes, inplace=False)

Applies the do operator to the graph and returns a new DAG with the transformed graph.

The do-operator, do(X = x) has the effect of removing all edges from the parents of X and setting X to the given value x.

Parameters:

  • nodes (list, array-like) – The names of the nodes to apply the do-operator for.

  • inplace (boolean (default: False)) – If inplace=True, makes the changes to the current object, otherwise returns a new instance.

Returns:

Modified DAG – A new instance of DAG modified by the do-operator

Return type:

pgmpy.base.DAG

Examples

Initialize a DAG >>> graph = DAG() >>> graph.add_edges_from([(‘X’, ‘A’), … (‘A’, ‘Y’), … (‘A’, ‘B’)]) >>> # Applying the do-operator will return a new DAG with the desired structure. >>> graph_do_A = graph.do(‘A’) >>> # Which we can verify is missing the edges we would expect. >>> graph_do_A.edges OutEdgeView([(‘A’, ‘B’), (‘A’, ‘Y’)])

References

Causality: Models, Reasoning, and Inference, Judea Pearl (2000). p.70.

edge_attr_dict_factory

alias of dict

edge_subgraph(edges)

Returns the subgraph induced by the specified edges.

The induced subgraph contains each edge in edges and each node incident to any one of those edges.

Parameters:

edges (iterable) – An iterable of edges in this graph.

Returns:

G – An edge-induced subgraph of this graph with the same edge attributes.

Return type:

Graph

Notes

The graph, edge, and node attributes in the returned subgraph view are references to the corresponding attributes in the original graph. The view is read-only.

To create a full graph version of the subgraph with its own copy of the edge or node attributes, use:

G.edge_subgraph(edges).copy()

Examples

>>> G = nx.path_graph(5)
>>> H = G.edge_subgraph([(0, 1), (3, 4)])
>>> list(H.nodes)
[0, 1, 3, 4]
>>> list(H.edges)
[(0, 1), (3, 4)]
property edges

An OutEdgeView of the DiGraph as G.edges or G.edges().

edges(self, nbunch=None, data=False, default=None)

The OutEdgeView provides set-like operations on the edge-tuples as well as edge attribute lookup. When called, it also provides an EdgeDataView object which allows control of access to edge attributes (but does not provide set-like operations). Hence, G.edges[u, v][‘color’] provides the value of the color attribute for edge (u, v) while for (u, v, c) in G.edges.data(‘color’, default=’red’): iterates through all the edges yielding the color attribute with default ‘red’ if no color attribute exists.

Parameters:

  • nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges from these nodes.

  • data (string or bool, optional (default=False)) – The edge attribute returned in 3-tuple (u, v, ddict[data]). If True, return edge attribute dict in 3-tuple (u, v, ddict). If False, return 2-tuple (u, v).

  • default (value, optional (default=None)) – Value used for edges that don’t have the requested attribute. Only relevant if data is not True or False.

Returns:

edges – A view of edge attributes, usually it iterates over (u, v) or (u, v, d) tuples of edges, but can also be used for attribute lookup as edges[u, v][‘foo’].

Return type:

OutEdgeView

See also

in_edges, out_edges

Notes

Nodes in nbunch that are not in the graph will be (quietly) ignored. For directed graphs this returns the out-edges.

Examples

>>> G = nx.DiGraph()  # or MultiDiGraph, etc
>>> nx.add_path(G, [0, 1, 2])
>>> G.add_edge(2, 3, weight=5)
>>> [e for e in G.edges]
[(0, 1), (1, 2), (2, 3)]
>>> G.edges.data()  # default data is {} (empty dict)
OutEdgeDataView([(0, 1, {}), (1, 2, {}), (2, 3, {'weight': 5})])
>>> G.edges.data("weight", default=1)
OutEdgeDataView([(0, 1, 1), (1, 2, 1), (2, 3, 5)])
>>> G.edges([0, 2])  # only edges originating from these nodes
OutEdgeDataView([(0, 1), (2, 3)])
>>> G.edges(0)  # only edges from node 0
OutEdgeDataView([(0, 1)])
fit(data, estimator='MLE')[source]

Learns the CPD of the model from data.

Since the assumption is that the 2-TBN stays constant throughtout the model, the algorithm iterates over every 2 consecutive time slices in the data and updates the CPDs based on it.

Parameters:

  • data (pandas.DataFrame instance) – The column names must be of the form (variable, time_slice). The time-slices must start from 0.

  • estimator (str) – Currently only Maximum Likelihood Estimator is supported.

Returns:

None

Return type:

The CPDs are added to the model instance.

Examples

>>> import numpy as np
>>> import pandas as pd
>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> model = DBN(
>>>     [
>>>         (("A", 0), ("B", 0)),
>>>         (("A", 0), ("C", 0)),
>>>         (("B", 0), ("D", 0)),
>>>         (("C", 0), ("D", 0)),
>>>         (("A", 0), ("A", 1)),
>>>         (("B", 0), ("B", 1)),
>>>         (("C", 0), ("C", 1)),
>>>         (("D", 0), ("D", 1)),
>>>     ]
>>> )
>>> data = np.random.randint(low=0, high=2, size=(1000, 20))
>>> colnames = []
>>> for t in range(5):
...     colnames.extend([("A", t), ("B", t), ("C", t), ("D", t)])
>>> df = pd.DataFrame(data, columns=colnames)
>>> model.fit(df)
get_ancestral_graph(nodes)

Returns the ancestral graph of the given nodes. The ancestral graph only contains the nodes which are ancestors of atleast one of the variables in node.

Parameters:

node (iterable) – List of nodes whose ancestral graph needs to be computed.

Returns:

Ancestral Graph

Return type:

pgmpy.base.DAG

Examples

>>> from pgmpy.base import DAG
>>> dag = DAG([('A', 'C'), ('B', 'C'), ('D', 'A'), ('D', 'B')])
>>> anc_dag = dag.get_ancestral_graph(nodes=['A', 'B'])
>>> anc_dag.edges()
OutEdgeView([('D', 'A'), ('D', 'B')])
get_children(node)

Returns a list of children of node. Throws an error if the node is not present in the graph.

Parameters:

node (string, int or any hashable python object.) – The node whose children would be returned.

Examples

>>> from pgmpy.base import DAG
>>> g = DAG(ebunch=[('A', 'B'), ('C', 'B'), ('B', 'D'),
                              ('B', 'E'), ('B', 'F'), ('E', 'G')])
>>> g.get_children(node='B')
['D', 'E', 'F']
get_constant_bn(t_slice=0)[source]

Returns a normal Bayesian Network object which has nodes from the first two time slices and all the edges in the first time slice and edges going from first to second time slice. The returned Bayesian Network basically represents the part of the DBN which remains constant.

The node names are changed to strings in the form {var}_{time}.

get_cpds(node=None, time_slice=None)[source]

Returns the CPDs that have been associated with the network.

