Learning Parameters Donald Bren School of Informationand 学习参数唐纳德布伦信息学院.pptVIP

Learning Bayesian Networks from Data Nir Friedman U.C. Berkeley /~nir Outline Introduction Bayesian networks: a review Parameter learning: Complete data Parameter learning: Incomplete data Structure learning: Complete data Application: classification Learning causal relationships Structure learning: Incomplete data Conclusion Learning (in this context) Process Input: dataset and prior information Output: Bayesian network Prior information: background knowledge a Bayesian network (or fragments of it) time ordering prior probabilities ... Bayesian Networks Bayesian Networks Qualitative part: statistical independence statements (causality!) Directed acyclic graph (DAG) Nodes - random variables of interest (exhaustive and mutually exclusive states) Edges - direct (causal) influence Monitoring Intensive-Care Patients The “alarm” network 37 variables, 509 parameters (instead of 237) Qualitative part Nodes are independent of non-descendants given their parents P(R|E=y,A) = P(R|E=y) for all values of R,A,EGiven that there is and earthquake, I can predict a radio announcement regardless of whether the alarm sounds d-separation: a graph theoretic criterionfor reading independence statementsCan be computed in linear time(on the number of edges) d-separation Two variables are independent if all paths between them are blocked by evidence Three cases: Common cause Intermediate cause Common Effect Example I(X,Y|Z) denotes X and Y are independent given Z I(R,B) ~I(R,B|A) I(R,B|E,A) ~I(R,C|B) Quantitative Part Associated with each node Xi there is a set of conditional probability distributions P(Xi|Pai:?) If variables are discrete, ? is usually multinomial Variables can be continuous, ? can be a linear Gaussian Combinations of discrete and continuous are only constrained by available inference mechanisms What Can We Do with Bayesian Networks? Probabilistic inference: belief update P(E =Y| R = Y, C = Y) Probabilistic inference: belief revision Argmax{E,B}