Merge and chop in the computation for isotonic regressions

Hu, Xiaomi; Hansohm, Jürgen

doi:10.1016/j.jspi.2007.12.004

Cited by 5 publications

(2 citation statements)

References 7 publications

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“…Recently, there has been a great deal of interest in developing new algorithms for isotonic regression [19], [20] and in generalizing the basic shape-constrained paradigms for developing statistically more sophisticated formulations that include isotonic regression constraints [21]- [23].…”

Section: Related Workmentioning

confidence: 99%

“…5). The cases where the breakpoint count exceeds are avoided by not storing their state vectors in the list (lines [17][18][19][20]. Once each list is fully generated, to ensure local optimality, we need to do a local minimum search within each list on the ce values of the vectors having the same slope and number of breakpoints, and replace them with the minimum value.…”

Section: A Limiting the Number Of Level Setsmentioning

confidence: 99%

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Nonparametric Combinatorial Regression for Shape Constrained Modeling

Koushanfar

Majzoobi

Potkonjak

2010

IEEE Trans. Signal Process.

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Abstract-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.

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