This paper introduces a new data analysis method for big data using a newly
defined regression model named multiple model linear regression(MMLR), which
separates input datasets into subsets and construct local linear regression
models of them. The proposed data analysis method is shown to be more efficient
and flexible than other regression based methods. This paper also proposes an
approximate algorithm to construct MMLR models based on
$(\epsilon,\delta)$-estimator, and gives mathematical proofs of the correctness
and efficiency of MMLR algorithm, of which the time complexity is linear with
respect to the size of input datasets. This paper also empirically implements
the method on both synthetic and real-world datasets, the algorithm shows to
have comparable performance to existing regression methods in many cases, while
it takes almost the shortest time to provide a high prediction accuracy.

本研究提出了一种新的数据分析方法，使用一种名为多模型线性回归（MMLR）的新定义的回归模型，将输入数据集分成子集并构建局部线性回归模型。该方法比其他基于回归的方法更高效、更灵活。研究还提出了一种基于（ε，δ）- 估计器的近似算法来构建 MMLR 模型，并对 MMLR 算法的正确性和效率进行了数学证明，其时间复杂度与输入数据集的大小成线性关系。此外，研究还在合成数据集和真实世界数据集上进行了实证实验，结果显示算法在许多情况下具有与现有回归方法可比的性能，同时提供了很高的预测准确度而几乎不需要花费过多时间。