Conditional Selective Inference for Robust Regression and Outlier Detection using Piecewise-Linear Homotopy Continuation
This work addresses a specific statistical inference challenge for data analysts in noisy environments, offering a novel method but with incremental improvements over existing selective inference frameworks.
The paper tackles the problem of conducting statistical inference after outlier removal in robust regression, proposing a conditional selective inference method using homotopy continuation to handle non-linear selection events, and demonstrates good performance on synthetic and real data.
In practical data analysis under noisy environment, it is common to first use robust methods to identify outliers, and then to conduct further analysis after removing the outliers. In this paper, we consider statistical inference of the model estimated after outliers are removed, which can be interpreted as a selective inference (SI) problem. To use conditional SI framework, it is necessary to characterize the events of how the robust method identifies outliers. Unfortunately, the existing methods cannot be directly used here because they are applicable to the case where the selection events can be represented by linear/quadratic constraints. In this paper, we propose a conditional SI method for popular robust regressions by using homotopy method. We show that the proposed conditional SI method is applicable to a wide class of robust regression and outlier detection methods and has good empirical performance on both synthetic data and real data experiments.