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Lecture 24-Statistical Learning

Lecture 24-Statistical Learning - CS 561 Artificial...

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CS 561: Artificial Intelligence Instructor: Sofus A. Macskassy, [email protected] TAs: Nadeesha Ranashinghe ( [email protected] ) William Yeoh ( [email protected] ) Harris Chiu ( [email protected] ) 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)
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Online Course Evaluation Instructions for DEN Students On campus students need to fill out the paper evaluations in class Course evaluation period is Monday, April 12th - Friday, April 30th. Follow these steps: 1. Log-in to the DEN portal website http://mapp.usc.edu. 2. From “My Start Page” click on the DEN Tools link. 3. Once the DEN Tools window pops-up, click on Course Evaluation . 4. Complete the evaluation and hit submit. DEN students should NOT fill out a paper evaluation! DEN online evaluations are completely anonymous. Reminder e-mails will be sent out. Distance Education Network USC Viterbi School of Engineering
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CS561 - Lecture 24 - Macskassy - Spring 2010 3 Statistical Learning [AIMA Ch 20] Part I: Bayesian learning Maximum a posteriori and maximum likelihood learning Bayes net learning - ML parameter learning with complete data - linear regression Part II: Neural Networks - Brains - Perceptrons - Multi-layer perceptrons - Applications of neural networks
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CS561 - Lecture 24 - Macskassy - Spring 2010 4 Part I: Full Bayesian learning View learning as Bayesian updating of a probability distribution over the hypothesis space H is the hypothesis variable, values h 1 , h 2 , … , prior P (H) j th observation d j gives the outcome of random variable D j training data d =d 1 , …, d N Given the data so far, each hypothesis has a posterior probability: P(h i j d ) = ® P( d j h i )P(h i ) where P( d j h i ) is called the likelihood Predictions use a likelihood-weighted average over the hypotheses: P (X j d ) = § i P (X j d , h i )P(h i j d ) = § i P (X j h i )P(h i j d ) No need to pick one best-guess hypothesis!
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CS561 - Lecture 24 - Macskassy - Spring 2010 5 Example Suppose there are five kinds of bags of candies: 10% are h 1 : 100% cherry candies 20% are h 2 : 75% cherry candies + 25% lime candies 40% are h 3 : 50% cherry candies + 50% lime candies 20% are h 4 : 25% cherry candies + 75% lime candies 10% are h 5 : 100% lime candies Then we observe candies drawn from some bag: What kind of bag is it? What flavor will the next candy be?
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CS561 - Lecture 24 - Macskassy - Spring 2010 6 Posterior probability of hypetheses 10% are h 1 : 100% cherry 20% are h 2 : 75% cherry + 25% lime 40% are h 3 : 50% cherry + 50% lime 20% are h 4 : 25% cherry + 75% lime 10% are h 5 : 100% lime
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CS561 - Lecture 24 - Macskassy - Spring 2010 7 Prediction probabilities
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