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 #3: Complex Hessian Matrices

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 2

Reference

Appendix B (Complex Hessian Matrices, pp. 720-729):

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 #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 3

Setting

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

Real Arguments

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 5

Real Arguments

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 6

Real Arguments

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 7

Real Arguments

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 8

Real Arguments

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 9

Real Arguments

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 10

Example #B.1 10 10

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 11

Example #B.1 11 11

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

Complex Arguments

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 13

Complex Arguments

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Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 14

Complex Arguments

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 15

Complex Arguments

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Real Hessian Matrix

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Real Hessian Matrix

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Real Hessian Matrix

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Real Hessian Matrix

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 20

Real Hessian Matrix

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 21

Real Hessian Matrix

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 22

Real Hessian Matrix

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Real Hessian Matrix

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Real Hessian Matrix

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Complex Hessian Matrix

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Complex Hessian Matrix

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Complex Hessian Matrix

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Complex Hessian Matrix

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 29

Complex Hessian Matrix

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

Relating Both Representations

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 31

Relation between Representations

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 32

Relation between Representations

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Relation between Representations

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 34

Relation between Representations

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Relation between Representations

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 36

Summary

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 37

Summary

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 38

Example #B.2 38 38

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Example #B.2 39 39

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Example #B.2 40 40

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Example #B.2 41 41

Lecture #3: Complex Hessian Matrices EE210B: Inference over Networks (A. H. Sayed) 42

Example #B.3 42 42

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