Information-driven learning, distributed fusion, and planning

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1 ARO ARO MURI MURI on on Value-centered Theory Theory for for Adaptive Learning, Inference, Tracking, and and Exploitation -driven learning, distributed fusion, and planning Co-PI Alfred Hero University Michigan

2 Our main thrust this year Quantify and optimize VoI by: dimensionality reduction, nearest neighbor aggregation, and human-in-the-loop. Progress 1: -driven learning: Learning structure in high dimension: Kronecker PCA For spatio-temporal sources Kronecker PCA captures information much more efficiently than standard (low-rank) PCA Progress 2: Distributed information fusion: Distributed inference: local 2 nd order nbd marginalization Performs as well as global fusion w/o message passing Progress 3: Human-in-the-loop planning and processing Cooperative human-machine 20 questions framework Human adds early information gain for target detection

3 Progress 1: driven learning Last year: KGlasso MSE scaling laws Unachievable region 20 uncorrelated sequences KGlasso has best scaling law in n,p Task: Estimate spatio-temporal covariance Time index i Tsiligkaridis, Hero, Zhou, 2012

4 Progress 1: -driven learning This year: Kronecker PCA (See poster) Deficiency: Single KP may not be adequate fit to covariance A Solution: Use a sum KPs to approximate covariance -> K-PCA Standard PCA Kronecker PCA r r Property (Pistsianis and Van Loan 1992): K-PCA is complete expansion Our K-PCA algorithm: Spectral solution to convex minimization problem Theorem [1]: For pq x pq covariance C the MSE Kronecker PCA approximation C r to C is bounded C C r F 2 [1] Tsiligkaridis & H TSP 2013 mmm rrrr R r R R C F 2 + C r p 2 + q 2 n

5 Progress 1: -driven learning Kronecker PCA (See poster) Kronecker spectrum Eigenspectrum [1] Tsiligkaridis & H TSP 2013

6 Objective: predict states measured by SN Model: Gauss-Markov random field: Progress 2: Distributed information fusion in sensor networks Theorem [1]: For pq x pq sample cov C the MSE Kronecker PCA rank r is bounded 2 C C r F mmm rrrr R r R R C F 2 + C r p 2 + q 2 n Standard: Iterative ML by message passing Proposed: Non-iterative by 2-NN relaxation Meng,Wei,Wiesel,H, AISTATS 2013(NP Award)

7 Progress 3: Human-in-the-loop processing Cooperative localization (See poster) Optimal queries are equalizing bisection rules Human advantage: can account for context Human limitation: limited visual accuity Human MSE gain ratio Tsiligkaridis, Sadler & Hero, ICASSP 2013

8 Summary year 2 activities This year s research directly impacts -driven learning Kronecker PCA provides much better fit to spatio-temporal data than standard PCA. VoI for prediction/detection/classification is improved. Distributed information fusion Second-order neighborhood information has nearly as high value as global information about SN. exploitation Inclusion human-in-the-loop provides up to 15% MSE gain in early iterations. Value human-provided information characterized by resolution acuity parameter kappa.

9 Ongoing and future focus areas and collaborations Working towards a unified VoI theory sensing spatiotemporal processes: VoI-driven mission planning with target-dependent payfs (UM/MIT) (Poster today - Mu, Newstadt, How, H) theoretic bounds and algorithms for learning/fusion/planning that account for side-information (human inputs, low rank, sparse, Kronecker structure) geometric theory VoI (UM/ASU) Applications to anomaly detection in video, SNs and radar (UM/OSU/AFRL). Experimental validation studies: Stware defined radar testbed (UM/OSU/ASU/MIT). Refined human models and experiments (UM/UCSD)

10 Publications in year 2 T. Tsiligkaridis, A.O. Hero, S. Zhou, "Convergence properties Kronecker graphical lasso algorithms," IEEE Trans on SP, 2013 T. Tsiligkaridis N and A.O. Hero, ``Covariance Estimation in High Dimensions via Kronecker Product Expansions,'' IEEE Trans on SP, D. Wei and A.O. Hero, "Multistage adaptive estimation sparse Signals," IEEE Journal Selected Topics in Signal Processing, Dennis Wei and Alfred O. Hero, III, "Adaptive spectrum sensing and estimation," ICASSP 2013, Vancouver. Z. Meng, D. Wei, A. Wiesel, A.O. Hero, "Distributed Learning Gaussian Graphical Models via Marginal Likelihoods, AISTAT. Theodoros Tsiligkaridis and Alfred O. Hero III, "Low Separation Rank Covariance Estimation using Kronecker Product Expansions," IEEE ISIT 2013, Istanbul. Theodoros Tsiligkaridis, Brian M. Sadler and Alfred O. Hero III, "A collaborative 20 questions model for target search with humanmachine interaction," ICASSP 2013, Vancouver.