前向模型的辨识：一种非参数方法
Identification of forward models: a nonparametric approach
浏览论文内容
中文总结 AI 辅助
本文提出一种基于核的非参数方法，通过求解非线性Tikhonov正则化问题来辨识前向模型的脉冲响应，并利用拉普拉斯近似优化边际似然，实验验证了其有效性。
中文摘要 AI 辅助
本文提出了一种新的基于核的方法，用于辨识前向模型的脉冲响应。由此产生的估计器导致一个非线性Tikhonov正则化问题，我们证明了该问题解的存在性。这一结果使得通过高阶带外生输入的自回归滑动平均（MAX）模型来逼近前向模型是合理的，即使用该模型得到的数值解在估计中仅引入可忽略的偏差。我们还考虑了通过优化边际似然来估计核超参数的问题。由于边际似然不存在闭式表达式，我们提出了一种依赖于边际似然拉普拉斯近似的评估方法。最后，我们讨论了一些数值实验，以展示所提出方法的有效性。
英文摘要
In this paper we propose a new kernel-based method for the identification of the impulse responses of forward models. The resulting estimator leads to a nonlinear Tikhonov regularization problem for which we prove the existence of a solution. The latter result makes legitimate to approximate the forward model through a high-order Moving Average with eXogenous input (MAX) model, i.e. the numerical solution found using this model introduces only a negligible bias in the estimate. The optimization of the marginal likelihood to estimate the kernel hyperparameters is also taken into account. Since there does not exist a closed-form expression for the marginal likelihood, we present an evaluation method that relies on the Laplace approximation of the marginal likelihood. Finally, some numerical experiments are discussed to show the effectiveness of the proposed method.
