LECTURE #19: Long-Term Network Dynamics...2 Lecture #19: Long-Term Network Dynamics EE210B:...

Proc. IEEE, vol. 102, no. 4, pp. 460-497, April 2014. Foundations and Trends in Machine Learning, vol. 7, no. 4-5, pp. 311-801, July 2014.

Course EE210B Spring Quarter 2015

1

Professor Ali H. Sayed UCLA Electrical Engineering

INFERENCE OVER NETWORKS

LECTURE #19: Long-Term Network Dynamics

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed) 2

Reference

Chapter 10 (Long-Term Network Dynamics, pp. 552-573):

A. H. Sayed, ``Adaptation, learning, and optimization over networks,'' Foundations and Trends in Machine Learning, vol. 7, issue 4-5, pp. 311-801, NOW Publishers, 2014.

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Setting 3

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Setting 4

Proc. IEEE, vol. 102, no. 4, pp. 460-497, April 2014. Foundations and Trends in Machine Learning, vol. 7, no. 4-5, pp. 311-801, July 2014.

Course EE210B Spring Quarter 2015

Long-Term Model

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Long-Term Error Model 6

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Long-Term Error Model 7

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Long-Term Error Model 8

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Long-Term Error Model 9

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Long-Term Error Model 10

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Long-Term Error Model 11

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Long-Term Error Model 12

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Long-Term Error Model 13

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Long-Term Error Model 14

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Long-Term Error Model 15

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Long-Term Error Model 16

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Long-Term Error Model 17

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Long-Term Error Model 18

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Long-Term Error Model 19

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Long-Term Error Model 20

Proc. IEEE, vol. 102, no. 4, pp. 460-497, April 2014. Foundations and Trends in Machine Learning, vol. 7, no. 4-5, pp. 311-801, July 2014.

Course EE210B Spring Quarter 2015

Approximation Error

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Size of Approximation Error 22

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Size of Approximation Error 23

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Size of Approximation Error 24

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 25

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 26

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 27

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 28

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 29

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 30

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 31

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 32

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 33

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 34

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 35

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 36

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 37

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 38

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 39

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 40

Proc. IEEE, vol. 102, no. 4, pp. 460-497, April 2014. Foundations and Trends in Machine Learning, vol. 7, no. 4-5, pp. 311-801, July 2014.

Course EE210B Spring Quarter 2015

Second-Order Stability

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Second-Order Error Moment 42

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Second-Order Error Moment 43

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 44

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 45

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 46

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 47

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 48

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 49

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Sketch of Proof 50

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Sketch of Proof 51

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Back to Detailed Proof 52

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 53

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 54

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 55

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 56

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 57

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 58

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 59

Proc. IEEE, vol. 102, no. 4, pp. 460-497, April 2014. Foundations and Trends in Machine Learning, vol. 7, no. 4-5, pp. 311-801, July 2014.

Course EE210B Spring Quarter 2015

Fourth-Order Stability

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Fourth-Order Error Moment 61

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Fourth-Order Error Moment 62

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 63

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Sketch of Proof 64

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 65

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 66

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 67

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 68

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Back to Detailed Proof 69

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 70

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 71

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 72

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 73

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 74

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 75

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 76

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 77

Proc. IEEE, vol. 102, no. 4, pp. 460-497, April 2014. Foundations and Trends in Machine Learning, vol. 7, no. 4-5, pp. 311-801, July 2014.

Course EE210B Spring Quarter 2015

First-Order Stability

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

First-Order Error Moment 79

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 80

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 81

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 82

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 83

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Proof 84

Proc. IEEE, vol. 102, no. 4, pp. 460-497, April 2014. Foundations and Trends in Machine Learning, vol. 7, no. 4-5, pp. 311-801, July 2014.

Course EE210B Spring Quarter 2015

Comparing Consensus & Diffusion

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Setting 86

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.1 87

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.1 88

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.1 89

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.1 90

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.1 91

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.2 92

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.2 93

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.2 94

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.2 95

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.2 96

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.2 97

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.2 98

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.2 99

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.2 100

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.2 101

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.2 102

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.2 103

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.2 104

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.2 105

Lecture #19: Long-Term Network Dynamics EE210B: Inference over Networks (A. H. Sayed)

Example #10.2 106

Proc. IEEE, vol. 102, no. 4, pp. 460-497, April 2014. Foundations and Trends in Machine Learning, vol. 7, no. 4-5, pp. 311-801, July 2014.

Course EE210B Spring Quarter 2015

End of Lecture