introduction to machine learninggdicaro/10315/lectures/... · step 2 using that estimate, i.e., do...

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Teacher: Gianni A. Di Caro Lecture 30: Latent Variable Models, Gaussian Mixture Models, Expectation - Maximization - 2 Introduction to Machine Learning 10 - 315 Fall ‘19 Disclaimer: These slides can include material from different sources. I’ll happy to explicitly acknowledge a source if required. Contact me for requests.

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Page 1: Introduction to Machine Learninggdicaro/10315/lectures/... · Step 2 using that estimate, i.e., do arg maxe E n _ 1 log p(xn, this will be identical to ALT-OPT Intro to Machine Learning

Teacher:Gianni A. Di Caro

Lecture 30:Latent Variable Models, Gaussian Mixture Models, Expectation-Maximization - 2

Introduction to Machine Learning10-315 Fall ‘19

Disclaimer: These slides can include material from different sources. I’ll happy to explicitly acknowledge a source if required. Contact me for requests.

Page 2: Introduction to Machine Learninggdicaro/10315/lectures/... · Step 2 using that estimate, i.e., do arg maxe E n _ 1 log p(xn, this will be identical to ALT-OPT Intro to Machine Learning

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All the following slides are from Piyush Rai (IIT)

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Page 4: Introduction to Machine Learninggdicaro/10315/lectures/... · Step 2 using that estimate, i.e., do arg maxe E n _ 1 log p(xn, this will be identical to ALT-OPT Intro to Machine Learning

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Recap: Generative Classification with GMM, Complete Data

µ1

µ2

µ3

µ1

µ2

µ3

Closed-form solutions

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Recap: Generative Classification with GMM, Complete Data

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Recap: GMM Parameter Estimation with InComplete Data

Different!

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Recap: ALT-OPT as EM

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Recap: ALT-OPT / EM for GMM by optimizing ℒ(q, Θ)

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Recap: ALT-OPT / EM for GMM by optimizing ℒ(q, Θ)

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