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Mark Paskin - Stanford AI Lab

A Short Course on Graphical Models 1. Introduction to probability theory Mark Paskin 1. Reasoning under uncertainty In many settings, we must try to understand what is going on in a system when we have imperfect or incomplete information. Two reasons why we might reason under uncertainty: 1. laziness (modeling every detail of a complex system is costly). 2. ignorance (we may not completely understand the system). Example: deploy a network of smoke sensors to detect fires in a building. Our model will reflect both laziness and ignorance: We are too lazy to model what, besides fire, can trigger the sensors;. We are too ignorant to model how fire creates smoke, what density of smoke is required to trigger the sensors, etc. 2. Using probability theory to reason under uncertainty Probabilities quantify uncertainty regarding the occurrence of events. Are there alternatives? Yes, , Dempster-Shafer theory , disjunctive uncertainty, etc. (Fuzzy Logic is about imprecision, not uncertainty.)

Probability Theory is key to the study of action and communication: { Decision Theory combines Probability Theory with Utility Theory. { Information Theory is \the logarithm of Probability Theory".

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