考虑模型相关性的组合预测过程中单项模型筛选研究

Single Model Screening for Combination Forecast Considering Model Correlation

针对组合预测过程中单项模型筛选难以刻画模型之间相关性的问题,采用模糊测度和模糊积分来刻画模型的相关性,并对单项模型预测结果进行集成,进而提出一种考虑模型相关性的组合预测过程中单项模型筛选方法.采用2可加模糊测度来刻画不同模型之间的相关性,并利用Choquet积分依据模糊测度值,将单项模型的预测值集成起来,形成组合预测结果.在这个组合预测过程中,采用基于模糊测度定义的Shapley值和交互作用指标来对单项模型进行筛选.为了验证文章提出的考虑模型相关性的组合预测单项模型筛选方法的有效性,选择软件工程领域的软件成本估算问题进行算例分析,选择基于案例推理方法(CBR)、最小二乘回归(OLS)、支持向量回归机(SVR)、分类回归树(CART)、人工神经网络(ANN)等数据驱动模型作为软件成本组合预测过程中的单项模型.选择常用的Desharnias数据库来验证模型的有效性.实证结果表明文章提出的单项模型筛选方法是一种有效方法,经过筛选后的组合预测模型能有效提高软件成本估算的精度,此外,研究结果还表明组合估算过程中最重要的模型(Sharply值最大)并不是估算精度最高的模型,即单个模型的重要性与该模型的估算精度没有必然联系,说明传统的以单个模型估算精度为依据的组合预测模型存在着一定的缺陷.

For the difficult of model screening considering model correlation, this paper uses fuzzy measure and fuzzy integral to characterize the model correlation, and then proposes a model to consider a combination of relevance the process of screeningmethods to predict individual models. 2-order additive fuzzy measures is applied to characterize the correlation between the different models and Choquet integral is used to integrate the result from single model. In the combination forecasting process, Shapley value and the interaction index are defined to screen single model. In order to verify the validity of the proposed model, the paper selects software effort estimation problems as example. Five data-driven software effort estimation models, case-based reasoning （CBR）, least squares regression （OLS）, support vector regression （SVR）, classification and regression tree （CART）, artificial neural network （ANN）, are used as the single model. Desharnias database is utilized to verify the model. The empirical results show that the proposed model is an effective method of screening methods, and improve software cost estimation accuracy effectively. In addition, the results also indicate that a combination of the most important estimation model （Sharply maximum value） is not the most accurate estimation of the model, namely the importance of a single model and estimation accuracy of the model are not necessarily linked, indicating that the traditional model of a single estimate accuracy combination forecasting model based on the existence of certain defects.