Inspired by the tremendous achievements of meta-learning in various fields, this paper proposes the local quadratic embedding learning (LQEL) algorithm for regression problems based on metric learning and neural networks (NNs). First, Mahalanobis metric learning is improved by optimizing the global consistency of the metrics between instances in the input and output space. Then, we further prove that the improved metric learning problem is equivalent to a convex programming problem by relaxing the constraints. Based on the hypothesis of local quadratic interpolation, the algorithm introduces two lightweight NNs; one is used to learn the coefficient matrix in the local quadratic model, and the other is implemented for weight assignment for the prediction results obtained from different local neighbors. Finally, the two sub-models are embedded in a unified regression framework, and the parameters are learned by means of a stochastic gradient descent (SGD) algorithm. The proposed algorithm can make full use of the information implied in target labels to find more reliable reference instances. Moreover, it prevents the model degradation caused by sensor drift and unmeasurable variables by modeling variable differences with the LQEL algorithm. Simulation results on multiple benchmark datasets and two practical industrial applications show that the proposed method outperforms several popular regression methods.

受元学习在各个领域取得的巨大成就的启发，本文提出了基于度量学习和神经网络（NN）的回归问题的局部二次嵌入学习（LQEL）算法。首先，通过优化输入和输出空间中实例之间度量的全局一致性来改进马氏度量学习。然后，我们通过放松约束进一步证明改进的度量学习问题等价于凸规划问题。基于局部二次插值的假设，该算法引入了两个轻量级神经网络；一个用于学习局部二次模型中的系数矩阵，另一个用于对从不同局部邻居获得的预测结果进行权重分配。最后，两个子模型嵌入在一个统一的回归框架中，通过随机梯度下降（SGD）算法学习参数。所提出的算法可以充分利用目标标签中隐含的信息来找到更可靠的参考实例。此外，它通过使用 LQEL 算法对变量差异进行建模，防止由传感器漂移和不可测量变量引起的模型退化。多个基准数据集和两个实际工业应用的仿真结果表明，所提出的方法优于几种流行的回归方法。此外，它通过使用 LQEL 算法对变量差异进行建模，防止由传感器漂移和不可测量变量引起的模型退化。多个基准数据集和两个实际工业应用的仿真结果表明，所提出的方法优于几种流行的回归方法。此外，它通过使用 LQEL 算法对变量差异进行建模，防止由传感器漂移和不可测量变量引起的模型退化。多个基准数据集和两个实际工业应用的仿真结果表明，所提出的方法优于几种流行的回归方法。