标题： 基于增量种子EM算法的分块线性回归 显示英文标题

标题： Incremental Seeded EM Algorithm for Clusterwise Linear Regression

摘要： 本文提出了增量种子期望最大化算法，该算法改进了传统的期望最大化计算流程，用于分组或有限混合线性回归任务。 所提出的方法表现出显著更好的性能，特别是在高维输入、噪声数据或大量聚类的场景中。 除了新算法外，本文还引入了 $\textit{Resolvability}$ 和 $\textit{X-predictability}$ 的概念，这些概念使得对分组回归问题的讨论更加严谨。 可解决性指数是通过模型得出的参数来量化，并且结果表明它与模型质量有很强的联系，而无需了解真实情况。 这使得 $\textit{Resolvability}$ 特别适用于评估分组回归模型的质量，进而评估由此得出的结论。 显示英文摘要

摘要： This paper proposes Incremental Seeded Expectation Maximization, an algorithm that improves upon the traditional Expectation Maximization computational flow for clusterwise or finite mixture linear regression tasks. The proposed method shows significantly better performance, particularly in scenarios involving high-dimensional input, noisy data, or a large number of clusters. Alongside the new algorithm, this paper introduces the concepts of $\textit{Resolvability}$ and $\textit{X-predictability}$, which enable more rigorous discussions of clusterwise regression problems. The resolvability index is quantified using parameters derived from the model, and results demonstrate its strong connection to model quality without requiring knowledge of the ground truth. This makes the $\textit{Resolvability}$ especially useful for assessing the quality of clusterwise regression models, and by extension, the conclusions drawn from them.