2016/07/14 by Jayadev Acharya, Acharya, Jayadev, Ilias Diakonikolas +5 · 2 citations
Computer Science · Engineering · Mathematics · #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning and Algorithms #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1607.03990
openalex publication_date 2016/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the fixed design segmented regression problem: Given noisy samples from a piecewise linear function f, we want to recover f up to a desired accuracy in mean-squared error. Previous rigorous approaches for this problem rely on dynamic programming (DP) and, while sample efficient, have running time quadratic in the sample size. As our main contribution, we provide new sample near-linear time algorithms for the problem that -- while not being minimax optimal -- achieve a significantly better sample-time tradeoff on large datasets compared to the DP approach. Our experimental evaluation shows that, compared with the DP approach, our algorithms provide a convergence rate that is only off by a factor of 2 to 4, while achieving speedups of three orders of magnitude.