Parameters:

  • node (tuple (node_name, time_slice)) – The node should be in the following form (node_name, time_slice). Here, node_name is the node that is inserted while the time_slice is an integer value, which denotes the index of the time_slice that the node belongs to.

  • time_slice (int) – The time_slice should be a positive integer greater than or equal to zero.

Examples

>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> from pgmpy.factors.discrete import TabularCPD
>>> dbn = DBN()
>>> dbn.add_edges_from([(('D',0),('G',0)),(('I',0),('G',0)),(('D',0),('D',1)),(('I',0),('I',1))])
>>> grade_cpd =  TabularCPD(('G',0), 3, [[0.3,0.05,0.9,0.5],
...                                      [0.4,0.25,0.08,0.3],
...                                      [0.3,0.7,0.02,0.2]], [('I', 0),('D', 0)],[2,2])
>>> dbn.add_cpds(grade_cpd)
>>> dbn.get_cpds()
get_edge_data(u, v, default=None)

Returns the attribute dictionary associated with edge (u, v).

This is identical to G[u][v] except the default is returned instead of an exception if the edge doesn’t exist.

Parameters:

  • u (nodes) –

  • v (nodes) –

  • default (any Python object (default=None)) – Value to return if the edge (u, v) is not found.

Returns:

edge_dict – The edge attribute dictionary.

Return type:

dictionary

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G[0][1]
{}

Warning: Assigning to G[u][v] is not permitted. But it is safe to assign attributes G[u][v][‘foo’]

>>> G[0][1]["weight"] = 7
>>> G[0][1]["weight"]
7
>>> G[1][0]["weight"]
7

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.get_edge_data(0, 1)  # default edge data is {}
{}
>>> e = (0, 1)
>>> G.get_edge_data(*e)  # tuple form
{}
>>> G.get_edge_data("a", "b", default=0)  # edge not in graph, return 0
0
get_immoralities()

Finds all the immoralities in the model A v-structure X -> Z <- Y is an immorality if there is no direct edge between X and Y .

Returns:

Immoralities – A set of all the immoralities in the model

Return type:

set

Examples

>>> from pgmpy.base import DAG
>>> student = DAG()
>>> student.add_edges_from([('diff', 'grade'), ('intel', 'grade'),
...                         ('intel', 'SAT'), ('grade', 'letter')])
>>> student.get_immoralities()
{('diff', 'intel')}
get_independencies(latex=False, include_latents=False)

Computes independencies in the DAG, by checking d-seperation.

Parameters:

  • latex (boolean) – If latex=True then latex string of the independence assertion would be created.

  • include_latents (boolean) – If True, includes latent variables in the independencies. Otherwise, only generates independencies on observed variables.

Examples

>>> from pgmpy.base import DAG
>>> chain = DAG([('X', 'Y'), ('Y', 'Z')])
>>> chain.get_independencies()
(X ⟂ Z | Y)
(Z ⟂ X | Y)
get_inter_edges()[source]

Returns the inter-slice edges present in the 2-TBN.

Examples

>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> dbn = DBN()
>>> dbn.add_edges_from([(('D', 0), ('G', 0)), (('I', 0), ('G', 0)),
...                     (('G', 0), ('L', 0)), (('D', 0), ('D', 1)),
...                     (('I', 0), ('I', 1)), (('G', 0), ('G', 1)),
...                     (('G', 0), ('L', 1)), (('L', 0), ('L', 1))])
>>> dbn.get_inter_edges()
[(('D', 0), ('D', 1)),
 (('G', 0), ('G', 1)),
 (('G', 0), ('L', 1)),
 (('I', 0), ('I', 1)),
 (('L', 0), ('L', 1))]
get_interface_nodes(time_slice=0)[source]

Returns the nodes in the first timeslice whose children are present in the first timeslice.

Parameters:

time_slice (int) – The timeslice should be a positive value greater than or equal to zero

Examples

>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> dbn = DBN()
>>> dbn.add_nodes_from(['D', 'G', 'I', 'S', 'L'])
>>> dbn.add_edges_from([(('D',0),('G',0)),(('I',0),('G',0)),(('G',0),('L',0)),(('D',0),('D',1))])
>>> dbn.get_interface_nodes()
[('D', 0)]
get_intra_edges(time_slice=0)[source]

Returns the intra slice edges present in the 2-TBN.

Parameters:

time_slice (int (whole number)) – The time slice for which to get intra edges. The timeslice should be a positive value or zero.

Examples

>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> dbn = DBN()
>>> dbn.add_nodes_from(['D', 'G', 'I', 'S', 'L'])
>>> dbn.add_edges_from([(('D', 0), ('G', 0)), (('I', 0), ('G', 0)),
...                     (('G', 0), ('L', 0)), (('D', 0), ('D', 1)),
...                     (('I', 0), ('I', 1)), (('G', 0), ('G', 1)),
...                     (('G', 0), ('L', 1)), (('L', 0), ('L', 1))])
>>> dbn.get_intra_edges()
[(('D', 0), ('G', 0)), (('G', 0), ('L', 0)), (('I', 0), ('G', 0))]
get_leaves()

Returns a list of leaves of the graph.

Examples

>>> from pgmpy.base import DAG
>>> graph = DAG([('A', 'B'), ('B', 'C'), ('B', 'D')])
>>> graph.get_leaves()
['C', 'D']
get_markov_blanket(node)[source]

Returns a markov blanket for a random variable. In the case of Bayesian Networks, the markov blanket is the set of node’s parents, its children and its children’s other parents.

Returns:

Markov Blanket – List of nodes in the markov blanket of node.

Return type:

list

Parameters:

node (string, int or any hashable python object.) – The node whose markov blanket would be returned.

Examples

>>> from pgmpy.base import DAG
>>> from pgmpy.factors.discrete import TabularCPD
>>> G = DAG([('x', 'y'), ('z', 'y'), ('y', 'w'), ('y', 'v'), ('u', 'w'),
                       ('s', 'v'), ('w', 't'), ('w', 'm'), ('v', 'n'), ('v', 'q')])
>>> G.get_markov_blanket('y')
['s', 'w', 'x', 'u', 'z', 'v']
get_parents(node)

Returns a list of parents of node.

Throws an error if the node is not present in the graph.

Parameters:

node (string, int or any hashable python object.) – The node whose parents would be returned.

Examples

>>> from pgmpy.base import DAG
>>> G = DAG(ebunch=[('diff', 'grade'), ('intel', 'grade')])
>>> G.get_parents(node='grade')
['diff', 'intel']
static get_random(n_nodes=5, edge_prob=0.5, latents=False)

Returns a randomly generated DAG with n_nodes number of nodes with edge probability being edge_prob.

Parameters:

  • n_nodes (int) – The number of nodes in the randomly generated DAG.

  • edge_prob (float) – The probability of edge between any two nodes in the topologically sorted DAG.

  • latents (bool (default: False)) – If True, includes latent variables in the generated DAG.

Returns:

Random DAG – The randomly generated DAG.

