针对模相近数据的启发式核密度估计器
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1.人工智能与数字经济广东省实验室(深圳);2.深圳大学

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广东省自然科学基金面上项目 (2023A1515011667);深圳市基础研究重点项目(JCYJ20220818100205012);深圳市基础研究项目(JCYJ20210324093609026)


Heuristic Kernel Density Estimator for Modal-Proximity Data
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1.Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ);2.Shenzhen University

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    摘要:

    区别于经典的基于Parzen窗口法的概率密度函数估计器构建策略,提出了基于近邻误差度量函数的启发式核密度估计器(Heuristic Kernel Density Estimator,HKDE),用以提升对模相近数据概率密度函数拟合的准确性。首次从数据不确定性和模型不确定性的角度分析了传统核密度估计器解决模相近数据概率密度函数估计问题时的缺陷:利用概率密度值对于直方图箱宽参数的收敛性确定观测数据的启发式概率密度值,降低数据概率密度值计算的不确定性;基于启发式概率密度值构建用于确定核密度估计器最优带宽的目标函数,降低最优带宽优化过程中的不确定性。在18个模相近数据集上对新估计器HKDE的可行性、合理性和有效性进行了系统性地验证,实验结果表明,与七种具有代表性的概率密度函数估计器相比,HKDE能够获得更加优异的概率分布近似表现,具有比其他估计器更低的估计误差,能够确定出更接近真实值的概率密度函数估计值。

    Abstract:

    Different from the classical probability density estimator construction strategies based on Parzen window method, we proposed a Heuristic Kernel Density Estimator (HKDE) based on nearest neighbor error measurement function, to improve the accuracy of fitting probability density function of modal-proximity data. From the perspective of data and model uncertainties, we analyzed the defects of traditional kernel density estimators in solving the problem of probability density estimation of modal-proximity data. The heuristic probability density values that can reduce the uncertainty of observed data were obtained by referring to the convergence of probability density values with respect to the histogram box width. Based on the heuristic probability density value, we constructed the sophisticated objective function to determine the optimal bandwidth for kernel density estimator by reducing the model uncertainty. Extensive experiments on 18 modal-proximity datasets were conducted to validate the feasibility, rationality and effectiveness of the designed HKDE. Results show that HKDE can obtain a better approximate performance of probability distribution than seven existing representative probability density function estimators. HKDE has lower estimation error and closer probability density function estimates to the real density values than other kernel density estimators.

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  • 收稿日期:2024-05-29
  • 最后修改日期:2024-10-09
  • 录用日期:2025-01-24
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