论文标题
部分可观测时空混沌系统的无模型预测
Penalization-induced shrinking without rotation in high dimensional GLM regression: a cavity analysis
论文作者
论文摘要
在高维回归中，协变量的数量是观察次数的顺序，山脊惩罚通常被用作防止过度拟合的补救措施。不幸的是，对于相关的协变量，这种正则化通常会诱导通用线性模型不仅缩小了估计的参数矢量的收缩，而且还相对于真实向量，也是不需要的\ emph {rotation}。我们通过分析显示如何使用脊惩罚的概括可以消除此问题，并使用空腔方法分析了高维度方案中相应估计器的渐近性能。我们的结果还为调整控制收缩量的参数提供了定量理由。我们将我们的理论预测与模拟数据进行比较，并找到出色的一致性。
In high dimensional regression, where the number of covariates is of the order of the number of observations, ridge penalization is often used as a remedy against overfitting. Unfortunately, for correlated covariates such regularisation typically induces in generalized linear models not only shrinking of the estimated parameter vector, but also an unwanted \emph{rotation} relative to the true vector. We show analytically how this problem can be removed by using a generalization of ridge penalization, and we analyse the asymptotic properties of the corresponding estimators in the high dimensional regime, using the cavity method. Our results also provide a quantitative rationale for tuning the parameter that controlling the amount of shrinking. We compare our theoretical predictions with simulated data and find excellent agreement.
