Bayesian Network
A Bayesian network is a graphical probabilistic model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). Each node corresponds to a random variable, and edges represent probabilistic dependencies. Conditional dependencies are quantified using conditional probability tables (CPTs).
Key idea
The strength of Bayesian networks lies in their ability to encode and compute uncertainty using Bayes’ theorem. They allow probabilistic inference: given some evidence, the network can compute the likelihood of other events or outcomes.
Applications
- Medical diagnosis: computing disease probabilities based on observed symptoms.
- Risk analysis in finance or engineering.
- Natural Language Processing (NLP): part-of-speech tagging, semantic analysis.
- Decision support systems for planning and forecasting.
Bayesian networks are often described as maps of uncertainty. Unlike purely deterministic models, they explicitly encode probabilities, allowing systems to reason in environments where information is incomplete or noisy. This makes them especially useful in fields like medicine or risk management, where decisions must often be made without full certainty.
Each node in the network is associated with a conditional probability table (CPT), which quantifies how the variable depends on its parents in the graph. Through inference algorithms such as variable elimination or belief propagation, the network can update its probabilities dynamically as new evidence is observed.
One of the key strengths of Bayesian networks is their ability to combine expert knowledge with data-driven learning. In practice, experts may define the graph structure based on domain understanding, while the conditional probabilities are estimated from data. This hybrid approach makes them interpretable and transparent compared to black-box models. However, scalability can be challenging: exact inference becomes computationally expensive as the network grows, leading researchers to develop approximation methods like Monte Carlo sampling.
Reference
- Koller, D., & Friedman, N. (2009). Probabilistic Graphical Models: Principles and Techniques. MIT Press.
