MIT16_410F10_lec19a

MIT16_410F10_lec19a - 3/6/00 Introduction to Probabilistic...

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3/6/00 1 11/17/10 copyright Brian Williams, 2005-10 1 Brian C. Williams 16.410/16.413 November 17 th , 2010 Brian C. Williams, copyright 2000-09 Introduction to Probabilistic Reasoning Assignment • Homework: Problem Set #8: Linear Programming, due today, Wednesday, November 16 th . Problem Set #9: Probabilistic Reasoning, out today, due Wednesday, November 24 th . • Readings: Today: Review of Probabilities and Probabilistic Reasoning. AIMA Chapter 13. AIMA Chapter 14, Sections. 1-5. Monday: HMMs, localization & mapping AIMA Chapter 15, Sections. 1-3. 11/17/10 copyright Brian Williams, 2005-10 2 Image credit: NASA.
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3/6/00 2 Notation S, Q, R, P Logical sentences Φ Background theory (a sentence). not, and ( ), or (v), implies ( ), “if and only if “ (iff, ). Standard logical connectives where iff “if and only if”. M(S), entails, Models of sentence S, entails, false. A, B, C Sets. U, φ Universe of all elements, empty set. , , ~, - Set union, intersection, inverse and difference. Equivalent to. V: Variable or vector of variables. V i : The ith variable of vector V. V, v i : A particular assignment to V; short form for V= v, V i = v i . V t : V at time t. V i:j : A sequence of V from time i to time j. 11/17/10 copyright Brian Williams, 2005-10 3 Notation S: States or state vector. O: Observables or observation vector. X: Mode or mode vector. S0, S1 Stuck at 0/1 mode. Prefix (k) L Returns the first k elements of list L. Sort L by R Sorts list L in increasing order based on relation R. s i ith sample in sample space U. P(X) The probability of X occurring. P(X|Y) The probability of X, conditioned on Y occurring. A C | B) A is conditionally independent of C given B. 11/17/10 copyright Brian Williams, 2005-10 4
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3/6/00 3 Outline • Motivation • Set Theoretic View of Propositional Logic • From Propositional Logic to Probabilities • Probabilistic Inference – General Queries and Inference Methods – Bayes Net Inference – Model-based Diagnosis (Optional) 11/17/10 copyright Brian Williams, 2005-10 5 Multiple Faults Occur • three shorts, tank-line and pressure jacket burst, panel flies off. Lecture 16: Framed as CSP. How do we compare the space of alternative diagnoses? How do we explain the cause of failure? How do we prefer diagnoses that explain failure? 11/17/10 copyright Brian Williams, 2005-10 6 APOLLO 13 Image source: NASA.
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3/6/00 4 Due to the unknown mode, there tends to be an exponential number of diagnoses. U Candidates with UNKNOWN failure modes Good G Candidates with KNOWN failure modes Good F1 Fn G U U 11/17/10 7 1. Introduce fault models. More constraining, hence more easy to rule out.
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MIT16_410F10_lec19a - 3/6/00 Introduction to Probabilistic...

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