Principles of adaptation i complex systems在复杂系统中的适应性原则.pptVIP

Bayesian approaches to knowledge representation and reasoningPart 1(Chapter 13) Bayesianism vs. Frequentism Classical probability: Frequentists Probability of a particular event is defined relative to its frequency in a sample space of events. E.g., probability of “the coin will come up heads on the next trial” is defined relative to the frequency of heads in a sample space of coin tosses. Bayesian probability: Combine measure of “prior” belief you have in a proposition with your subsequent observations of events. Example: Bayesian can assign probability to statement “The first e-mail message ever written was not spam” but frequentist cannot. Bayesian Knowledge Representation and Reasoning Question: Given the data D and our prior beliefs, what is the probability that h is the correct hypothesis? (spam example) Bayesian terminology (example -- spam recognition) Random variable X: returns one of a set of values {x1, x2, ...,xm}, or a continuous value in interval [a,b] with probability distribution D(X). Data D: {v1, v2, v3, ...} Set of observed values of random variables X1, X2, X3, ... Hypothesis h: Function taking instance j and returning classification of j (e.g., “spam” or “not spam”). Space of hypotheses H: Set of all possible hypotheses Prior probability of h: P(h): Probability that hypothesis h is true given our prior knowledge If no prior knowledge, all h ? H are equally probable Posterior probability of h: P(h|D): Probability that hypothesis h is true, given the data D. Likelihood of D: P(D|h): Probability that we will see data D, given hypothesis h is true. Example: Using Bayes Rule Hypotheses: h = “message m is spam” ?h = “message m is not spam” Data: + = message m contains “viagra” – = message m does not contain “viagra” P(+) = P(+ | h) P(h) + P(+ | ?h)P(?h) = 0.6 * .1 + .03 * .9 = 0.09 P(–) = 0.91 P(h | +) = P(+ | h) P(h) / P(+) = 0.6 * 0.1 / .09 = .67 How would we learn these prior probabili