Title: Flexible Selective Inference with Flow-based Transport Maps Show Chinese title

Title: 基于流的传输映射的灵活选择推理

Abstract: Data-carving methods perform selective inference by conditioning the distribution of data on the observed selection event. However, existing data-carving approaches typically require an analytically tractable characterization of the selection event. This paper introduces a new method that leverages tools from flow-based generative modeling to approximate a potentially complex conditional distribution, even when the underlying selection event lacks an analytical description -- take, for example, the data-adaptive tuning of model parameters. The key idea is to learn a transport map that pushes forward a simple reference distribution to the conditional distribution given selection. This map is efficiently learned via a normalizing flow, without imposing any further restrictions on the nature of the selection event. Through extensive numerical experiments on both simulated and real data, we demonstrate that this method enables flexible selective inference by providing: (i) valid p-values and confidence sets for adaptively selected hypotheses and parameters, (ii) a closed-form expression for the conditional density function, enabling likelihood-based and quantile-based inference, and (iii) adjustments for intractable selection steps that can be easily integrated with existing methods designed to account for the tractable steps in a selection procedure involving multiple steps. Show Chinese abstract

Abstract: 数据雕刻方法通过条件化数据分布以观测到的选择事件来进行选择性推断。 然而，现有的数据雕刻方法通常需要对选择事件进行解析可处理的特征描述。 本文介绍了一种新方法，该方法利用基于流的生成模型工具来近似潜在复杂的条件分布，即使底层选择事件缺乏解析描述——例如，模型参数的数据自适应调整。 关键思想是学习一个传输映射，将一个简单的参考分布推向给定选择的条件分布。 此映射通过归一化流高效地学习，而无需对选择事件的本质施加任何进一步限制。 通过在模拟和真实数据上的大量数值实验，我们证明了这种方法通过以下方式实现了灵活的选择性推断：(i) 为自适应选择的假设和参数提供有效的 p 值和置信集，(ii) 条件密度函数的闭式表达式，支持基于似然和基于分位数的推断，以及 (iii) 对无法处理的选择步骤进行调整，可以轻松与现有方法集成，以考虑涉及多步选择程序中的可处理步骤。