Reducing the projection onto the monotone extended second-order cone to the pool-adjacent-violators algorithm of isotonic regression

How to project onto the monotone nonnegative cone using Pool Adjacent Violators type algorithms

The metric projection onto an order nonnegative cone from the metric projection onto the corresponding order cone is derived. Particularly, we can use Pool Adjacent Violators-type algorithms developed for projecting onto the monotone cone for projecting onto the monotone nonnegative cone too.

基于主动集的递归方法求解具有广义序约束的凸保序回归

An active-set based recursive approach for solving convex isotonic regression with generalized order restrictions

本文研究由有向树诱导的广义序约束凸保序回归问题，受PAV算法启发提出一种基于主动集的递归求解方法，在温和假设下实现了多项式时间复杂度。

Primal-Dual Active-Set Methods for Isotonic Regression and Trend Filtering

Isotonic regression (IR) is a non-parametric calibration method used in supervised learning. For performing large-scale IR, we propose a primal-dual active-set (PDAS) algorithm which, in contrast to the state-of-the-art Pool Adjacent Violators (PAV) algorithm, can be parallized and is easily warm-started thus well-suited in the online settings. We prove that, like the PAV algorithm, our PDAS algorithm for IR is convergent and has a work complexity of O(n), though our numerical experiments suggest that our PDAS algorithm is often faster than PAV. In addition, we propose PDAS variants (with safe…

An exact dynamic programming approach to segmented isotonic regression

This paper proposes a polynomial-time algorithm to construct the monotone stepwise curve that minimizes the sum of squared errors with respect to a given cloud of data points. The fitted curve is also constrained on the maximum number of steps it can be composed of and on the minimum step length. Our algorithm relies on dynamic programming and is built on the basis that said curve-fitting task can be tackled as a shortest-path type of problem. Numerical results on synthetic and realistic data sets reveal that our algorithm is able to provide the globally optimal monotone stepwise curve fit for…