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Bayesian wrap-up (probably)

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Revenge of the swallow. The Kolter & Maloof paper. Next time: Intro to ... say that airspeeds of individual swallows, x, are Gaussianly distributed with ... – PowerPoint PPT presentation

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Title: Bayesian wrap-up (probably)


1
Bayesian wrap-up (probably)
2
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
  • 900-1030 (next few weeks)

3
Blatant advertisement
  • CS dept is hiring faculty this semester
  • Job talks Tues/Thurs for next month
  • 1100 AM-1215 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

4
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

5
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

6
Exercise
  • Suppose you want to estimate the average air
    speed of an unladen (African) swallow
  • Lets say that airspeeds of individual swallows,
    x, are Gaussianly distributed with mean and
    variance 1
  • Lets say, also, that we think the mean is
    around 50 kph, but were not sure exactly what
    it is. But our uncertainty (variance) is 10 kph.
  • Derive the posterior estimate of the mean
    airspeed.

7
Posterior Gaussian Airspeed
8
Posterior Gaussian Airspeed
9
Posterior Gaussian Airspeed
Lets look just at the numerator for a second...
10
Posterior Gaussian Airspeed
After a little rearrangement (completing the
square)...
I.e., our posterior can be written as a Gaussian
itself w/ a special mean and variance...
Ok, a lot...
11
Posterior Gaussian Airspeed
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