论文标题
具有网络对准信号和相关设计的最小二乘回归的广义弹性网
The Generalized Elastic Net for least squares regression with network-aligned signal and correlated design
论文作者
论文摘要
我们提出了一个新颖的$ \ ell_1+\ ell_2 $ -penalty，我们称为广义弹性网，对于回归问题，在这些回归问题上，特征向量由给定图的顶点索引，并且认为真实信号相对于此图表而言是平滑或分段的常数。在相关的高斯设计的假设下，我们得出了预测和估计误差的上限，这些误差依赖图和估计误差，由回归矢量的未呈现部分的参数速率组成，而另一个术语则取决于我们的网络对齐假设。我们还基于Lagrange双重目标提供了协调下降程序，以计算此估计器的大规模问题。最后，我们将提出的估计器与许多实际和合成数据集的现有正规估计器进行比较，并讨论其潜在局限性。
We propose a novel $\ell_1+\ell_2$-penalty, which we refer to as the Generalized Elastic Net, for regression problems where the feature vectors are indexed by vertices of a given graph and the true signal is believed to be smooth or piecewise constant with respect to this graph. Under the assumption of correlated Gaussian design, we derive upper bounds for the prediction and estimation errors, which are graph-dependent and consist of a parametric rate for the unpenalized portion of the regression vector and another term that depends on our network alignment assumption. We also provide a coordinate descent procedure based on the Lagrange dual objective to compute this estimator for large-scale problems. Finally, we compare our proposed estimator to existing regularized estimators on a number of real and synthetic datasets and discuss its potential limitations.
