I've just spent the last 3 hours reading every post, question, Medium article, and textbook entry on conditional independence, and I still don't really understand it. Can somebody explain what it means in layman's terms? I think I'm getting tripped up on the semantics.
One example I frequently come upon is: a person's height and vocabulary are conditionally independent, given age. What I don't understand is, what are they when not given age? Dependent? Wikipedia says so.
This is preposterous to me. Height is not dependent upon vocabulary, nor vice versa. (This brings up another question: does dependent mean "caused by?" Does it mean "correlated with?") In any case, it seems to me that any two events are either empirically independent or they are empirically dependent. Their relationship to each other cannot magically change. Bart and Lisa are still brother and sister regardless of whether or not we know that Homer is father to both.
The existence of a notion called "conditional" independence doesn't make sense to me. And the semantics confuse me. Indeed, it seems that height and vocabulary are conditionally dependent--on age! In other words, age is a variable that binds these things (making them less independent).
My head is in knots.