Lecture 15. Probabilistic Models on Graph
نویسنده
چکیده
A probabilistic model defines the joint distribution for a set of random variables. For example, imagine that a friend of yours claims to possess psychic powers – in particular, the power of psychokinesis. He proposes to demonstrate these powers by flipping a coin, and influencing the outcome to produce heads. You suggest that a better test might be to see if he can levitate a pencil, since the coin producing heads could also be explained by some kind of sleight of hand, such as substituting a two-headed coin. We can express all possible outcomes of the proposed tests, as well as their causes, using the binary random variables X1, X2, X3, and X4 to represent (respectively) the truth of the coin being flipped and producing heads, the pencil levitating, your friend having psychic powers, and the use of a two-headed coin. Any set of beliefs about these outcomes can be encoded in a joint probability distribution, P (x1, x2, x3, x4). For example, the probability that the coin comes up heads (x1 = 1) should be higher if your friend actually does have psychic powers (x3 = 1). Once we have defined a joint distribution on X1, X2, X3, and X4, we can reason about the implications of events involving these variables. For example, if flipping the coin produces heads (x1 = 1), then the probability distribution over the remaining variables is
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