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 #2: Complex Gradients Vectors
36
Embed
LECTURE #2 C: ompel x Gradients Vectors · 3 . Lecture #2: Complex Gradient Vectors. EE210B: Inference over Networks (A. H. Sayed) Reference . Appendix A (Complex Gradient Vectors,
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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 #2: Complex Gradients Vectors
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
Part I: Background Material
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 3
Reference
Appendix A (Complex Gradient Vectors, pp. 712-719):
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 #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 4
Setting
.
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 5
Cauchy-Riemann Conditions
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 6
Cauchy-Riemann Conditions
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 7
Cauchy-Riemann Conditions
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 8
Cauchy-Riemann Conditions
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 9
Cauchy-Riemann Conditions
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 10
Example #A.1 10 10
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 11
Example #A.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
Scalar Arguments
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 13
Scalar Arguments
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 14
Scalar Arguments
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 15
Scalar Arguments
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 16
Scalar Arguments
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 17
Scalar Arguments
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 18
Example #A.2 18 18
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 19
Example #A.2 19 19
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
Vector Arguments
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 21
Vector Arguments
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 22
Vector Arguments
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 23
Vector Arguments
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 24
Vector Arguments
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 25
Vector Arguments
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 26
Example #A.3 26 26
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 27
Example #A.3 27 27
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 #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 29
Real Arguments
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 30
Real Arguments
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 31
Example #A.4 31 31
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 32
Example #A.4 32 32
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 33
Example #A.4 33 33
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 34
Example #A.4 34 34
Lecture #2: Complex Gradient Vectors EE210B: Inference over Networks (A. H. Sayed) 35
Example #A.5 35 35
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.