Parameter Estimation#

Once the structure of a graphical model is known, the next step is estimating its numerical parameters from data. For a Bayesian network, this means learning the conditional probability distribution (CPD) for every node given its parents.

Note

Prerequisite: This guide assumes you already have a graph structure, either from Causal Discovery or built manually with Defining a Custom Model.

At a Glance#

Unified API: A single model.fit(data, estimator=...) call handles all estimation methods.
Prior-Based Smoothing: Bayesian estimation with Dirichlet priors for sparse data.
Missing Data and Latent Variables: Expectation Maximization for incomplete observations.
Parallel Estimation: Speed up fitting for larger models with n_jobs.

API#

The recommended entry point is model.fit(...). Provide the graph, the data, and the estimator class:

from pgmpy.example_models import load_model
from pgmpy.estimators import MaximumLikelihoodEstimator
from pgmpy.models import DiscreteBayesianNetwork

reference = load_model("bnlearn/alarm")
data = reference.simulate(n_samples=1000, seed=42, show_progress=False)

model = DiscreteBayesianNetwork(reference.edges())
model.fit(data, estimator=MaximumLikelihoodEstimator)

print(model.get_cpds("HISTORY"))

Switching the estimation method only requires changing the estimator argument. For finer control, you can instantiate estimator classes directly and call their parameter-generation methods before adding the CPDs to the model.

Prior-Based Smoothing#

When data is sparse, maximum likelihood estimates can be unreliable. The Bayesian estimator adds Dirichlet priors (pseudo-counts and equivalent sample size) to smooth the estimated distributions and incorporate prior beliefs.

Missing Data and Latent Variables#

When the dataset has missing values or the model contains latent variables, simple counting is not enough. The Expectation Maximization estimator handles this through iterative estimation, alternating between imputing missing values and updating parameters.

Parallel Estimation#

The n_jobs parameter in model.fit(...) parallelizes parameter estimation across nodes, which can speed up fitting for larger models. The state_names parameter lets you specify the supported states explicitly when some states may not appear in small datasets.

API Reference#

For the full list of supported estimators: