2019/11/24 by Hanyuan Hang, Hang, Hanyuan · 1 citation
Computer Science · Engineering · Mathematics · #Algorithm #Anomaly Detection Techniques and Applications #Applied mathematics #Artificial intelligence #Computer science #Convergence (economics) #Density estimation #Estimator #Fault Detection and Control Systems #Histogram #Image (mathematics) #Mathematical analysis #Mathematics #Norm (philosophy) #Statistics #Subspace topology #Water Systems and Optimization #cs.LG #math.ST #stat.ML #stat.TH
paper · pdf · doi:10.48550/arxiv.1911.11581
published in arXiv (Cornell University) (Cornell University) · arXiv admin note: text overlap with arXiv:1905.03729
arxiv created 2019/11/24 · openalex publication_date 2019/11/24 · arxiv updated 2019/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate an algorithm named histogram transform ensembles (HTE) density estimator whose effectiveness is supported by both solid theoretical analysis and significant experimental performance. On the theoretical side, by decomposing the error term into approximation error and estimation error, we are able to conduct the following analysis: First of all, we establish the universal consistency under L1(μ)-norm. Secondly, under the assumption that the underlying density function resides in the Hölder space C0,α, we prove almost optimal convergence rates for both single and ensemble density estimators under L1(μ)-norm and L∞(μ)-norm for different tail distributions, whereas in contrast, for its subspace C1,α consisting of smoother functions, almost optimal convergence rates can only be established for the ensembles and the lower bound of the single estimators illustrates the benefits of ensembles over single density estimators. In the experiments, we first carry out simulations to illustrate that histogram transform ensembles surpass single histogram transforms, which offers powerful evidence to support the theoretical results in the space C1,α. Moreover, to further exert the experimental performances, we propose an adaptive version of HTE and study the parameters by generating several synthetic datasets with diversities in dimensions and distributions. Last but not least, real data experiments with other state-of-the-art density estimators demonstrate the accuracy of the adaptive HTE algorithm.