论文标题
更强大和一般LASSO选择性推理的参数编程方法
Parametric Programming Approach for More Powerful and General Lasso Selective Inference
论文作者
论文摘要
在过去的几年中，对选择性推理（SI）进行了积极研究，以对线性模型的特征进行推断，这些特征是通过特征选择方法（例如Lasso）自适应选择的。 SI的基本思想是在选择事件上进行推理条件。不幸的是，Lasso原始SI方法的主要局限性不仅是根据所选功能进行的，而且在其迹象上进行的推断 - 这导致由于过度调节而导致权力损失。尽管可以通过考虑所有可能的符号组合的选择事件的结合来规避这种限制，但是只有当所选特征的数量足够小时，这才可行。为了解决此计算瓶颈，我们提出了一种基于参数编程的方法，即使我们具有数千个活动特征，也可以在不适合符号的情况下进行SI。主要思想是在测试统计数据的方向上计算套索解决方案的连续路径，并通过遵循解决方案路径来识别与特征选择事件相对应的数据空间的子集。提出的基于参数编程的方法不仅避免了上述计算瓶颈，而且还可以在各个方面提高SI的性能和实用性。我们进行了几项实验，以证明我们提出的方法的有效性和效率。
Selective Inference (SI) has been actively studied in the past few years for conducting inference on the features of linear models that are adaptively selected by feature selection methods such as Lasso. The basic idea of SI is to make inference conditional on the selection event. Unfortunately, the main limitation of the original SI approach for Lasso is that the inference is conducted not only conditional on the selected features but also on their signs -- this leads to loss of power because of over-conditioning. Although this limitation can be circumvented by considering the union of such selection events for all possible combinations of signs, this is only feasible when the number of selected features is sufficiently small. To address this computational bottleneck, we propose a parametric programming-based method that can conduct SI without conditioning on signs even when we have thousands of active features. The main idea is to compute the continuum path of Lasso solutions in the direction of a test statistic, and identify the subset of the data space corresponding to the feature selection event by following the solution path. The proposed parametric programming-based method not only avoids the aforementioned computational bottleneck but also improves the performance and practicality of SI for Lasso in various respects. We conduct several experiments to demonstrate the effectiveness and efficiency of our proposed method.
