Tibshirani Robert, Suo Xiaotong
Department of Health Research, & Policy, and Statistics, Stanford University, Stanford, CA 94305.
Institute for Computational & Mathematical Engineering, Stanford University, Huang Engineering Center, 475 Via Ortega, Suite 060, Stanford, CA 94305.
Technometrics. 2016;58(4):415-423. doi: 10.1080/00401706.2015.1079245. Epub 2016 Oct 11.
We consider regression scenarios where it is natural to impose an order constraint on the coefficients. We propose an order-constrained version of -regularized regression (Lasso) for this problem, and show how to solve it efficiently using the well-known Pool Adjacent Violators Algorithm as its proximal operator. The main application of this idea is to time-lagged regression, where we predict an outcome at time from features at the previous time points. In this setting it is natural to assume that the coefficients decay as we move farther away from , and hence the order constraint is reasonable. Potential application areas include financial time series and prediction of dynamic patient outcomes based on clinical measurements. We illustrate this idea on real and simulated data.
我们考虑回归场景，在这些场景中对系数施加顺序约束是很自然的。针对此问题，我们提出了一种 - 正则化回归（套索回归）的顺序约束版本，并展示了如何使用著名的池相邻违规者算法作为其近端算子来高效求解。这个想法的主要应用是时间滞后回归，即我们根据前 个时间点的特征来预测时间 时的结果。在这种情况下，自然可以假设随着我们离 越来越远，系数会衰减，因此顺序约束是合理的。潜在的应用领域包括金融时间序列以及基于临床测量对动态患者结果的预测。我们在真实数据和模拟数据上说明了这个想法。
