Bayesian network: Difference between revisions
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Each edge identifies a causal relation, usually temporal: something that happened in the future cannot cause something to happen in the past. As such, the graph is ''acyclic''. | Each edge identifies a causal relation, usually temporal: something that happened in the future cannot cause something to happen in the past. As such, the graph is ''acyclic''. | ||
= Joint probability = | |||
Bayesian networks are primarily used to calculate the ''joint probability'' of an event given its dependencies. This can be done with the following formula | |||
<math> | |||
P(x_1, x_2,\ldots,x_n)=\prod_{i=1}^nP(x_i|Parents(x_i)) | |||
</math> | |||
Revision as of 05:54, 24 May 2024
The Bayesian network is a network probabilistic, graphical model that describes dependencies.
Application
Bayesian networks have applications in machine learning tasks that deal with dependent features.
An example is Part-of-speech, where words are grammatically classified in a string. This involves a complex network of dependencies between object, subject, verbs, nouns, etc. that can be modeled and optimized with a Bayesian network.
Properties
DAG
Bayesian networks are directed, acyclic graphs.
Each edge identifies a causal relation, usually temporal: something that happened in the future cannot cause something to happen in the past. As such, the graph is acyclic.
Joint probability
Bayesian networks are primarily used to calculate the joint probability of an event given its dependencies. This can be done with the following formula
