Hill Climb Search

class pgmpy.estimators.HillClimbSearch(data, use_cache=True, **kwargs)

estimate(scoring_method='k2score', start_dag=None, fixed_edges={}, tabu_length=100, max_indegree=None, black_list=None, white_list=None, epsilon=0.0001, max_iter=1000000.0, show_progress=True)

Performs local hill climb search to estimates the DAG structure that has optimal score, according to the scoring method supplied. Starts at model start_dag and proceeds by step-by-step network modifications until a local maximum is reached. Only estimates network structure, no parametrization.

Parameters:

• scoring_method (str or StructureScore instance) – The score to be optimized during structure estimation. Supported structure scores: k2score, bdeuscore, bdsscore, bicscore. Also accepts a custom score but it should be an instance of StructureScore.

• start_dag (DAG instance) – The starting point for the local search. By default a completely disconnected network is used.

• fixed_edges (iterable) – A list of edges that will always be there in the final learned model. The algorithm will add these edges at the start of the algorithm and will never change it.

• tabu_length (int) – If provided, the last tabu_length graph modifications cannot be reversed during the search procedure. This serves to enforce a wider exploration of the search space. Default value: 100.

• max_indegree (int or None) – If provided and unequal None, the procedure only searches among models where all nodes have at most max_indegree parents. Defaults to None.

• black_list (list or None) – If a list of edges is provided as black_list, they are excluded from the search and the resulting model will not contain any of those edges. Default: None

• white_list (list or None) – If a list of edges is provided as white_list, the search is limited to those edges. The resulting model will then only contain edges that are in white_list. Default: None

• epsilon (float (default: 1e-4)) – Defines the exit condition. If the improvement in score is less than epsilon, the learned model is returned.

• max_iter (int (default: 1e6)) – The maximum number of iterations allowed. Returns the learned model when the number of iterations is greater than max_iter.

Returns:

Estimated model – A DAG at a (local) score maximum.

Return type:

pgmpy.base.DAG

Examples

>>> import pandas as pd
>>> import numpy as np
>>> from pgmpy.estimators import HillClimbSearch, BicScore
>>> # create data sample with 9 random variables:
... data = pd.DataFrame(np.random.randint(0, 5, size=(5000, 9)), columns=list('ABCDEFGHI'))
>>> # add 10th dependent variable
... data['J'] = data['A'] * data['B']
>>> est = HillClimbSearch(data)
>>> best_model = est.estimate(scoring_method=BicScore(data))
>>> sorted(best_model.nodes())
['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J']
>>> best_model.edges()
OutEdgeView([('B', 'J'), ('A', 'J')])
>>> # search a model with restriction on the number of parents:
>>> est.estimate(max_indegree=1).edges()
OutEdgeView([('J', 'A'), ('B', 'J')])

Structure Score

BDeu Score

class pgmpy.estimators.BDeuScore(data, equivalent_sample_size=10, **kwargs)

local_score(variable, parents)

Computes a score that measures how much a given variable is “influenced” by a given list of potential parents.

Bic Score

class pgmpy.estimators.BicScore(data, **kwargs)

local_score(variable, parents)

Computes a score that measures how much a given variable is “influenced” by a given list of potential parents.

K2 Score

class pgmpy.estimators.K2Score(data, **kwargs)

local_score(variable, parents)

Computes a score that measures how much a given variable is “influenced” by a given list of potential parents.

BDsScore

class pgmpy.estimators.BDsScore(data, equivalent_sample_size=10, **kwargs)

structure_prior(model)

Implements the marginal uniform prior for the graph structure where each arc is independent with the probability of an arc for any two nodes in either direction is 1/4 and the probability of no arc between any two nodes is 1/2.

structure_prior_ratio(operation)

Return the log ratio of the prior probabilities for a given proposed change to the DAG.