Learning, Bayesian Probability, Graphical Models, and Abduction David Poole University of British Columbia 1 Induction and abduction logic MDL programming Bayesian principle learning probabilistic Bayesian statistical Horn networks learning abduction neural possible logical networks worlds abduction semantics 2 Overview • Causal and evidential modelling & reasoning • Bayesian networks, Bayesian conditioning & abduction • Noise, overfitting, and Bayesian learning 3 Causal & Evidential Modelling Causal modelling: −! causes effects " " of interest observed −! vision: scene image −! diagnosis: disease symptoms −! learning: model data 4 Evidential modelling: −! effects causes −! vision: image scene −! diagnosis: symptoms diseases −! learning: data model 5 Causal & Evidential Reasoning observation evidential reasoning cause causal reasoning prediction 6 Reasoning & Modelling Strategies How do we do causal and evidential reasoning, given modelling strategies? Evidential modelling & only evidential • reasoning (Mycin, Neural Networks). Model evidentially + causally • (problem: consistency, redundancy, knowledge acquisition) Model causally; use different reasoning • strategies for causal & evidential reasoning. (deduction + abduction or Bayes’ theorem) 7 Bayes’ Rule [de Moivre 1718, Bayes 1763, Laplace 1774] j P.e h/P.h/ j D P.h e/ P.e/ Proof: ^ D j P.h e/ P.e h/P.h/ D j P.h e/P.e/ 8 Lesson #1 You should know the difference between • evidential & causal modelling • evidential & causal reasoning There seems to be a relationship between Bayes’ theorem and abduction — used for the same task. 9 Overview • Causal and evidential modelling & reasoning • Bayesian networks, Bayesian conditioning & abduction • Noise, overfitting, and Bayesian learning 10