Conditional Independence

Probability · Axiom Academy

LESSON Conditional Independence Independence that depends on context: events can be independent given certain conditions 1. Defining Conditional Independence Events A and B are conditionally independent given C if knowing A provides no information about B once we know C. Formally, this means the conditional probabilities factor into a product. 2. Conditional vs Unconditional Independence Conditional independence is NOT the same as unconditional independence. Knowing C can change the relationship between A and B. Four distinct scenarios are possible! Consider Alice's scores on two exams. The scores are dependent (good students do well on both). But given Alice's intelligence level C, her scores become conditionally independent—each exam tests her ability independently. 4. Why Conditional Independence Matters Conditional independence is fundamental in machine learning, Bayesian networks, and causal inference. It allows us to simplify complex probability models by identifying which variables become independent given others.

This is the written version of the interactive lesson above. See the full Probability course.