改进型平均移位柱状图估算概率密度并对互信息作相关分析

Correlation analysis of mutual information by probability density estimated from improved averaged-shifted-histogram

中文关键词  平均移位柱状图  互信息  相关性分析  时间序列预测

英文关键词  averaged-shifted-histogram  mutual information  correlation analysis  time series prediction

中文摘要

      将平均移位柱状图(averaged shifted histogram, ASH)概率密度估计中二次型平滑权值与均匀权值进行结合, 提出一种改进的概率密度估计方法: IASH(improved averaged shifted histogram). 通过相应区间内样本数目的方差确定原平滑权值与均匀权值之间的比例系数, 动态的改变平滑权值: 对ASH概率密度估计中边缘值部分的平滑权值按比例进行补偿, 改善过平滑的问题, 提高了IASH概率密度估计的精度. 在此基础上应用互信息进行变量间的相关性分析, 选择输入变量, 实现多元时间序列的预测. 采用人工数据和实际Housing数据进行仿真分析, 仿真结果验证了改进后方法的有效性.

英文摘要

      We introduce the method of improved averaged-shifted-histogram(IASH) to estimate the probability density by combining the quadratic smooth weight with the uniform smooth weight. The ratio of the original smooth weight to the uniform smooth weight is dynamically adjusted according to the variance of the number of samples in the corresponding interval, thus the smooth weight for the edge part of the probability density obtained by the method of averaged-shiftedhistogram(ASH) is proportionally compensated, mitigating the excessive smoothness and improving the precision in the estimation of probability density by the method of IASH. Using the estimated probability density, we perform the correlation analysis based on the mutual information between two variables, and select input variables to predict the multivariate time series. Simulations with the synthetic data and Housing data show the efficacy of the proposed method.