1. 10701 Recitation Pengtao Xie
GMM and EM
10701 Recitation
Pengtao Xie
2/23/2019

2. Outline
Gaussian Mixture Model
Expectation Maximization
2/23/2019

3. Motivation
2/23/2019

4. Formulation
K clusters
2/23/2019

5. GMM is a distribution
2/23/2019

6. GMM is a distribution
2/23/2019

7. Outline
Gaussian Mixture Model
Expectation Maximization
2/23/2019

8. Definitions
Input data, local variables, model parameters, inference, learning
2/23/2019

9. Expectation Maximization
Bound is tight if
2/23/2019

10. Expectation Maximization
2/23/2019

11. Expectation Maximization
Coordinate Ascent
Loop until convergence {
1. Fix , estimate
E step
2. Fix , estimate
M step }
2/23/2019

12. E Step
2/23/2019

13. M Step
2/23/2019

14. Pattern Recognition and Machine Learning, Bishop Suggested Readings
Slides courtesy
Pattern Recognition and Machine Learning,
Bishop
Suggested Readings
Bishop, 9.2 and 9.3
2/23/2019