Bayesian Network
Last Updated: July 29, 2026 | By Mihail Sebastian | AI Dictionary
A probabilistic model that represents variables and their dependencies as a directed graph, so evidence about one variable updates beliefs about the rest.
What is a Bayesian Network?
A Bayesian network is a probabilistic model that represents variables as nodes in a directed graph, where each edge marks a direct influence and each node carries the probability of its values given its parents. Feed it evidence about any variable, and the probabilities of all the others update.
The structure is the point. Instead of one giant table covering every combination of variables, the graph states which variables directly affect which, and everything else follows from that.
How a Bayesian Network Works
The graph must be acyclic: influence flows forward, never in a loop. Each node stores a conditional probability table – the chance of each of its values for every combination of its parents’ values.
Together, graph and tables define the full joint probability distribution compactly:
\[ P(X_1, \dots, X_n) = \prod_{i=1}^{n} P\big(X_i \mid \mathrm{parents}(X_i)\big) \]Inference runs in any direction. From causes you predict effects; from observed effects you reason backward to likely causes, which is what suits the method to diagnosis.
Bayesian Network vs Naive Bayes
The practical difference: a Bayesian network encodes how variables influence one another, while Naive Bayes assumes the features do not interact at all. Naive Bayes is in fact the simplest possible Bayesian network – one class node with every feature attached directly to it, and no other edges allowed.
| Criterion | Bayesian Network | Naive Bayes |
|---|---|---|
| Feature dependencies | Encoded explicitly as edges in a directed graph | Assumed away (independent given the class) |
| Structure | Designed by experts or learned from data | Fixed: one class node, features attached to it |
| Typical job | Reasoning under uncertainty across related variables | Fast classification, especially of text |
Example of a Bayesian Network
The textbook network has three variables: Rain, Sprinkler, and Wet Grass. Rain influences the sprinkler (an automatic system skips watering when it rains) and wets the grass; the sprinkler wets the grass too. Three nodes, three edges, a small probability table at each node.
You walk outside and find the grass wet. The network reasons backward: both rain and the sprinkler become more probable. Then you notice the sprinkler running, and the probability of rain drops back down, because the sprinkler already accounts for the evidence.
That last step is called explaining away. It is the kind of reasoning a Bayesian network performs automatically once structure and tables are in place.
Related AI terms: Naive Bayes · Joint Probability Distribution · Gaussian Process · Knowledge Representation
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Mihail Sebastian — Writes about AI governance, regulation, and the technology behind them. Placeholder bio — replace with a real credential line. About