2020/11/06 by Zhensheng Yu, Yu, Zhensheng, Xuyu Chen +3
Computer Science · Engineering · Mathematics · #90C06 #90C25 #90C39 #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Image and Signal Denoising Methods #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2011.03305
openalex publication_date 2020/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Shape restricted statistical estimation problems have been extensively studied, with many important practical applications in signal processing, bioinformatics, and machine learning. In this paper, we propose and study a generalized nearly isotonic optimization (GNIO) model, which recovers, as special cases, many classic problems in shape constrained statistical regression, such as isotonic regression, nearly isotonic regression and unimodal regression problems. We develop an efficient and easy-to-implement dynamic programming algorithm for solving the proposed model whose recursion nature is carefully uncovered and exploited. For special ℓ2-GNIO problems, implementation details and the optimal \cal O(n) running time analysis of our algorithm are discussed. Numerical experiments, including the comparisons among our approach, the powerful commercial solver Gurobi, and existing fast algorithms for solving ℓ1-GNIO and ℓ2-GNIO problems, on both simulated and real data sets, are presented to demonstrate the high efficiency and robustness of our proposed algorithm in solving large scale GNIO problems.