深圳大学学报理工版

可适应变宽核密度估计器(kernel density estimator with adaptive varying bandwidth, KDE-AVB)是一种基于单个数据点的概率密度估计方法,它以单个数据点为处理对象,利用置信区间交叉法则确定核密度估计器的最优窗口宽度.为加快可适应变宽核密度估计器对最优窗口宽度的寻找,通过引入一种可变的标准差项因子去确定置信区间的上下边界,提出一种改进的可适应变宽核密度估计器(improved kernel density estimator with adaptive varying bandwidth, IKDE-AVB).可变标准差项因子的引入不仅加快了可适应变宽核密度估计器搜索最优窗口宽度的速度,且在一定程度上降低了“过平滑”概率密度估计现象发生的风险.对KDE-AVB和IKDE-AVB的仿真结果表明,IKDE-AVB不仅获得了更快的训练速度(最高降低64%),同时提升了概率密度的估计精度(估计误差最高降低63%).

The kernel density estimator with adaptive varying bandwidth(KDE-AVB)estimates the probability density for the given data in a point-wise manner, which determines the optimal bandwidth based on the intersection of confidence intervals(ICI)rule. In order to speed up the search of optimal bandwidth, this paper proposes an improved kernel density estimator with adaptive varying bandwidth(IKDE-AVB)by introducing a flexible standard derivation term factor to calculate the upper and lower boundaries of confidence intervals. The flexible standard derivation term factor not only increases the speed of searching the optimal bandwidth, but also reduces the risk of “over-smoothed” probability density estimation. In comparison with the classical KDE-AVB, IKDE-AVB not only obtains the faster training speed(64% faster at most in training time)but also improves the estimation accuracy of probability density(63% reduction at most in prediction error). The experimental results demonstrate the feasibility and effectiveness of IKDE-AVB.

引言
1 核密度估计法
2 KDE-AVB
3 IKDE-AVB
4 实验结果与分析
5 结语

表1 核密度估计法(h=0.2)<br/>Table 1 Kernel density estimation method(h=0.2)

表1 核密度估计法(h=0.2)
Table 1 Kernel density estimation method(h=0.2)

图1 核密度估计法效果图(h=0.2)<br/>Fig.1 Kernel density estimation method(h=0.2)

图1 核密度估计法效果图(h=0.2)
Fig.1 Kernel density estimation method(h=0.2)

图2 基正态分布随窗口宽度增加的变化<br/>Fig.2 Variation of base normal distribution with increase of bandwidth

图2 基正态分布随窗口宽度增加的变化
Fig.2 Variation of base normal distribution with increase of bandwidth

图3 置信区间下边界和上边界调整<br/>Fig.3 Adjustment of lower boundary and upper boundary of confidence interval

图3 置信区间下边界和上边界调整
Fig.3 Adjustment of lower boundary and upper boundary of confidence interval

图4 区间效用的图形化表示<br/>Fig.4 Illustration of interval utility

图4 区间效用的图形化表示
Fig.4 Illustration of interval utility

图5 正态分布数据集(见补充材料表S1和S2)<br/>Fig.5 Data sets obeying normal distribution (see Tables S1 and S2 of the supplementary material)

图5 正态分布数据集(见补充材料表S1和S2)
Fig.5 Data sets obeying normal distribution (see Tables S1 and S2 of the supplementary material)

图6 指数分布数据集(见补充材料表S3和S4)<br/>Fig.6 Data sets obeying exponential distribution (see Tables S3 and S4 of the supplementary material)

图6 指数分布数据集(见补充材料表S3和S4)
Fig.6 Data sets obeying exponential distribution (see Tables S3 and S4 of the supplementary material)

图7 瑞利分布数据集(见补充材料表S5和S6)<br/>Fig.7 Data sets obeying Rayleigh distribution (see Tables S5 and S6 of the supplementary material)

图7 瑞利分布数据集(见补充材料表S5和S6)
Fig.7 Data sets obeying Rayleigh distribution (see Tables S5 and S6 of the supplementary material)

图8 贝塔分布数据集(见补充材料表S7和S8)<br/>Fig.8 Data sets obeying beta distribution (see Tables S7 and S8 of the supplementary material)

图8 贝塔分布数据集(见补充材料表S7和S8)
Fig.8 Data sets obeying beta distribution (see Tables S7 and S8 of the supplementary material)

图9 伽玛分布数据集(见补充材料表S9和S10)<br/>Fig.9 Data sets obeying gamma distribution (see Tables S9 and S10 of the supplementary material)

图9 伽玛分布数据集(见补充材料表S9和S10)
Fig.9 Data sets obeying gamma distribution (see Tables S9 and S10 of the supplementary material)

表2 当Г=5时KDE-AVB与IKDE-AVB在正态分布数据集上的对比结果<br/>Table 2 Comparative results between KDE-AVB and IKDE-AVB on normal distribution when Г=5

表2 当Г=5时KDE-AVB与IKDE-AVB在正态分布数据集上的对比结果
Table 2 Comparative results between KDE-AVB and IKDE-AVB on normal distribution when Г=5

表3 当Г=5时KDE-AVB与IKDE-AVB在指数分布数据集上的对比结果<br/>Table 3 Comparative results between KDE-AVB and IKDE-AVB on exponential distribution when Г=5

表3 当Г=5时KDE-AVB与IKDE-AVB在指数分布数据集上的对比结果
Table 3 Comparative results between KDE-AVB and IKDE-AVB on exponential distribution when Г=5

表4 当Г=5时KDE-AVB与IKDE-AVB在瑞利分布数据集上的对比结果<br/>Table 4 Comparative results between KDE-AVB and IKDE-AVB on Rayleigh distribution when Г=5

表4 当Г=5时KDE-AVB与IKDE-AVB在瑞利分布数据集上的对比结果
Table 4 Comparative results between KDE-AVB and IKDE-AVB on Rayleigh distribution when Г=5

表5 当Г=5时KDE-AVB与IKDE-AVB在贝塔分布数据集上的对比结果<br/>Table 5 Comparative results between KDE-AVB and IKDE-AVB on beta distribution when Г=5

表5 当Г=5时KDE-AVB与IKDE-AVB在贝塔分布数据集上的对比结果
Table 5 Comparative results between KDE-AVB and IKDE-AVB on beta distribution when Г=5

表6 当Г=5时KDE-AVB与IKDE-AVB在伽玛分布数据集上的对比结果<br/>Table 6 Comparative results between KDE-AVB and IKDE-AVB on gamma distribution when Г=5

表6 当Г=5时KDE-AVB与IKDE-AVB在伽玛分布数据集上的对比结果
Table 6 Comparative results between KDE-AVB and IKDE-AVB on gamma distribution when Г=5

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备注

引言

1 核密度估计法

2 KDE-AVB

3 IKDE-AVB

4 实验结果与分析

5 结语

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期刊信息

备注

引言