What are Bayesian Networks (BN) ?

A Bayesian Network (BN) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). In a Bayesian Network, nodes represent variables, and edges represent probabilistic dependencies between them. The key idea is to model the joint probability distribution of the variables using the chain rule of probability, where each variable is conditionally dependent only on its parents in the graph.

Bayesian Networks are widely used in various fields, including machine learning, artificial intelligence, and statistics, for tasks such as probabilistic reasoning, inference, decision making, and modeling complex systems. They offer a compact and intuitive representation of uncertainty and are particularly useful when dealing with incomplete or uncertain information.

Key properties and concepts of Bayesian Networks include:

1. Conditional Independence: Nodes in the graph are conditionally independent of their non-descendants given their parents.
2. Inference: Bayesian Networks allow for efficient probabilistic inference, where given observed evidence (values of certain variables), the network can compute the posterior probability distribution over other variables of interest.
3. Learning: Bayesian Networks can be learned from data using various techniques such as parameter estimation (learning the conditional probability distributions) and structure learning (learning the graphical structure).
4. Causal Inference: Bayesian Networks can help in understanding causal relationships between variables by examining the graph’s structure and the directionality of edges.

Overall, Bayesian Networks provide a powerful framework for modeling uncertainty and dependencies in complex systems, making them a valuable tool in many machine learning and data analysis tasks.