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模型估计是机器学习领域一个重要的研究内容,动态数据的模型估计是系统辨识和系统控制的基础.针对AR时间序列模型辨识问题,证明了在给定阶数下AR模型参数的最小二乘估计本质上也是一种矩估计.根据结构风险最小化原理,通过对模型拟合度和模型复杂度的折衷,提出了基于稀疏结构迭代的AR序列模型估计算法,并讨论了基于广义岭估计的最优正则化参数选取规则.数值结果表明,方法能以节省参数的方式有效地实现AR模型的辨识,比矩估计法结果有明显改善.
Model estimation is an important research field in machine learning, and the model estimation of dynamic data is the basis of system identification and system control.For the identification of AR time series models, the least-squares estimation of AR model parameters at a given order is proved Which is essentially a kind of moment estimation.According to the principle of structural risk minimization, an AR sequence model estimation algorithm based on sparse structure iteration is proposed through the trade-off between model fitting degree and model complexity, and the algorithm based on generalized ridge estimation Optimal regularization parameter selection rules.The numerical results show that the method can effectively identify the AR model by saving the parameters, and the result of the specific moment estimation method is obviously improved.