多任务高斯过程回归的模型平均

Model Averaging for Multi-Task Gaussian Process Regression

模型平均因其稳健性好、预测精度高等优点在当代统计学和计量经济学界有广泛应用。多任务高斯过程回归同时考虑了输入变量之间和输出变量之间的相关性,能够得到更为准确的预测值。考虑到输出之间的相关性,本文先构建多任务高斯过程回归模型(MGPR),再进行模型平均及选择;不考虑输出之间的相关性时,分别构建单任务高斯过程回归(GPR),再进行模型平均及选择。数值模拟结果表明,输出噪声为同方差时,MGPR的模型平均比GPR具有更小的损失风险,且MGPR的计算效率相对较高。输出噪声同方差时,采用中国少数民族地区城市化率、非农业人口比例及受教育年限的实际数据;输出噪声异方差时,采用苄醇转化率和转频率的实际数据,均表明MGPR的模型平均具有更小的损失风险。

Model averaging, owing to its advantages of robustness and high predictive accuracy, finds exten-sive application in contemporary statistics and econometrics. Multi-task Gaussian process regres-sion, considering both the interdependencies among input variables and the correlations among output variables, enables more precise predictions. Taking into account the inter-output correla-tions, this paper constructs a Multi-Task Gaussian Process Regression model (MGPR) followed by model averaging and selection. Conversely, when disregarding inter-output correlations, single-task Gaussian Process Regression (GPR) models are individually constructed, followed by the same pro-cess of model averaging and selection. Numerical simulation results demonstrate that when the output noise exhibits homoscedastic variance, MGPR’s model averaging exhibits lower loss risk compared to GPR, with relatively higher computational efficiency. For the case of homoscedastic output noise, actual data on urbanization rates in China’s ethnic minority regions, non- agricultural population ratios, and years of education are employed. In the case of heteroscedastic output noise, real data on benzyl alcohol conversion rates and turnover frequencies are utilized, both indicating that MGPR’s model averaging yields lower loss risk.