Return type:

pgmpy.base.DAG

Examples

>>> from pgmpy.base import DAG
>>> random_dag = DAG.get_random(n_nodes=10, edge_prob=0.3)
>>> random_dag.nodes()
NodeView((0, 1, 2, 3, 4, 5, 6, 7, 8, 9))
>>> random_dag.edges()
OutEdgeView([(0, 6), (1, 6), (1, 7), (7, 9), (2, 5), (2, 7), (2, 8), (5, 9), (3, 7)])
get_roots()

Returns a list of roots of the graph.

Examples

>>> from pgmpy.base import DAG
>>> graph = DAG([('A', 'B'), ('B', 'C'), ('B', 'D'), ('E', 'B')])
>>> graph.get_roots()
['A', 'E']
get_slice_nodes(time_slice=0)[source]

Returns the nodes present in a particular timeslice

Parameters:

time_slice (int) – The timeslice should be a positive value greater than or equal to zero

Examples

>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> dbn = DBN()
>>> dbn.add_nodes_from(['D', 'G', 'I', 'S', 'L'])
>>> dbn.add_edges_from([(('D', 0),('G', 0)),(('I', 0),('G', 0)),(('G', 0),('L', 0)),(('D', 0),('D', 1))])
>>> dbn.get_slice_nodes()
graph_attr_dict_factory

alias of dict

has_edge(u, v)

Returns True if the edge (u, v) is in the graph.

This is the same as v in G[u] without KeyError exceptions.

Parameters:

  • u (nodes) – Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects.

  • v (nodes) – Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects.

Returns:

edge_ind – True if edge is in the graph, False otherwise.

Return type:

bool

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.has_edge(0, 1)  # using two nodes
True
>>> e = (0, 1)
>>> G.has_edge(*e)  #  e is a 2-tuple (u, v)
True
>>> e = (0, 1, {"weight": 7})
>>> G.has_edge(*e[:2])  # e is a 3-tuple (u, v, data_dictionary)
True

The following syntax are equivalent:

>>> G.has_edge(0, 1)
True
>>> 1 in G[0]  # though this gives KeyError if 0 not in G
True
has_node(n)

Returns True if the graph contains the node n.

Identical to n in G

Parameters:

n (node) –

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.has_node(0)
True

It is more readable and simpler to use

>>> 0 in G
True
has_predecessor(u, v)

Returns True if node u has predecessor v.

This is true if graph has the edge u<-v.

has_successor(u, v)

Returns True if node u has successor v.

This is true if graph has the edge u->v.

property in_degree

An InDegreeView for (node, in_degree) or in_degree for single node.

The node in_degree is the number of edges pointing to the node. The weighted node degree is the sum of the edge weights for edges incident to that node.

This object provides an iteration over (node, in_degree) as well as lookup for the degree for a single node.

Parameters:

  • nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges incident to these nodes.

  • weight (string or None, optional (default=None)) – The name of an edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. The degree is the sum of the edge weights adjacent to the node.

Returns:

  • If a single node is requested

  • deg (int) – In-degree of the node

  • OR if multiple nodes are requested

  • nd_iter (iterator) – The iterator returns two-tuples of (node, in-degree).

See also

degree, out_degree

Examples

>>> G = nx.DiGraph()
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.in_degree(0)  # node 0 with degree 0
0
>>> list(G.in_degree([0, 1, 2]))
[(0, 0), (1, 1), (2, 1)]
in_degree_iter(nbunch=None, weight=None)
property in_edges

A view of the in edges of the graph as G.in_edges or G.in_edges().

in_edges(self, nbunch=None, data=False, default=None):

Parameters:

  • nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges incident to these nodes.

  • data (string or bool, optional (default=False)) – The edge attribute returned in 3-tuple (u, v, ddict[data]). If True, return edge attribute dict in 3-tuple (u, v, ddict). If False, return 2-tuple (u, v).

  • default (value, optional (default=None)) – Value used for edges that don’t have the requested attribute. Only relevant if data is not True or False.

Returns:

in_edges – A view of edge attributes, usually it iterates over (u, v) or (u, v, d) tuples of edges, but can also be used for attribute lookup as edges[u, v][‘foo’].

Return type:

InEdgeView or InEdgeDataView

Examples

>>> G = nx.DiGraph()
>>> G.add_edge(1, 2, color='blue')
>>> G.in_edges()
InEdgeView([(1, 2)])
>>> G.in_edges(nbunch=2)
InEdgeDataView([(1, 2)])

See also

edges

initialize_initial_state()[source]

This method will automatically re-adjust the cpds and the edges added to the Bayesian Network. If an edge that is added as an intra time slice edge in the 0th timeslice, this method will automatically add it in the 1st timeslice. It will also add the cpds. However, to call this method, one needs to add cpds as well as the edges in the Bayesian Network of the whole skeleton including the 0th and the 1st timeslice,.

Examples

>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> from pgmpy.factors.discrete import TabularCPD
>>> student = DBN()
>>> student.add_nodes_from(['D', 'G', 'I', 'S', 'L'])
>>> student.add_edges_from([(('D', 0),('G', 0)),(('I', 0),('G', 0)),(('D', 0),('D', 1)),(('I', 0),('I', 1))])
>>> grade_cpd = TabularCPD(('G', 0), 3, [[0.3, 0.05, 0.9, 0.5],
...                                      [0.4, 0.25, 0.08, 0.3],
...                                      [0.3, 0.7, 0.02, 0.2]],
...                        evidence=[('I', 0),('D', 0)],
...                        evidence_card=[2, 2])
>>> d_i_cpd = TabularCPD(('D', 1), 2, [[0.6, 0.3],
...                                    [0.4, 0.7]],
...                      evidence=[('D', 0)],
...                      evidence_card=[2])
>>> diff_cpd = TabularCPD(('D', 0), 2, [[0.6, 0.4]])
>>> intel_cpd = TabularCPD(('I',0), 2, [[0.7, 0.3]])
>>> i_i_cpd = TabularCPD(('I', 1), 2, [[0.5, 0.4],
...                                    [0.5, 0.6]],
...                      evidence=[('I', 0)],
...                      evidence_card=[2])
>>> student.add_cpds(grade_cpd, d_i_cpd, diff_cpd, intel_cpd, i_i_cpd)
>>> student.initialize_initial_state()
is_dconnected(start, end, observed=None)

Returns True if there is an active trail (i.e. d-connection) between start and end node given that observed is observed.

Parameters:

  • start (int, str, any hashable python object.) – The nodes in the DAG between which to check the d-connection/active trail.

  • end (int, str, any hashable python object.) – The nodes in the DAG between which to check the d-connection/active trail.

  • observed (list, array-like (optional)) – If given the active trail would be computed assuming these nodes to be observed.

