论文标题
对个性化预测的惩罚角度回归
Penalized angular regression for personalized predictions
论文作者
论文摘要
在许多预测应用中，个性化已成为一个重要功能。我们引入了一种惩罚性的回归方法，该方法固有地实施了惩罚中的个性化。个性化角度（PAN）回归构建回归系数，这些系数特定于为其产生预测的协变量向量，从而个性化回归模型本身。这是通过在回归系数的超球参数化中惩罚角度来实现的。对于正交设计矩阵，表明PAN估计是对低维其特征向量方程的解决方案。使用参数引导程序选择调谐参数，模拟表明，PAN回归可以在预测误差方面超越普通最小二乘和脊回归。我们进一步证明，通过将PAN罚款与$ L_ {2} $惩罚相结合，所得方法将具有均匀的平方平方预测错误，而不是ridge回归。最后，我们在医疗应用中演示了该方法。
Personalization is becoming an important feature in many predictive applications. We introduce a penalized regression method implementing personalization inherently in the penalty. Personalized angle (PAN) regression constructs regression coefficients that are specific to the covariate vector for which one is producing a prediction, thus personalizing the regression model itself. This is achieved by penalizing the angles in a hyperspherical parametrization of the regression coefficients. For an orthogonal design matrix, it is shown that the PAN estimate is the solution to a low-dimensional eigenvector equation. Using a parametric bootstrap procedure to select the tuning parameter, simulations show that PAN regression can outperform ordinary least squares and ridge regression in terms of prediction error. We further prove that by combining the PAN penalty with an $L_{2}$ penalty the resulting method will have uniformly smaller mean squared prediction error than ridge regression, asymptotically. Finally, we demonstrate the method in a medical application.
