Conditional independence
Two variables are conditionally independent given specified information when their conditional joint distribution factors into the product of their conditional distributions.
Causal AI
A conditional independence constraint is a requirement that specified variables be independent given specified values or events of other variables.
- How it is used
- Uses independence constraints to simplify probability models, simulate joint distributions, and challenge proposed causal DAGs.
- How deep it goes
- Defines the probability equality, works through factorization and graphical implications, and examines limitations of testing it in data.
- Examples
- Uses inherited blood types, sprinkler and rain, a three-variable sampling process, and graph-based d-separation code.
- What you can do after
- Apply it via pgmpy or NetworkX to inspect graph constraints, then evaluate those constraints against data without treating tests as proof.
Causal Inference for Data Science
Conditional independence is a probabilistic property in which two variables are independent after restricting attention to specified values or information about another variable.
- How it is used
- Guides adjustment choices by identifying when conditioning blocks or opens associations in causal DAGs.
- How deep it goes
- Defines the probability idea, develops worked examples, and connects it to d-separation without fully deriving all graph implications.
- Examples
- Uses commuting delays, perturbed numbers, synthetic chain and fork data, dice sums, and university admission selection.
- What you can do after
- Evaluate/understand which variables can block associations or induce them when conditioned on in a DAG.
Read how Causal Inference for Data Science explains conditional independence →
Related concepts
- d-separationcontrasts with · D-separation is a graphical criterion for determining whether a conditioning set blocks all relevant paths between variables in a graph, implying conditional independence under the graph’s assumptions.
- ignorabilityequivalent to · Ignorability is the causal assumption that treatment assignment is conditionally independent of potential outcomes given specified covariates or confounders.
- causal Markov propertyproduced by · The causal Markov property states that each variable is conditionally independent of its nondescendants given its causal parents in a directed acyclic graph.
- naive bayes classifierconfigures · A Naive Bayes classifier is a probabilistic classification model that applies Bayes’ theorem while assuming features are conditionally independent given the class.
- constraint-based algorithmused by · A constraint-based algorithm infers candidate causal graphs by testing conditional-independence constraints in observed data and comparing them with graphical separation constraints.
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