Examples

>>> from pgmpy.base import DAG
>>> student = DAG()
>>> student.add_nodes_from(['diff', 'intel', 'grades', 'letter', 'sat'])
>>> student.add_edges_from([('diff', 'grades'), ('intel', 'grades'), ('grades', 'letter'),
...                         ('intel', 'sat')])
>>> student.is_dconnected('diff', 'intel')
False
>>> student.is_dconnected('grades', 'sat')
True
is_directed()

Returns True if graph is directed, False otherwise.

is_iequivalent(model)

Checks whether the given model is I-equivalent

Two graphs G1 and G2 are said to be I-equivalent if they have same skeleton and have same set of immoralities.

Parameters:

model (A DAG object, for which you want to check I-equivalence) –

Returns:

I-equivalence – True if both are I-equivalent, False otherwise

Return type:

boolean

Examples

>>> from pgmpy.base import DAG
>>> G = DAG()
>>> G.add_edges_from([('V', 'W'), ('W', 'X'),
...                   ('X', 'Y'), ('Z', 'Y')])
>>> G1 = DAG()
>>> G1.add_edges_from([('W', 'V'), ('X', 'W'),
...                    ('X', 'Y'), ('Z', 'Y')])
>>> G.is_iequivalent(G1)
True
is_multigraph()

Returns True if graph is a multigraph, False otherwise.

local_independencies(variables)

Returns an instance of Independencies containing the local independencies of each of the variables.

Parameters:

variables (str or array like) – variables whose local independencies are to be found.

Examples

>>> from pgmpy.base import DAG
>>> student = DAG()
>>> student.add_edges_from([('diff', 'grade'), ('intel', 'grade'),
>>>                         ('grade', 'letter'), ('intel', 'SAT')])
>>> ind = student.local_independencies('grade')
>>> ind
(grade ⟂ SAT | diff, intel)
minimal_dseparator(start, end)

Finds the minimal d-separating set for start and end.

Parameters:

  • start (node) – The first node.

  • end (node) – The second node.

Examples

>>> dag = DAG([('A', 'B'), ('B', 'C')])
>>> dag.minimal_dseparator(start='A', end='C')
{'B'}

References

[1] Algorithm 4, Page 10: Tian, Jin, Azaria Paz, and Judea Pearl. Finding minimal d-separators. Computer Science Department, University of California, 1998.

moralize()[source]

Removes all the immoralities in the Network and creates a moral graph (UndirectedGraph).

A v-structure X->Z<-Y is an immorality if there is no directed edge between X and Y.

Examples

>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> dbn = DBN([(('D',0), ('G',0)), (('I',0), ('G',0))])
>>> moral_graph = dbn.moralize()
>>> moral_graph.edges()
EdgeView([(('G', 0), ('I', 0)),
          (('G', 0), ('D', 0)),
          (('D', 1), ('I', 1)),
          (('D', 1), ('G', 1)),
          (('I', 0), ('D', 0)),
          (('G', 1), ('I', 1))])
property name

String identifier of the graph.

This graph attribute appears in the attribute dict G.graph keyed by the string “name”. as well as an attribute (technically a property) G.name. This is entirely user controlled.

nbunch_iter(nbunch=None)

Returns an iterator over nodes contained in nbunch that are also in the graph.

The nodes in nbunch are checked for membership in the graph and if not are silently ignored.

Parameters:

nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges incident to these nodes.

Returns:

niter – An iterator over nodes in nbunch that are also in the graph. If nbunch is None, iterate over all nodes in the graph.

Return type:

iterator

Raises:

NetworkXError – If nbunch is not a node or sequence of nodes. If a node in nbunch is not hashable.

See also

Graph.__iter__

Notes

When nbunch is an iterator, the returned iterator yields values directly from nbunch, becoming exhausted when nbunch is exhausted.

To test whether nbunch is a single node, one can use “if nbunch in self:”, even after processing with this routine.

If nbunch is not a node or a (possibly empty) sequence/iterator or None, a NetworkXError is raised. Also, if any object in nbunch is not hashable, a NetworkXError is raised.

neighbors(n)

Returns an iterator over successor nodes of n.

A successor of n is a node m such that there exists a directed edge from n to m.

Parameters:

n (node) – A node in the graph

Raises:

NetworkXError – If n is not in the graph.

See also

predecessors

Notes

neighbors() and successors() are the same.

node_attr_dict_factory

alias of dict

node_dict_factory

alias of dict

property nodes

A NodeView of the Graph as G.nodes or G.nodes().

Can be used as G.nodes for data lookup and for set-like operations. Can also be used as G.nodes(data=’color’, default=None) to return a NodeDataView which reports specific node data but no set operations. It presents a dict-like interface as well with G.nodes.items() iterating over (node, nodedata) 2-tuples and G.nodes[3][‘foo’] providing the value of the foo attribute for node 3. In addition, a view G.nodes.data(‘foo’) provides a dict-like interface to the foo attribute of each node. G.nodes.data(‘foo’, default=1) provides a default for nodes that do not have attribute foo.

Parameters:

  • data (string or bool, optional (default=False)) – The node attribute returned in 2-tuple (n, ddict[data]). If True, return entire node attribute dict as (n, ddict). If False, return just the nodes n.

  • default (value, optional (default=None)) – Value used for nodes that don’t have the requested attribute. Only relevant if data is not True or False.

Returns:

Allows set-like operations over the nodes as well as node attribute dict lookup and calling to get a NodeDataView. A NodeDataView iterates over (n, data) and has no set operations. A NodeView iterates over n and includes set operations.

When called, if data is False, an iterator over nodes. Otherwise an iterator of 2-tuples (node, attribute value) where the attribute is specified in data. If data is True then the attribute becomes the entire data dictionary.

Return type:

NodeView

Notes

If your node data is not needed, it is simpler and equivalent to use the expression for n in G, or list(G).

Examples

There are two simple ways of getting a list of all nodes in the graph:

>>> G = nx.path_graph(3)
>>> list(G.nodes)
[0, 1, 2]
>>> list(G)
[0, 1, 2]

To get the node data along with the nodes:

>>> G.add_node(1, time="5pm")
>>> G.nodes[0]["foo"] = "bar"
>>> list(G.nodes(data=True))
[(0, {'foo': 'bar'}), (1, {'time': '5pm'}), (2, {})]
>>> list(G.nodes.data())
[(0, {'foo': 'bar'}), (1, {'time': '5pm'}), (2, {})]

>>> list(G.nodes(data="foo"))
[(0, 'bar'), (1, None), (2, None)]
>>> list(G.nodes.data("foo"))
[(0, 'bar'), (1, None), (2, None)]

>>> list(G.nodes(data="time"))
[(0, None), (1, '5pm'), (2, None)]
>>> list(G.nodes.data("time"))
[(0, None), (1, '5pm'), (2, None)]

>>> list(G.nodes(data="time", default="Not Available"))
[(0, 'Not Available'), (1, '5pm'), (2, 'Not Available')]
>>> list(G.nodes.data("time", default="Not Available"))
[(0, 'Not Available'), (1, '5pm'), (2, 'Not Available')]

If some of your nodes have an attribute and the rest are assumed to have a default attribute value you can create a dictionary from node/attribute pairs using the default keyword argument to guarantee the value is never None:

>>> G = nx.Graph()
>>> G.add_node(0)
>>> G.add_node(1, weight=2)
>>> G.add_node(2, weight=3)
>>> dict(G.nodes(data="weight", default=1))
{0: 1, 1: 2, 2: 3}
number_of_edges(u=None, v=None)

Returns the number of edges between two nodes.

