Algorithms to Learn Parameters

In this lesson, we will explore some of the most popular algorithms for parameter estimation. We will discuss their key concepts and implementation using the CausalNex library.

We emphasize a fundamental insight: the importance of consistent CPDs. Consistent CPDs are crucial for validating learning against the real-world phenomena we seek to model. A consistent CPD, one that reflects varied probabilities across its structure, indicates meaningful learning. Conversely, a CPD exhibiting uniform values signals a lack of learning, essentially mirroring a disconnect from the intended application context. This insight stems from the core understanding of conditional probabilities.

Additionally, we will introduce the evaluation of the ROC curve for these algorithms, providing a quantitative measure of learning output performance. This analysis will help us understand not just the quality of the CPDs generated but also the predictive power and reliability of each algorithm in real-world modeling scenarios.

What are the algorithms for learning the parameters?

Algorithms for learning the parameters of a Bayesian network refer to the techniques used to estimate the numerical values of the CPDs associated with each node in the network, given a dataset of observations.

Learning the parameters involves estimating the CPDs from the available data so that the network accurately reflects the underlying relationships and dependencies in the dataset. This process is essential for making accurate inferences and predictions using the Bayesian network.

These algorithms provide different ways to learn the parameters of a Bayesian network and can be applied depending on the available data, prior knowledge, and desired level of accuracy and uncertainty in the resulting model.

There are several algorithms for learning the parameters of a Bayesian network. Let's see what they are.

Maximum Likelihood Estimation (MLE)

Maximum Likelihood Estimation (MLE) is a widely used statistical method for estimating the parameters of a probability distribution by maximizing the likelihood function. In the context of Bayesian networks, MLE finds the CPDs that maximize the likelihood of observing the given data.

With a larger sample size, MLE can often be preferred because the influence of the prior becomes less significant as the amount of data increases. The data itself carries enough information to accurately estimate the model's parameters, and the results of MLE will converge toward the true parameters as the sample size grows, according to the law of large numbers.

In our code, we use by default the BayesianEstimator method to learn the Bayesian network.

The next code snippet plots the CPD of the diabetes node.