LECTURE #6: Mean-Value Theorems - ASL · 2 Lecture #6: Mean-Value Theorems EE210B: Inference over...

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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 #6: Mean-Value Theorems

Transcript of LECTURE #6: Mean-Value Theorems - ASL · 2 Lecture #6: Mean-Value Theorems EE210B: Inference over...

Page 1: LECTURE #6: Mean-Value Theorems - ASL · 2 Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) References Appendix D (Mean-Value Theorems, pp. 744-748):

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 #6: Mean-Value Theorems

Page 2: LECTURE #6: Mean-Value Theorems - ASL · 2 Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) References Appendix D (Mean-Value Theorems, pp. 744-748):

Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) 2

References

Appendix D (Mean-Value Theorems, pp. 744-748):

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.

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Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) 3

Setting

Page 4: LECTURE #6: Mean-Value Theorems - ASL · 2 Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) References Appendix D (Mean-Value Theorems, pp. 744-748):

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

Page 5: LECTURE #6: Mean-Value Theorems - ASL · 2 Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) References Appendix D (Mean-Value Theorems, pp. 744-748):

Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) 5

Real Arguments

Page 6: LECTURE #6: Mean-Value Theorems - ASL · 2 Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) References Appendix D (Mean-Value Theorems, pp. 744-748):

Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) 6

Real Arguments

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Real Arguments

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Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) 8

Real Arguments

Page 9: LECTURE #6: Mean-Value Theorems - ASL · 2 Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) References Appendix D (Mean-Value Theorems, pp. 744-748):

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Real Arguments

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Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) 10

Real Arguments

Page 11: LECTURE #6: Mean-Value Theorems - ASL · 2 Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) References Appendix D (Mean-Value Theorems, pp. 744-748):

Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) 11

Real Arguments

Page 12: LECTURE #6: Mean-Value Theorems - ASL · 2 Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) References Appendix D (Mean-Value Theorems, pp. 744-748):

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

Page 13: LECTURE #6: Mean-Value Theorems - ASL · 2 Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) References Appendix D (Mean-Value Theorems, pp. 744-748):

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Complex Arguments

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Complex Arguments

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Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) 15

Complex Arguments

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Complex Arguments

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Complex Arguments

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Complex Arguments

Page 19: LECTURE #6: Mean-Value Theorems - ASL · 2 Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) References Appendix D (Mean-Value Theorems, pp. 744-748):

Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) 19

Complex Arguments

Page 20: LECTURE #6: Mean-Value Theorems - ASL · 2 Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) References Appendix D (Mean-Value Theorems, pp. 744-748):

Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) 20

Complex Arguments

Page 21: LECTURE #6: Mean-Value Theorems - ASL · 2 Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) References Appendix D (Mean-Value Theorems, pp. 744-748):

Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) 21

Example #D.1 21 21

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Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) 22

Example #D.1 22 22

Page 23: LECTURE #6: Mean-Value Theorems - ASL · 2 Lecture #6: Mean-Value Theorems EE210B: Inference over Networks (A. H. Sayed) References Appendix D (Mean-Value Theorems, pp. 744-748):

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


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