Parameters:

  • u (nodes, optional (default=all edges)) – If u and v are specified, return the number of edges between u and v. Otherwise return the total number of all edges.

  • v (nodes, optional (default=all edges)) – If u and v are specified, return the number of edges between u and v. Otherwise return the total number of all edges.

Returns:

nedges – The number of edges in the graph. If nodes u and v are specified return the number of edges between those nodes. If the graph is directed, this only returns the number of edges from u to v.

Return type:

int

See also

size

Examples

For undirected graphs, this method counts the total number of edges in the graph:

>>> G = nx.path_graph(4)
>>> G.number_of_edges()
3

If you specify two nodes, this counts the total number of edges joining the two nodes:

>>> G.number_of_edges(0, 1)
1

For directed graphs, this method can count the total number of directed edges from u to v:

>>> G = nx.DiGraph()
>>> G.add_edge(0, 1)
>>> G.add_edge(1, 0)
>>> G.number_of_edges(0, 1)
1
number_of_nodes()

Returns the number of nodes in the graph.

Returns:

nnodes – The number of nodes in the graph.

Return type:

int

See also

order

identical method

__len__

identical method

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.number_of_nodes()
3
order()

Returns the number of nodes in the graph.

Returns:

nnodes – The number of nodes in the graph.

Return type:

int

See also

number_of_nodes

identical method

__len__

identical method

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.order()
3
property out_degree

An OutDegreeView for (node, out_degree)

The node out_degree is the number of edges pointing out of the node. The weighted node degree is the sum of the edge weights for edges incident to that node.

This object provides an iterator over (node, out_degree) as well as lookup for the degree for a single node.

Parameters:

  • nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges incident to these nodes.

  • weight (string or None, optional (default=None)) – The name of an edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. The degree is the sum of the edge weights adjacent to the node.

Returns:

  • If a single node is requested

  • deg (int) – Out-degree of the node

  • OR if multiple nodes are requested

  • nd_iter (iterator) – The iterator returns two-tuples of (node, out-degree).

See also

degree, in_degree

Examples

>>> G = nx.DiGraph()
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.out_degree(0)  # node 0 with degree 1
1
>>> list(G.out_degree([0, 1, 2]))
[(0, 1), (1, 1), (2, 1)]
out_degree_iter(nbunch=None, weight=None)
property out_edges

An OutEdgeView of the DiGraph as G.edges or G.edges().

edges(self, nbunch=None, data=False, default=None)

The OutEdgeView provides set-like operations on the edge-tuples as well as edge attribute lookup. When called, it also provides an EdgeDataView object which allows control of access to edge attributes (but does not provide set-like operations). Hence, G.edges[u, v][‘color’] provides the value of the color attribute for edge (u, v) while for (u, v, c) in G.edges.data(‘color’, default=’red’): iterates through all the edges yielding the color attribute with default ‘red’ if no color attribute exists.

Parameters:

  • nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges from these nodes.

  • data (string or bool, optional (default=False)) – The edge attribute returned in 3-tuple (u, v, ddict[data]). If True, return edge attribute dict in 3-tuple (u, v, ddict). If False, return 2-tuple (u, v).

  • default (value, optional (default=None)) – Value used for edges that don’t have the requested attribute. Only relevant if data is not True or False.

Returns:

edges – A view of edge attributes, usually it iterates over (u, v) or (u, v, d) tuples of edges, but can also be used for attribute lookup as edges[u, v][‘foo’].

Return type:

OutEdgeView

See also

in_edges, out_edges

Notes

Nodes in nbunch that are not in the graph will be (quietly) ignored. For directed graphs this returns the out-edges.

Examples

>>> G = nx.DiGraph()  # or MultiDiGraph, etc
>>> nx.add_path(G, [0, 1, 2])
>>> G.add_edge(2, 3, weight=5)
>>> [e for e in G.edges]
[(0, 1), (1, 2), (2, 3)]
>>> G.edges.data()  # default data is {} (empty dict)
OutEdgeDataView([(0, 1, {}), (1, 2, {}), (2, 3, {'weight': 5})])
>>> G.edges.data("weight", default=1)
OutEdgeDataView([(0, 1, 1), (1, 2, 1), (2, 3, 5)])
>>> G.edges([0, 2])  # only edges originating from these nodes
OutEdgeDataView([(0, 1), (2, 3)])
>>> G.edges(0)  # only edges from node 0
OutEdgeDataView([(0, 1)])
property pred

Graph adjacency object holding the predecessors of each node.

This object is a read-only dict-like structure with node keys and neighbor-dict values. The neighbor-dict is keyed by neighbor to the edge-data-dict. So G.pred[2][3][‘color’] = ‘blue’ sets the color of the edge (3, 2) to “blue”.

Iterating over G.pred behaves like a dict. Useful idioms include for nbr, datadict in G.pred[n].items():. A data-view not provided by dicts also exists: for nbr, foovalue in G.pred[node].data(‘foo’): A default can be set via a default argument to the data method.

predecessors(n)

Returns an iterator over predecessor nodes of n.

A predecessor of n is a node m such that there exists a directed edge from m to n.

Parameters:

n (node) – A node in the graph

Raises:

NetworkXError – If n is not in the graph.

See also

successors

remove_cpds(*cpds)[source]

Removes the cpds that are provided in the argument.

Parameters:

*cpds (list, set, tuple (array-like)) – List of CPDs which are to be associated with the model. Each CPD should be an instance of TabularCPD.

Examples

>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> from pgmpy.factors.discrete import TabularCPD
>>> dbn = DBN()
>>> dbn.add_edges_from([(('D',0),('G',0)),(('I',0),('G',0)),(('D',0),('D',1)),(('I',0),('I',1))])
>>> grade_cpd =  TabularCPD(('G',0), 3, [[0.3,0.05,0.9,0.5],
...                                      [0.4,0.25,0.08,0.3],
...                                      [0.3,0.7,0.02,0.2]], [('I', 0),('D', 0)],[2,2])
>>> dbn.add_cpds(grade_cpd)
>>> dbn.get_cpds()
[<TabularCPD representing P(('G', 0):3 | ('I', 0):2, ('D', 0):2) at 0x3348ab0>]
>>> dbn.remove_cpds(grade_cpd)
>>> dbn.get_cpds()
[]
remove_edge(u, v)

Remove the edge between u and v.

Parameters:

  • u (nodes) – Remove the edge between nodes u and v.

  • v (nodes) – Remove the edge between nodes u and v.

