论文标题
通过$ r^2 $调整惩罚估算的调整参数选择
Tuning Parameter Selection for Penalized Estimation via $R^2$
论文作者
论文摘要
惩罚估计的调整参数选择策略对于确定既可以解释又可预测的模型至关重要。但是，流行的策略（例如，通过交叉验证最大程度地减少平均平方的预测误差）倾向于选择具有更多预测指标的模型。本文提出了一种简单而强大的交叉验证策略，基于观察到的值和预测值之间的最大平方相关性，而不是为了支持恢复的目的而不是最大程度地减少平方误差丢失。该策略可以应用于所有惩罚最小二乘估计器，我们表明，在某些条件下，该指标会隐含执行偏差调整。特别关注套索估计量，其中我们的策略与松弛的套索估计量密切相关。我们在功能性变量选择问题上展示了我们的方法，以确定表面肌电图传感器的最佳放置以控制机器人的手提假体。
The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation) tend to select models with more predictors than necessary. This paper proposes a simple, yet powerful cross-validation strategy based on maximizing squared correlations between the observed and predicted values, rather than minimizing squared error loss for the purposes of support recovery. The strategy can be applied to all penalized least-squares estimators and we show that, under certain conditions, the metric implicitly performs a bias adjustment. Specific attention is given to the Lasso estimator, in which our strategy is closely related to the Relaxed Lasso estimator. We demonstrate our approach on a functional variable selection problem to identify optimal placement of surface electromyogram sensors to control a robotic hand prosthesis.
