Energy Efficient Routing for Statistical Inference of Markov Random - PowerPoint PPT Presentation

Energy Efficient Routing for Statistical Inference of Markov Random Fields A. Anandkumar 1 L. Tong 1 A. Swami 2 1 School of Electrical and Computer Engineering Cornell University, Ithaca, NY 14853 2 Army Research Laboratory, Adelphi MD 20783 Conference on Information Sciences and Systems 2007 . Supported by the Army Research Laboratory CTA A. Anandkumar, L.Tong, A. Swami (Cornell) Routing for Inference of MRF CISS 2007 1 / 23

Classical Distributed Detection and Routing Distributed Detection Classical Routing Quantization rule @ sensors Generic Performance Metric ◮ Throughput, Avg. delay Inference rule @ fusion center Layered architecture separates Conditionally IID sensor data from application : Suboptimal Communication ◮ Perfect reception Modular, simple to implement ◮ Rate constraints Issues in Wireless Sensor Networks Sensor Signal Field Sensor Characteristics Limited battery Large coverage area Limited processing capability Large number of sensors Limited transmission range Correlated sensor readings Prone to failures Arbitrary sensor placement Design of Routing for Detection in Wireless Sensor Networks A. Anandkumar, L.Tong, A. Swami (Cornell) Routing for Inference of MRF CISS 2007 2 / 23

Minimum Energy Routing for Inference Setup Fusion center Correlated sensor readings Optimal detection at fusion center Minimum total energy consumption Theorem (Dynkin) Transmission graph Likelihood function is minimal sufficient statistic for inference Minimum Energy Routing for Inference Minimize total energy of routing such that the sequence of transmissions ensures that likelihood function is delivered to fusion center A. Anandkumar, L.Tong, A. Swami (Cornell) Routing for Inference of MRF CISS 2007 3 / 23

In-Network Processing Categories Forwarding: Transmission of raw data without processing Fusion: Intermediate processing before reaching fusion center Data Forwarding Data Fusion Energy efficient Direct transmission Shortest path Depends on data model Influence of Correlation Structure of Data on Fusion Mechanism A. Anandkumar, L.Tong, A. Swami (Cornell) Routing for Inference of MRF CISS 2007 4 / 23

Related Work Data Aggregation Correlated Data Gathering Joint-Entropy based Coding: Special form of fusion Cristescu et al. , 2006 Incoming packets to 1 packet LEACH, PEGASIS, LEGA etc., Compute special fn.: sum, max Fusion in MRF Survey (Rajagopalan & Varshney 2006, Giridar & Kumar 2006) Belief Propagation (Pearl 1986): Dist. Comp. of marginals Cond. Independent: LLR is a sum Dynamic Prog. to tracking Minimum energy routing: MST, (Williams et al. 2006) directed towards fusion center Inference with 1-bit comm. (Kreidl et al. 2006) Chernoff Routing (Sung et al. ) Link-metric for detection 1-D Gauss-Markov process A. Anandkumar, L.Tong, A. Swami (Cornell) Routing for Inference of MRF CISS 2007 5 / 23

Our Approach and Contributions Routing correlated data for detection not dealt before Employ the Markov-random field model for correlation Single-shot scheme (not flow-based) Formulate minimum energy problem Provide a simple algorithm with approx. bound of 2 A. Anandkumar, L.Tong, A. Swami (Cornell) Routing for Inference of MRF CISS 2007 6 / 23

Outline Introduction 1 Markov Random Field 2 Statistical Inference 3 Routing in MRF 4 A. Anandkumar, L.Tong, A. Swami (Cornell) Routing for Inference of MRF CISS 2007 7 / 23

Model for Correlated Data : Graphical Model Temporal signals 1 2 3 4 Conditional independence based on ordering Linear graph corresponding to autoregressive process of order 1 Fixed number of neighbors Causal (random processes) Spatial signals 6 5 16 Conditional independence 7 8 9 4 2 3 10 14 based on (undirected) 11 15 1 13 Dependency Graph 12 Variable set of neighbors Graph of German states and states with common borders are neighbors Maybe acausal Remark Dependency Graph is NOT related to Communication Capabilities, but to the Correlation Structure of Data! A. Anandkumar, L.Tong, A. Swami (Cornell) Routing for Inference of MRF CISS 2007 8 / 23

Markov Random Field 8 MRF with Dependency Graph G d ( V , E ) 7 1 Y ( V ) = { Y i : i ∈ V} is MRF with G d ( V , E ) if 6 3 5 PDF is positive and it satisfies Markov property 4 2 In figure Equivalent Properties Components of DG Global Markov Y A ⊥ Y B | Y C , are independent A , B , C are disjoint, C separates A, B Y 3 ⊥ Y V\{ 1 , 2 , 5 } | Y 1 , 2 , 5 Local Markov A = { i } , B = V\{ i, N e ( i ) } , C = N e ( i ) Y 1 ⊥ Y 2 given rest of network Pairwise Markov Y i ⊥ Y j | Y V\{ i,j } ⇐ ⇒ ( i, j ) / ∈ E A. Anandkumar, L.Tong, A. Swami (Cornell) Routing for Inference of MRF CISS 2007 9 / 23

Energy Efficient Routing for Statistical Inference of Markov Random - PowerPoint PPT Presentation

Energy Efficient Routing for Statistical Inference of Markov Random Fields A. Anandkumar 1 L. Tong 1 A. Swami 2 1 School of Electrical and Computer Engineering Cornell University, Ithaca, NY 14853 2 Army Research Laboratory, Adelphi MD 20783

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