Raises:

NetworkXError – If there is not an edge between u and v.

See also

remove_edges_from

remove a collection of edges

Examples

>>> G = nx.Graph()  # or DiGraph, etc
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.remove_edge(0, 1)
>>> e = (1, 2)
>>> G.remove_edge(*e)  # unpacks e from an edge tuple
>>> e = (2, 3, {"weight": 7})  # an edge with attribute data
>>> G.remove_edge(*e[:2])  # select first part of edge tuple
remove_edges_from(ebunch)

Remove all edges specified in ebunch.

Parameters:

ebunch (list or container of edge tuples) –

Each edge given in the list or container will be removed from the graph. The edges can be:

  • 2-tuples (u, v) edge between u and v.

  • 3-tuples (u, v, k) where k is ignored.

See also

remove_edge

remove a single edge

Notes

Will fail silently if an edge in ebunch is not in the graph.

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> ebunch = [(1, 2), (2, 3)]
>>> G.remove_edges_from(ebunch)
remove_node(n)

Remove node n.

Removes the node n and all adjacent edges. Attempting to remove a nonexistent node will raise an exception.

Parameters:

n (node) – A node in the graph

Raises:

NetworkXError – If n is not in the graph.

See also

remove_nodes_from

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> list(G.edges)
[(0, 1), (1, 2)]
>>> G.remove_node(1)
>>> list(G.edges)
[]
remove_nodes_from(nodes)

Remove multiple nodes.

Parameters:

nodes (iterable container) – A container of nodes (list, dict, set, etc.). If a node in the container is not in the graph it is silently ignored.

See also

remove_node

Notes

When removing nodes from an iterator over the graph you are changing, a RuntimeError will be raised with message: RuntimeError: dictionary changed size during iteration. This happens when the graph’s underlying dictionary is modified during iteration. To avoid this error, evaluate the iterator into a separate object, e.g. by using list(iterator_of_nodes), and pass this object to G.remove_nodes_from.

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> e = list(G.nodes)
>>> e
[0, 1, 2]
>>> G.remove_nodes_from(e)
>>> list(G.nodes)
[]

Evaluate an iterator over a graph if using it to modify the same graph

>>> G = nx.DiGraph([(0, 1), (1, 2), (3, 4)])
>>> # this command will fail, as the graph's dict is modified during iteration
>>> # G.remove_nodes_from(n for n in G.nodes if n < 2)
>>> # this command will work, since the dictionary underlying graph is not modified
>>> G.remove_nodes_from(list(n for n in G.nodes if n < 2))
reverse(copy=True)

Returns the reverse of the graph.

The reverse is a graph with the same nodes and edges but with the directions of the edges reversed.

Parameters:

copy (bool optional (default=True)) – If True, return a new DiGraph holding the reversed edges. If False, the reverse graph is created using a view of the original graph.

simulate(n_samples=10, n_time_slices=2, do=None, evidence=None, virtual_evidence=None, virtual_intervention=None, include_latents=False, seed=None, show_progress=True)[source]

Simulates time-series data from the specified model.

Parameters:

  • n_samples (int) – The number of data samples to simulate from the model.

  • n_time_slices (int) – The number of time slices for which to simulate the data.

  • do (dict) – The interventions to apply to the model. dict should be of the form {(variable_name, time_slice): state}

  • evidence (dict) – Observed evidence to apply to the model. dict should be of the form {(variable_name, time_slice): state}

  • virtual_evidence (list) – Probabilistically apply evidence to the model. virtual_evidence should be a list of pgmpy.factors.discrete.TabularCPD objects specifying the virtual probabilities.

  • virtual_intervention (list) – Also known as soft intervention. virtual_intervention should be a list of pgmpy.factors.discrete.TabularCPD objects specifying the virtual/soft intervention probabilities.

  • include_latents (boolean (default: False)) – Whether to include the latent variable values in the generated samples.

  • seed (int (default: None)) – If a value is provided, sets the seed for numpy.random.

  • show_progress (bool) – If True, shows a progress bar when generating samples.

Returns:

pandas.DataFrame

Return type:

A dataframe with the simulated data.

Examples

>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> from pgmpy.factors.discrete import TabularCPD
>>> dbn = DBN([(("D", 0), ("G", 0)), (("I", 0), ("G", 0)),
...            (("D", 0), ("D", 1)), (("I", 0), ("I", 1)),])
>>> diff_cpd = TabularCPD(("D", 0), 2, [[0.6], [0.4]])
>>> grade_cpd = TabularCPD(variable=("G", 0), variable_card=3,
...                        values=[[0.3, 0.05, 0.9, 0.5],
...                                [0.4, 0.25, 0.08, 0.3],
...                                [0.3, 0.7, 0.02, 0.2]],
...                        evidence=[("I", 0), ("D", 0)],
...                        evidence_card=[2, 2])
>>> d_i_cpd = TabularCPD(variable=("D", 1), variable_card=2,
...                      values=[[0.6, 0.3], [0.4, 0.7]],
...                      evidence=[("D", 0)],
...                      evidence_card=[2])
>>> intel_cpd = TabularCPD(("I", 0), 2, [[0.7], [0.3]])
>>> i_i_cpd = TabularCPD(variable=("I", 1), variable_card=2,
...                      values=[[0.5, 0.4], [0.5, 0.6]],
...                      evidence=[("I", 0)],
...                      evidence_card=[2])
>>> g_i_cpd = TabularCPD(variable=("G", 1), variable_card=3,
...                      values=[[0.3, 0.05, 0.9, 0.5],
...                              [0.4, 0.25, 0.08, 0.3],
...                              [0.3, 0.7, 0.02, 0.2]],
...                      evidence=[("I", 1), ("D", 1)],
...                      evidence_card=[2, 2])
>>> dbn.add_cpds(diff_cpd, grade_cpd, d_i_cpd, intel_cpd, i_i_cpd, g_i_cpd)

Normal simulation from the model.

>>> dbn.simulate(n_time_slices=4, n_samples=2)
   (D, 0)  (G, 0)  (I, 0)  (D, 1)  (G, 1)  (I, 1)  (D, 2)  (G, 2)  (D, 3)  (G, 3)  (I, 2)  (I, 3)
0       0       2       0       0       0       1       0       2       0       2       0       0
1       0       1       0       0       0       1       1       0       1       2       1       0

Simulation with evidence.

>>> dbn.simulate(n_time_slices=4, n_samples=2, evidence={('D', 0): 1, ('D', 2): 0})
   (D, 0)  (G, 0)  (I, 0)  (D, 1)  (G, 1)  (I, 1)  (D, 2)  (G, 2)  (D, 3)  (G, 3)  (I, 2)  (I, 3)
0       1       1       1       1       2       0       0       2       1       1       0       1
1       1       2       1       1       2       0       0       1       1       0       0       1

Simulation with virtual/soft evidence.

