基于实例与目标相关性的多目标稀疏回归算法

针对传统多目标回归算法无法处理输入与多输出间的非线性关系,且忽视了数据点在输入与输出之间的结构信息,导致算法泛化性能受限、缺乏稳健性等问题,提出一种基于实例与目标相关性的多目标稀疏回归(multi-target sparse regression with instances and targets correlations,MTR-ITC)算法.首先,通过嵌入潜变量空间来对复杂的输入与输出以及输出间的关联结构解耦,并利用核技巧和稀疏回归学习输入输出间的非线性关系和输出间的相关结构;然后,引入流形正则化项探索不同实例在输入与输出变量间的相关性,确保模型输出与真实结果在局部和全局结构的一致性,以提升模型泛化性能;最后,提出一种交替优化算法来对目标函数进行求解,使其能快速收敛至全局最优.在基准测试数据集上的实验表明,所提算法在不同MTR数据集上均具有较好的测试性能.

Multi-target sparse regression with instance and target correlations

To address the problem that traditional multitarget regression algorithms only focus on the linear correlation between input features and target outputs, but ignore the structural information between different instances, i.e., instance correlation and target correlation, which leads to limited performance of the algorithm, we propose a multi-target sparse regression algorithm based on instance and target correlation(MTR-ITC). First, we construct latent variable space to decouple the complex input-output and output correlation structures, and impose sparse constraints on the corresponding coefficient matrices to explicit encoding and sparse learning of inter-target correlations in the latent variable space. Then, manifold learning is introduced to explore the correlation between different instances in the input and output space to ensure that the model output is consistent with the real results in terms of local and global structure. Finally, an alternating optimization algorithm is proposed to solve the objective function optimally and converge it to the global optimum efficiently. Experiments on the benchmark test dataset show that the MTR-ITC improves the performance of the algorithm compared to existing representative algorithms, and its good convergence makes it possible to iterate and converge to the global optimum rapidly.