Near-optimal sensor placements in gaussian processes

Near-optimal sensor placements in gaussian processes (2005)

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by Andreas Krause , Ajit Singh , Carlos Guestrin , Chris Williams

Venue:	In ICML
Citations:	173 - 26 self

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@INPROCEEDINGS{Krause05near-optimalsensor,
    author = {Andreas Krause and Ajit Singh and Carlos Guestrin and Chris Williams},
    title = {Near-optimal sensor placements in gaussian processes},
    booktitle = {In ICML},
    year = {2005},
    publisher = {ICML}
}

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Abstract

When monitoring spatial phenomena, which can often be modeled as Gaussian processes (GPs), choosing sensor locations is a fundamental task. There are several common strategies to address this task, for example, geometry or disk models, placing sensors at the points of highest entropy (variance) in the GP model, and A-, D-, or E-optimal design. In this paper, we tackle the combinatorial optimization problem of maximizing the mutual information between the chosen locations and the locations which are not selected. We prove that the problem of finding the configuration that maximizes mutual information is NP-complete. To address this issue, we describe a polynomial-time approximation that is within (1 − 1/e) of the optimum by exploiting the submodularity of mutual information. We also show how submodularity can be used to obtain online bounds, and design branch and bound search procedures. We then extend our algorithm to exploit lazy evaluations and local structure in the GP, yielding significant speedups. We also extend our approach to find placements which are robust against node failures and uncertainties in the model. These extensions are again associated with rigorous theoretical approximation guarantees, exploiting the submodularity of the objective function. We demonstrate the advantages of our approach towards optimizing mutual information in a very extensive empirical study on two real-world data sets.

Citations

8558	Elements of Information Theory - Cover, Thomas - 1991
1955	Matrix computations - Golub, Loan - 1996
1148	Information Theory, Inference, and Learning Algorithms - MacKay - 2003
1103	Statistics for Spatial Data - Cressie - 1991
412	A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code - McKay, Beckman, et al. - 1979
400	An analysis of approximations for maximizing submodular set functions—I - Nemhauser, Wolsey, et al. - 1978
335	W.: Model-driven data acquisition in sensor networks - Deshpande, Guestrin, et al.
191	Approximation schemes for covering and packing problems in image processing - Hochbaum, Maass - 1985
66	Gaussian processes for machine learning - Seeger - 2004
65	A randomized art-gallery algorithm for sensor placement - Gonzalez-Banos, Latombe - 2001
53	An Exact Algorithm for Maximum Entropy Sampling - Ko, Jon, et al. - 1995
27	Nonstationary Gaussian Processes for Regression and Spatial Modelling - Paciorek - 2003
26	A Note on the Budgeted Maximization of Submodular Functions - Krause, Guestrin - 2005
18	Gaussian processes for active data mining of spatial aggregates - Ramakrishnan, Bailey-Kellogg, et al. - 2005
12	geoR: A package for geostatistical analysis - Jr, J, et al. - 2000
8	A review of some exchange algorithms for constructing discrete D-optimal designs - Nguyen, Miller - 1992
5	Truncated covariance matrices and toeplitz methods - Storkey - 1999