>>> dbn.simulate(n_time_slices=4, n_samples=2, virtual_evidence=[TabularCPD(('D', 2), 2, [[0.7], [0.3]])])
   (D, 0)  (G, 0)  (I, 0)  (D, 1)  (G, 1)  (I, 1)  (D, 2)  (G, 2)  (D, 3)  (G, 3)  (I, 2)  (I, 3)
0       0       1       0       0       1       0       0       0       1       0       1       1
1       0       1       0       0       0       1       0       0       0       0       1       1

Simulation with intervention.

>>> dbn.simulate(n_time_slices=4, n_samples=2, do={('D', 0): 1, ('D', 2): 0})
   (D, 0)  (G, 0)  (I, 0)  (D, 1)  (G, 1)  (I, 1)  (D, 2)  (G, 2)  (D, 3)  (G, 3)  (I, 2)  (I, 3)
0       1       0       1       1       0       1       0       2       0       0       0       1
1       1       1       0       1       2       1       0       0       1       1       1       1

Simulation with virtual/soft intervention.

>>> dbn.simulate(n_time_slices=4, n_samples=2, virtual_intervention=[TabularCPD(('D', 2), 2, [[0.7], [0.3]])])
   (D, 0)  (G, 0)  (I, 0)  (D, 1)  (G, 1)  (I, 1)  (D, 2)  (G, 2)  (D, 3)  (G, 3)  (I, 2)  (I, 3)
0       0       0       0       1       2       0       1       2       1       1       0       1
1       0       1       1       1       2       0       1       2       1       1       0       0
size(weight=None)

Returns the number of edges or total of all edge weights.

Parameters:

weight (string or None, optional (default=None)) – The edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1.

Returns:

size – The number of edges or (if weight keyword is provided) the total weight sum.

If weight is None, returns an int. Otherwise a float (or more general numeric if the weights are more general).

Return type:

numeric

See also

number_of_edges

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.size()
3

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_edge("a", "b", weight=2)
>>> G.add_edge("b", "c", weight=4)
>>> G.size()
2
>>> G.size(weight="weight")
6.0
subgraph(nodes)

Returns a SubGraph view of the subgraph induced on nodes.

The induced subgraph of the graph contains the nodes in nodes and the edges between those nodes.

Parameters:

nodes (list, iterable) – A container of nodes which will be iterated through once.

Returns:

G – A subgraph view of the graph. The graph structure cannot be changed but node/edge attributes can and are shared with the original graph.

Return type:

SubGraph View

Notes

The graph, edge and node attributes are shared with the original graph. Changes to the graph structure is ruled out by the view, but changes to attributes are reflected in the original graph.

To create a subgraph with its own copy of the edge/node attributes use: G.subgraph(nodes).copy()

For an inplace reduction of a graph to a subgraph you can remove nodes: G.remove_nodes_from([n for n in G if n not in set(nodes)])

Subgraph views are sometimes NOT what you want. In most cases where you want to do more than simply look at the induced edges, it makes more sense to just create the subgraph as its own graph with code like:

# Create a subgraph SG based on a (possibly multigraph) G
SG = G.__class__()
SG.add_nodes_from((n, G.nodes[n]) for n in largest_wcc)
if SG.is_multigraph():
    SG.add_edges_from((n, nbr, key, d)
        for n, nbrs in G.adj.items() if n in largest_wcc
        for nbr, keydict in nbrs.items() if nbr in largest_wcc
        for key, d in keydict.items())
else:
    SG.add_edges_from((n, nbr, d)
        for n, nbrs in G.adj.items() if n in largest_wcc
        for nbr, d in nbrs.items() if nbr in largest_wcc)
SG.graph.update(G.graph)

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> H = G.subgraph([0, 1, 2])
>>> list(H.edges)
[(0, 1), (1, 2)]
property succ

Graph adjacency object holding the successors of each node.

This object is a read-only dict-like structure with node keys and neighbor-dict values. The neighbor-dict is keyed by neighbor to the edge-data-dict. So G.succ[3][2][‘color’] = ‘blue’ sets the color of the edge (3, 2) to “blue”.

Iterating over G.succ behaves like a dict. Useful idioms include for nbr, datadict in G.succ[n].items():. A data-view not provided by dicts also exists: for nbr, foovalue in G.succ[node].data(‘foo’): and a default can be set via a default argument to the data method.

The neighbor information is also provided by subscripting the graph. So for nbr, foovalue in G[node].data(‘foo’, default=1): works.

For directed graphs, G.adj is identical to G.succ.

successors(n)

Returns an iterator over successor nodes of n.

A successor of n is a node m such that there exists a directed edge from n to m.

Parameters:

n (node) – A node in the graph

Raises:

NetworkXError – If n is not in the graph.

See also

predecessors

Notes

neighbors() and successors() are the same.

to_daft(node_pos='circular', latex=True, pgm_params={}, edge_params={}, node_params={})

Returns a daft (https://docs.daft-pgm.org/en/latest/) object which can be rendered for publication quality plots. The returned object’s render method can be called to see the plots.

Parameters:

  • node_pos (str or dict (default: circular)) –

    If str: Must be one of the following: circular, kamada_kawai, planar, random, shell, sprint,

    spectral, spiral. Please refer: https://networkx.org/documentation/stable//reference/drawing.html#module-networkx.drawing.layout for details on these layouts.

    If dict should be of the form {node: (x coordinate, y coordinate)} describing the x and y coordinate of each node.

    If no argument is provided uses circular layout.

  • latex (boolean) – Whether to use latex for rendering the node names.

  • pgm_params (dict (optional)) – Any additional parameters that need to be passed to daft.PGM initializer. Should be of the form: {param_name: param_value}

  • edge_params (dict (optional)) – Any additional edge parameters that need to be passed to daft.add_edge method. Should be of the form: {(u1, v1): {param_name: param_value}, (u2, v2): {…} }

  • node_params (dict (optional)) – Any additional node parameters that need to be passed to daft.add_node method. Should be of the form: {node1: {param_name: param_value}, node2: {…} }

Returns:

Daft object – Daft object for plotting the DAG.

Return type:

daft.PGM object

Examples

>>> from pgmpy.base import DAG
>>> dag = DAG([('a', 'b'), ('b', 'c'), ('d', 'c')])
>>> dag.to_daft(node_pos={'a': (0, 0), 'b': (1, 0), 'c': (2, 0), 'd': (1, 1)})
<daft.PGM at 0x7fc756e936d0>
>>> dag.to_daft(node_pos="circular")
<daft.PGM at 0x7f9bb48c5eb0>
>>> dag.to_daft(node_pos="circular", pgm_params={'observed_style': 'inner'})
<daft.PGM at 0x7f9bb48b0bb0>
>>> dag.to_daft(node_pos="circular",
...             edge_params={('a', 'b'): {'label': 2}},
...             node_params={'a': {'shape': 'rectangle'}})
<daft.PGM at 0x7f9bb48b0bb0>
to_directed(as_view=False)

Returns a directed representation of the graph.

