Deciding which predictors to use plays an integral role in deriving statistical models in a wide range of applications. Motivated by the challenges of predicting events across a telecommunications network, we propose a semi-automated, joint model-fitting and predictor selection procedure for linear regression models. Our approach can model and account for serial correlation in the regression residuals, produces sparse and interpretable models and can be used to jointly select models for a group of related responses. This is achieved through fitting linear models under constraints on the number of nonzero coefficients using a generalisation of a recently developed mixed integer quadratic optimisation approach. The resultant models from our approach achieve better predictive performance on the motivating telecommunications data than methods currently used by industry.

在广泛的应用中，确定要使用的预测变量在推导统计模型中起着不可或缺的作用。受在整个电信网络中预测事件的挑战所激发，我们提出了一种用于线性回归模型的半自动，联合模型拟合和预测器选择程序。我们的方法可以对回归残差中的序列相关性进行建模和说明，生成稀疏和可解释的模型，并且可以用于为一组相关响应联合选择模型。这是通过使用最近开发的混合整数二次优化方法的一般化，在非零系数的数量约束下拟合线性模型来实现的。