论文标题
多旋转kaczmarz用于潜在类别回归
Multi-Randomized Kaczmarz for Latent Class Regression
论文作者
论文摘要
线性回归有效地识别数据集中的可解释趋势，但是平均对数据中的亚组有可能不同的影响。我们基于随机Kaczmarz（RK）方法提出了一种迭代算法，以自动识别数据中的亚组并同时对这些组进行线性回归。我们证明了这种方法几乎确定的收敛，以及在某些条件下预期的线性收敛。结果是可解释的重量向量集合，用于回归变量，以捕获数据中的不同趋势。此外，我们通过证明该方法可以成功识别模拟数据中的两个趋势来实验验证我们的收敛结果。
Linear regression is effective at identifying interpretable trends in a data set, but averages out potentially different effects on subgroups within data. We propose an iterative algorithm based on the randomized Kaczmarz (RK) method to automatically identify subgroups in data and perform linear regression on these groups simultaneously. We prove almost sure convergence for this method, as well as linear convergence in expectation under certain conditions. The result is an interpretable collection of different weight vectors for the regressor variables that capture the different trends within data. Furthermore, we experimentally validate our convergence results by demonstrating the method can successfully identify two trends within simulated data.
