Bayesian wrap-up (probably). Administrivia My schedule has been chaos... Thank you for your understanding... Feedback on the student lectures? HW2 not.

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Presentation transcript:

Bayesian wrap-up (probably)

Administrivia My schedule has been chaos... Thank you for your understanding... Feedback on the student lectures? HW2 not back yet. Sorry. Soon. Announcements: Midterm exam: Tues, Mar 21 Final project: proposals due Tues, Mar 28 Notes on final project: today Office hours abbreviated tomorrow: 9:00-10:30 (next few weeks)

Blatant advertisement CS dept is hiring faculty this semester Job talks Tues/Thurs for next month 11:00 AM-12:15 PM; Woodward 149 Everyone is invited! Thurs, Mar 9: Shaojun Wang (Alberta Ingenuity Center for ML) “Exploiting Syntactic, Semantic and Lexical Regularities in Language Modeling”

Your place in history Last time: MLE Bayesian posteriors MAP (?) Swallows This time: Bayesianism reprised Revenge of the swallow The Kolter & Maloof paper Next time: Intro to Reinforcement learning

Reminder: Bayesian parameter estimation Produces a distribution over params, not single value Use Bayes’ rule to get there: Where: Generative distribution: Parameter prior: Model-free data distribution (prior): Posterior parameter distribution:

Exercise Suppose you want to estimate the average air speed of an unladen (African) swallow Let’s say that airspeeds of individual swallows, x, are Gaussianly distributed with mean and variance 1: Let’s say, also, that we think the mean is “around” 50 kph, but we’re not sure exactly what it is. But our uncertainty (variance) is 10 kph. Derive the posterior estimate of the mean airspeed.

Posterior Gaussian Airspeed

Let’s look just at the numerator for a second...

Posterior Gaussian Airspeed After a little * rearrangement (completing the square)... *Ok, a lot... I.e., our posterior can be written as a Gaussian itself w/ a special mean and variance...

Posterior Gaussian Airspeed Average of data (data mean) Prior mean Linear combination (weighted avg.)