论文标题
使用贝叶斯正则化处理大规模线性系统识别中的共线性
Dealing with collinearity in large-scale linear system identification using Bayesian regularization
论文作者
论文摘要
我们考虑识别大规模线性和稳定的动态系统，其输出可能是许多相关输入的结果。因此，严重的不良条件可能会影响估计问题。当通过许多子单元的互连给出的复杂物理系统进行建模时，这种情况通常是一种情况，在这些子单元的互连中可以遇到反馈和代数循环。我们基于贝叶斯正则化制定了一种策略，其中任何脉冲响应都被建模为实现零均值高斯过程的策略。稳定的样条协方差用于包括有关脉冲反应的平滑指数衰减的信息。然后，我们设计了一种新的马尔可夫链蒙特卡洛方案，该方案涉及共线性，并能够有效地重建冲动反应的后部。它基于Gibbs采样的变化，该变体根据影响不同输入的截然性水平来更新参数空间的重叠块。包括数值实验以测试数百个脉冲响应形成系统的方法的好处，并且输入相关性可能很高。
We consider the identification of large-scale linear and stable dynamic systems whose outputs may be the result of many correlated inputs. Hence, severe ill-conditioning may affect the estimation problem. This is a scenario often arising when modeling complex physical systems given by the interconnection of many sub-units where feedback and algebraic loops can be encountered. We develop a strategy based on Bayesian regularization where any impulse response is modeled as the realization of a zero-mean Gaussian process. The stable spline covariance is used to include information on smooth exponential decay of the impulse responses. We then design a new Markov chain Monte Carlo scheme that deals with collinearity and is able to efficiently reconstruct the posterior of the impulse responses. It is based on a variation of Gibbs sampling which updates possibly overlapping blocks of the parameter space on the basis of the level of collinearity affecting the different inputs. Numerical experiments are included to test the goodness of the approach where hundreds of impulse responses form the system and inputs correlation may be very high.
