Distributed regression: an efficient framework for modeling sensor network data
Proceedings of the 3rd international symposium on Information processing in sensor networks
The impact of spatial correlation on routing with compression in wireless sensor networks
Proceedings of the 3rd international symposium on Information processing in sensor networks
Nonparametric belief propagation for self-calibration in sensor networks
Proceedings of the 3rd international symposium on Information processing in sensor networks
Weighted isotonic regression under the L1 norm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A robust architecture for distributed inference in sensor networks
IPSN '05 Proceedings of the 4th international symposium on Information processing in sensor networks
Linear time isotonic and unimodal regression in the L1 and L∞ norms
Journal of Discrete Algorithms
A collaborative approach to in-place sensor calibration
IPSN'03 Proceedings of the 2nd international conference on Information processing in sensor networks
The Viterbi optimal runlength-constrained approximation nonlinearfilter
IEEE Transactions on Signal Processing
Mathematical programming algorithms for regression-based nonlinearfiltering in RN
IEEE Transactions on Signal Processing
Multivariate convex regression with adaptive partitioning
The Journal of Machine Learning Research
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We introduce a unified approach for calculating nonparametric shape constrained regression. Enforcement of the shape constraint often accounts for the impact of a physical phenomenon or a specific property. It also improves the model's predicability and facilitates subsequent optimizations. The regression models are built by transforming the problem into the combinatorial domain where the shape constraints are imposed by bounding the combinatorial search space. We start by addressing isotonicity shape constraint using a dynamic programming algorithm and demonstrate how the problem can be mapped to the graph combinatorics domain. Next we show how a number of other important shape constraints including unimodality, convexity, limited level set, and limited slope can be addressed using the same framework. The flexibility of proposed framework enables solving the shape constrained regression problem with an arbitrary user-defined error metric. This flexibility is exploited to add robustness against outliers to the model. The algorithms are described in detail and their computational complexity is established. The performance and effectiveness of the shape constrained regression is evaluated on traces of temperature and humidity measurements from a deployed sensor network where a high degree of accuracy and robustness is demonstrated.