Returns:

G – A directed graph with the same name, same nodes, and with each edge (u, v, data) replaced by two directed edges (u, v, data) and (v, u, data).

Return type:

DiGraph

Notes

This returns a “deepcopy” of the edge, node, and graph attributes which attempts to completely copy all of the data and references.

This is in contrast to the similar D=DiGraph(G) which returns a shallow copy of the data.

See the Python copy module for more information on shallow and deep copies, https://docs.python.org/3/library/copy.html.

Warning: If you have subclassed Graph to use dict-like objects in the data structure, those changes do not transfer to the DiGraph created by this method.

Examples

>>> G = nx.Graph()  # or MultiGraph, etc
>>> G.add_edge(0, 1)
>>> H = G.to_directed()
>>> list(H.edges)
[(0, 1), (1, 0)]

If already directed, return a (deep) copy

>>> G = nx.DiGraph()  # or MultiDiGraph, etc
>>> G.add_edge(0, 1)
>>> H = G.to_directed()
>>> list(H.edges)
[(0, 1)]
to_directed_class()

Returns the class to use for empty directed copies.

If you subclass the base classes, use this to designate what directed class to use for to_directed() copies.

to_graphviz()

Retuns a pygraphviz object for the DAG. pygraphviz is useful for visualizing the network structure.

Examples

>>> from pgmpy.utils import get_example_model
>>> model = get_example_model('alarm')
>>> model.to_graphviz()
<AGraph <Swig Object of type 'Agraph_t *' at 0x7fdea4cde040>>
to_undirected(reciprocal=False, as_view=False)

Returns an undirected representation of the digraph.

Parameters:

  • reciprocal (bool (optional)) – If True only keep edges that appear in both directions in the original digraph.

  • as_view (bool (optional, default=False)) – If True return an undirected view of the original directed graph.

Returns:

G – An undirected graph with the same name and nodes and with edge (u, v, data) if either (u, v, data) or (v, u, data) is in the digraph. If both edges exist in digraph and their edge data is different, only one edge is created with an arbitrary choice of which edge data to use. You must check and correct for this manually if desired.

Return type:

Graph

See also

Graph, copy, add_edge, add_edges_from

Notes

If edges in both directions (u, v) and (v, u) exist in the graph, attributes for the new undirected edge will be a combination of the attributes of the directed edges. The edge data is updated in the (arbitrary) order that the edges are encountered. For more customized control of the edge attributes use add_edge().

This returns a “deepcopy” of the edge, node, and graph attributes which attempts to completely copy all of the data and references.

This is in contrast to the similar G=DiGraph(D) which returns a shallow copy of the data.

See the Python copy module for more information on shallow and deep copies, https://docs.python.org/3/library/copy.html.

Warning: If you have subclassed DiGraph to use dict-like objects in the data structure, those changes do not transfer to the Graph created by this method.

Examples

>>> G = nx.path_graph(2)  # or MultiGraph, etc
>>> H = G.to_directed()
>>> list(H.edges)
[(0, 1), (1, 0)]
>>> G2 = H.to_undirected()
>>> list(G2.edges)
[(0, 1)]
to_undirected_class()

Returns the class to use for empty undirected copies.

If you subclass the base classes, use this to designate what directed class to use for to_directed() copies.

update(edges=None, nodes=None)

Update the graph using nodes/edges/graphs as input.

Like dict.update, this method takes a graph as input, adding the graph’s nodes and edges to this graph. It can also take two inputs: edges and nodes. Finally it can take either edges or nodes. To specify only nodes the keyword nodes must be used.

The collections of edges and nodes are treated similarly to the add_edges_from/add_nodes_from methods. When iterated, they should yield 2-tuples (u, v) or 3-tuples (u, v, datadict).

Parameters:

  • edges (Graph object, collection of edges, or None) – The first parameter can be a graph or some edges. If it has attributes nodes and edges, then it is taken to be a Graph-like object and those attributes are used as collections of nodes and edges to be added to the graph. If the first parameter does not have those attributes, it is treated as a collection of edges and added to the graph. If the first argument is None, no edges are added.

  • nodes (collection of nodes, or None) – The second parameter is treated as a collection of nodes to be added to the graph unless it is None. If edges is None and nodes is None an exception is raised. If the first parameter is a Graph, then nodes is ignored.

Examples

>>> G = nx.path_graph(5)
>>> G.update(nx.complete_graph(range(4, 10)))
>>> from itertools import combinations
>>> edges = (
...     (u, v, {"power": u * v})
...     for u, v in combinations(range(10, 20), 2)
...     if u * v < 225
... )
>>> nodes = [1000]  # for singleton, use a container
>>> G.update(edges, nodes)

Notes

It you want to update the graph using an adjacency structure it is straightforward to obtain the edges/nodes from adjacency. The following examples provide common cases, your adjacency may be slightly different and require tweaks of these examples:

>>> # dict-of-set/list/tuple
>>> adj = {1: {2, 3}, 2: {1, 3}, 3: {1, 2}}
>>> e = [(u, v) for u, nbrs in adj.items() for v in nbrs]
>>> G.update(edges=e, nodes=adj)

>>> DG = nx.DiGraph()
>>> # dict-of-dict-of-attribute
>>> adj = {1: {2: 1.3, 3: 0.7}, 2: {1: 1.4}, 3: {1: 0.7}}
>>> e = [
...     (u, v, {"weight": d})
...     for u, nbrs in adj.items()
...     for v, d in nbrs.items()
... ]
>>> DG.update(edges=e, nodes=adj)

>>> # dict-of-dict-of-dict
>>> adj = {1: {2: {"weight": 1.3}, 3: {"color": 0.7, "weight": 1.2}}}
>>> e = [
...     (u, v, {"weight": d})
...     for u, nbrs in adj.items()
...     for v, d in nbrs.items()
... ]
>>> DG.update(edges=e, nodes=adj)

>>> # predecessor adjacency (dict-of-set)
>>> pred = {1: {2, 3}, 2: {3}, 3: {3}}
>>> e = [(v, u) for u, nbrs in pred.items() for v in nbrs]

>>> # MultiGraph dict-of-dict-of-dict-of-attribute
>>> MDG = nx.MultiDiGraph()
>>> adj = {
...     1: {2: {0: {"weight": 1.3}, 1: {"weight": 1.2}}},
...     3: {2: {0: {"weight": 0.7}}},
... }
>>> e = [
...     (u, v, ekey, d)
...     for u, nbrs in adj.items()
...     for v, keydict in nbrs.items()
...     for ekey, d in keydict.items()
... ]
>>> MDG.update(edges=e)

See also

add_edges_from

add multiple edges to a graph

add_nodes_from

add multiple nodes to a graph

class pgmpy.models.DynamicBayesianNetwork.DynamicNode(node: str, time_slice: int)[source]

Bases: object

Class for representing the nodes of Dynamic Bayesian Networks.

node: str
time_slice: int
to_tuple() → tuple[source]

Returns a tuple representation as (node, time_slice) for DynamicNode object.