LECTURE #1: Motivation & Examples · 3 Lecture #1: Motivation and Examples 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
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Professor Ali H. Sayed UCLA Electrical Engineering
INFERENCE OVER NETWORKS
LECTURE #1: Motivation & Examples
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Lecture #1: Motivation and Examples EE210B: Inference over Networks (A. H. Sayed) 2
Contact Email: [email protected]
Web: http://www.ee.ucla.edu/asl
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References 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. A. H. Sayed, ``Adaptive networks,'' Proceedings of the IEEE, vol. 102, no. 4, pp. 460-497, April 2014.
A. H. Sayed et al, ``Diffusion strategies for adaptation and learning over networks,'' IEEE Signal Process. Mag., vol. 30, no. 3, pp. 155-171, May 2013.
A. H. Sayed, ``Diffusion adaptation over networks,'' in Academic Press Library in Signal Processing, vol. 3, pp. 323-454, Academic Press, Elsevier, 2014.
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Pre-Requisites
Prior training expected in:
Probability theory: scalar and vector random variables, pdf, mean, variance, correlation, independence. Linear algebra: matrices, inverses, range and null-spaces, rank, vector and matrix norms, Kronecker products, linear systems of equations, eigen-decomposition, singular-value decomposition, Jordan decomposition.
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Organization
The course consists largely of five parts:
1. Background Material: Linear Algebra and Matrix Theory Results, Complex Gradients and Complex Hessian Matrices, Convexity, Strict Convexity, and Strong Convexity, Mean-Value Theorems, Lipschitz Conditions.
2. Single-Agent Adaptation and Learning: Single-Agent Optimization, Stochastic-Gradient Optimization, Convergence and Stability Properties, Mean-Square-Error Performance.
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Organization
3. Centralized Adaptation and Learning: Batch and Centralized Processing, Convergence, Stability, and Performance, Comparison to Single-Agent Processing. 4. Multi-Agent Network Model: Graph Properties. Connected and Strongly-Connected Networks, Multi-Agent Inference Strategies, Limit Point and Pareto Optimality, Evolution of Network Dynamics.
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Organization
5. Multi-Agent Network Stability and Performance: Stability of Network Dynamics, Long-Term Error Dynamics, Performance of Multi-Agent Networks, Benefits of Cooperation, Role of Informed Agents, Adaptive Combination Strategies, Gossip and Asynchronous Strategies, Constrained Optimization, Proximal Strategies, ADMM Strategies, Clustering.
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Course deals with the topic of information processing over graphs.
Multi-agent networks for the distributed
solution of adaptation, learning, and optimization problems from streaming
data through localized interactions.
Motivation#1
Internet map (2005). Wikimedia commons.
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The results derived here are useful in:
Motivation#2
Comparing network configurations against each other; Comparing networks against batch solutions; Understanding limits of performance; Understanding benefits & pitfalls of cooperation; Highlighting interesting phenomena over networks.
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Motivation#3
Source: Image from Agents, Interaction, and Complexity Research Group website. University of Southampton.
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Motivation#4
We will examine the analysis and design of networked solutions plus
applications in: distributed sensing intrusion detection distributed estimation online learning pattern classification clustering distributed optimization multi-agent systems
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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
Concepts & Examples
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Deals with the discovery of global information from local interactions among dispersed agents.
danger
target
Common objective(s); In-network processing; Dispersed agents.
Distributed Processing
Features:
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Centralized Processing
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Exchange of data between the dispersed agents and a fusion center.
Cost of communications; Privacy & security considerations; Critical point of failure.
Fusion center
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Data already available at dispersed locations (cloud).
Power of cooperation mining of Big Data sets.
Privacy and security considerations.
Robustness and resilience (biological networks).
Robotic swarms (disaster areas).
Network science (social networks).
Source: IEEE SPM May 2013
Why Distributed Processing?
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http://www.misconceptionjunction.com Source: Professor S. Pratt Lab, ASU. Source: Wikimedia. Source: Wikimedia; Creative Commons License.
Nature provides splendid examples of real-time decentralized learning & adaptation.
Biological Networks
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One Useful Result
17 Each agent has a measurement . Objective: Compute average value.
Consensus Construction (1974)
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One Useful Application
YouTube: https://www.youtube.com/watch?v=2m-42ek85G4
repulsion
attraction
alignment
Technique used in The Lion King (1994) and Batman Returns (1992) to produce swarming effects.
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Source: http://youtu.be/zvfY8-3ktNA
Biological networks have more complex objectives such as tracking food sources or evading predators.
Issue#1: Cognition
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Source: Collective Animal Behavior Lab (I. D. Couzin, Princeton University)
Interactions are information-aware informed vs. uninformed agents
Issue#2: Interactions
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Adaptive Networks
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Adaptive agents: learn from streaming data. Cooperative agents: interact locally. Adaptive topology: re-wire the graph. Distributed optimization: solve meaningful problems.
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Example#1: Cooperation
Static target
Predator Fish
Emulating fish schooling and prey-predator behavior Cooperative Networks.
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Example#2: Competition
Emulating prey-predator behavior Network Competition
Static target
Fish Predator
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Example#3:Cognitive Radios
Secondary user
Primary user
swarming secondary users
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Example#4: Optimization
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Sparse representation of a signal using atoms from a dictionary, .
Example#5: Dictionary Learning
private dictionaries
private opinions
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Example#5: Dictionary Learning 27 27
(distributed dictionary learning)
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Relevant Questions
What strategies enable distributed learning?
How to ensure stable behavior?
What are the limits of performance?
Can we match centralized processing?
Does cooperation always help?
Does it help to have more agents?
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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
End of Lecture