Lecture 21-Probabilistic Reasoning over Time

Lecture 21-Probabilistic Reasoning over Time - CS 561:...

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Unformatted text preview: CS 561: Artificial Intelligence Instructor: Sofus A. Macskassy, macskass@usc.edu TAs: Nadeesha Ranashinghe ( nadeeshr@usc.edu ) William Yeoh ( wyeoh@usc.edu ) Harris Chiu ( chiciu@usc.edu ) Lectures: MW 5:00-6:20pm, OHE 122 / DEN Office hours: By appointment Class page: http://www-rcf.usc.edu/~macskass/CS561-Spring2010/ This class will use http://www.uscden.net/ and class webpage- Up to date information- Lecture notes - Relevant dates, links, etc. Course material: [AIMA] Artificial Intelligence: A Modern Approach, by Stuart Russell and Peter Norvig. (2nd ed) CS561 - Lecture 21 - Macskassy - Spring 2010 2 Temporal Probability Models [Ch 15] Time and uncertainty Inference: filtering, prediction, smoothing Hidden Markov models Kalman filters (a brief mention) Dynamic Bayesian networks Particle filtering CS561 - Lecture 21 - Macskassy - Spring 2010 3 Time and uncertainty The world changes; we need to track and predict it Diabetes management vs vehicle diagnosis Basic idea: copy state and evidence variables for each time step X t = set of unobservable state variables at time t e.g., BloodSugar t , StomachContents t , etc. E t = set of observable evidence variables at time t e.g., MeasuredBloodSugar t , PulseRate t , FoodEaten t This assumes discrete time ; step size depends on problem Notation: X a:b = X a , X a+1 , , X b-1 , X b CS561 - Lecture 21 - Macskassy - Spring 2010 4 Markov processes (Markov chains) Construct a Bayes net from these variables: parents? Markov assumption : X t depends on bounded subset of X 0:t-1 First-order Markov process : P ( X t j X 0:t-1 ) = P ( X t j X t-1 ) Second-order Markov process : P ( X t j X 0:t-1 ) = P ( X t j X t-2 , X t-1 ) First-order: Second-order: Sensor Markov assumption : P ( E t j X 0:t , E 0:t-1 ) = P ( E t j X t ) Stationary process: transition model P ( X t j X t-1 ) and sensor model P ( E t j X t ) fixed for all t CS561 - Lecture 21 - Macskassy - Spring 2010 5 Example First-order Markov assumption not exactly true in real world! Possible fixes: 1. Increase order of Markov process 2. Augment state , e.g., add Temp t , Pressure t Example: robot motion. Augment position and velocity with Battery t CS561 - Lecture 21 - Macskassy - Spring 2010 6 Inference tasks Filtering : P ( X t j e 1:t ) belief state input to the decision process of a rational agent Prediction : P ( X t+k j e 1:t ) for k > 0 evaluation of possible action sequences; like filtering without the evidence Smoothing : P ( X k j e 1:t ) for 0 k < t better estimate of past states, essential for learning Most likely explanation : arg max x 1:t P( x 1:t j e 1:t ) speech recognition, decoding with a noisy channel CS561 - Lecture 21 - Macskassy - Spring 2010 7 Filtering Aim: devise a recursive state estimation algorithm: I.e., prediction + estimation . Prediction by summing out X t : f 1:t+1 = Forward( f 1:t , e t+1 ) where f 1:t...
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Lecture 21-Probabilistic Reasoning over Time - CS 561:...

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