Nearly-Isotonic Regression

@article{Tibshirani2011NearlyIsotonicR,
  title={Nearly-Isotonic Regression},
  author={Ryan J. Tibshirani and Holger H{\"o}fling and Robert Tibshirani},
  journal={Technometrics},
  year={2011},
  volume={53},
  pages={54-61}
}
We consider the problem of approximating a sequence of data points with a “nearly-isotonic,” or nearly-monotone function. This is formulated as a convex optimization problem that yields a family of solutions, with one extreme member being the standard isotonic regression fit. We devise a simple algorithm to solve for the path of solutions, which can be viewed as a modified version of the well-known pool adjacent violators algorithm, and computes the entire path in O(n log n) operations (n being… CONTINUE READING

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