More Powerful and General Selective Inference for Stepwise Feature Selection using Homotopy Method
More Powerful and General Selective Inference for Stepwise Feature Selection using Homotopy Method
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发表时间：
2021
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通讯作者：
Kazuya Sugiyama;Vo Nguyen Le Duy;I. Takeuchi
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作者：
Kazuya Sugiyama;Vo Nguyen Le Duy;I. Takeuchi
条件选择推理（SI）作为一种新的数据驱动假设的统计推理框架得到了积极的研究。条件SI的基本思想是根据以一组线性和/或二次不等式为特征的选择事件做出有条件的推论。条件语义分析主要是在逐步特征选择（SFS）等特征选择的背景下进行的。现有条件SI方法的主要限制是由于过度调节而导致的功率损失，这是计算可追溯性所必需的。在这项研究中，我们利用同伦方法开发了一种更强大和通用的条件SI方法，使我们能够克服这一限制。基于同伦的SI对于更复杂的特征选择算法尤其有效。作为一个例子，我们开发了一种基于aic停止标准的前向后SFS的条件SI方法，并表明它不会受到算法复杂性增加的不利影响。我们进行了几个实验来证明该方法的有效性和效率。
Conditional selective inference (SI) has been actively studied as a new statistical inference framework for data-driven hypotheses. The basic idea of conditional SI is to make inferences conditional on the selection event characterized by a set of linear and/or quadratic inequalities. Conditional SI has been mainly studied in the context of feature selection such as stepwise feature selection (SFS). The main limitation of the existing conditional SI methods is the loss of power due to over-conditioning, which is required for computational tractability. In this study, we develop a more powerful and general conditional SI method for SFS using the homotopy method which enables us to overcome this limitation. The homotopy-based SI is especially effective for more complicated feature selection algorithms. As an example, we develop a conditional SI method for forward-backward SFS with AIC-based stopping criteria, and show that it is not adversely affected by the increased complexity of the algorithm. We conduct several experiments to demonstrate the effectiveness and efficiency of the proposed method.