arXiv:2608.04667stat.MLcs.LG2026-08

自动计算特征选择的精确统计检验,无需手动推导公式。

Automatic Statistical Test for Rationally Expressible Algorithms by Selective Inference, with Applications to Feature Selection

  • 将算法代码直接转为可验证的统计推断框架,无需人工推导选择条件。
  • 支持任意有理函数表达的算法,突破线性/二次约束限制。
  • 在真实和合成数据上保持零误差率,适合高精度特征筛选场景。

选择性推断(SI)可对由算法从数据中选取的假设提供统计有效的p值,纠正因同一数据既用于选择又用于检验而产生的偏差。然而,为新算法开发精确的SI流程,通常需专家手动推导并实现选择事件(即假设被选中的条件)。这一繁琐过程使得现有方法仅适用于少数特定算法。我们提出AutoSI框架,通过两种方式打破该障碍:首先,AutoSI能自动从算法的单个操作构建选择事件,用户只需以类似NumPy的代码形式编写算法,无需手工推导;其次,AutoSI扩展了可处理的选择事件类型——现有精确方法仅限于数据中线性或二次不等式定义的事件,而AutoSI可处理任何由数据有理函数(多项式之比)表达的算法。我们证明,AutoSI计算的p值在有限样本下精确有效。我们在三个特征选择方法上验证了该框架,每个仅需数十行代码。其中一种方法(基于交叉验证R²选择调参的lasso)无法在现有精确框架中实现,现由AutoSI成功支持。在合成与真实数据上的实验表明,所得p值严格控制第一类错误率(假阳性率)于名义水平,同时保持高检验效能。

原文摘要 · Abstract (English)

Selective inference (SI) provides statistically valid $p$-values for hypotheses selected by applying an algorithm to the data, correcting for the bias that arises when the same data are used both to select and to test a hypothesis. Developing an SI procedure for a new algorithm, however, has required an expert to derive, and then implement, the selection event, i.e., the conditions under which the hypothesis is selected. Repeating this specialized effort for every new algorithm is why exact SI has so far been available for only a narrow class. We propose AutoSI, a framework that removes this barrier in two ways. First, AutoSI constructs the selection event automatically from the algorithm's individual operations, so the user only writes the algorithm as ordinary NumPy-like code and derives nothing by hand. Second, AutoSI broadens the class of selection events SI can handle: existing exact methods are limited to selection events characterized by linear or quadratic inequalities in the data, whereas AutoSI covers any algorithm expressible through rational functions of the data (ratios of polynomials). We prove that the $p$-values computed by AutoSI are exactly valid in finite samples. We demonstrate AutoSI on three feature-selection methods, each written in a few dozen lines of code. One of these methods, the lasso with its tuning parameter selected by cross-validated $R^2$, cannot be handled within existing exact SI frameworks and is made possible by AutoSI. Experiments on synthetic and real datasets show that the resulting $p$-values control the type I error rate (i.e., the false positive rate) at the nominal level while retaining high power.

统计推断特征选择自动推理有理函数

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。