论文标题
利曼（Riemannian）优化线性混合模型中方差估计的优化
Riemannian Optimization for Variance Estimation in Linear Mixed Models
论文作者
论文摘要
线性混合模型中的方差参数估计是由于随机效应协方差矩阵的正定限制，许多经典非线性优化算法的挑战。我们通过利用参数空间的内在几何形状来对线性混合模型中的参数估计进行完全新颖的看法。我们将剩余最大似然估计的问题提出为黎曼歧管上的优化问题。基于引入的公式，我们通过Riemannian梯度和Riemannian Hessian提供了有关该问题的几何高阶信息。基于此，我们用Riemannian优化算法来测试我们的方法。与现有方法相比，我们的方法得出的方差参数估计值质量更高。
Variance parameter estimation in linear mixed models is a challenge for many classical nonlinear optimization algorithms due to the positive-definiteness constraint of the random effects covariance matrix. We take a completely novel view on parameter estimation in linear mixed models by exploiting the intrinsic geometry of the parameter space. We formulate the problem of residual maximum likelihood estimation as an optimization problem on a Riemannian manifold. Based on the introduced formulation, we give geometric higher-order information on the problem via the Riemannian gradient and the Riemannian Hessian. Based on that, we test our approach with Riemannian optimization algorithms numerically. Our approach yields a higher quality of the variance parameter estimates compared to existing approaches.
