Conditional Selective Inference for Robust Regression and Outlier Detection using Piecewise-Linear Homotopy Continuation

TL;DR

This paper introduces a conditional selective inference approach for robust regression and outlier detection, leveraging a homotopy method to handle complex selection events, with demonstrated effectiveness on synthetic and real datasets.

Contribution

It develops a novel conditional SI framework for robust regression using homotopy, extending applicability beyond linear/quadratic constraints.

Findings

Effective outlier detection in noisy data environments.

Applicable to a wide class of robust regression methods.

Good empirical performance on synthetic and real data.

Abstract

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.