AIC and BIC Curves for Bayesian Networks

Let’s begin our lesson by recognizing that several Bayesian network models based on multiple configurations exist (remember we can play with the input nodes, number of states, etc.). We also must select the model that best fits our data. We will then discuss two primary approaches to evaluate a model’s fitness: Akaike’s Information Criterion (AIC) and Bayesian Information Criterion (BIC).

These criteria play a crucial role in comparing and selecting the optimal Bayesian network configuration for our dataset, especially given the myriad of options and their varying complexities.

Throughout this lesson, we will delve into the concepts of AIC and BIC, understanding their mathematical underpinnings. We will explore how these criteria help us find the right balance between goodness-of-fit and model complexity, thus ensuring that our predictions are both robust and reliable.

Definitions

At a high level, Akaike's Information Criterion (AIC) and Bayesian Information Criterion (BIC) are both statistical measures used to compare and select the best model from a set of candidate BNs. They help us determine which model provides the best balance between fitting the data well and having low complexity.

AIC and BIC are based on the concept of information theory, which aims to quantify the information content in a model. Both criteria account for the model's goodness-of-fit, which is a measure of how well a model describes the data, and penalize models with more parameters to prevent overfitting.

AIC

Akaike's Information Criterion (AIC) is a model selection criterion defined by the following formula: