Two random variables X and Y are conditionally independent given a random variable Z if they are independent in the conditional distribution given Z. Conditional independence is central notion in probabilistic modeling, because a model's conditional independence assumptions often lead to tractable algorithms for inference and learning in that model.
This concept has the prerequisites:
- Know the definition of conditional independence
- Give examples to show that conditional independence does not imply independence, and vice versa
- It's likely that you're seeing this page because you want to learn about graphical models. If so, don't bother memorizing the rules of conditional independence; you'll get more intution and practice with them when you learn about graphical models. Just convince yourself that the basic properties make intuitive sense.
Core resources (we're sorry, we haven't finished tracking down resources for this concept yet)
Supplemental resources (the following are optional, but you may find them useful)
→ Mathematics StackExchange
- joriki provides several intuitive examples of conditional independence
Location: Article: Conditional Independence
- Ignore the stuff about sigma-algebras.
- Conditional independence is fundamental to probabilistic graphical models, including:
- Markov models , memoryless random sequences where each state is independent of the past conditioned on the previous state
- Bayesian networks , which (roughly) represent causal structure
- Markov random fields , which model which random variables directly interact with each other
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