# Selective Inference via Marginal Screening for High Dimensional Classification

## TL;DR

This paper develops a selective inference framework for high-dimensional binary classification using logistic regression after marginal screening, enabling valid hypothesis testing with controlled error rates.

## Contribution

It introduces a novel selective inference method for logistic regression post-marginal screening in high dimensions, extending existing Gaussian linear model techniques.

## Key findings

- The method asymptotically controls selective type I error.
- Simulation studies confirm the statistical power of the proposed test.
- Compared favorably with data splitting and other approaches.

## Abstract

Post-selection inference is a statistical technique for determining salient variables after model or variable selection. Recently, selective inference, a kind of post-selection inference framework, has garnered the attention in the statistics and machine learning communities. By conditioning on a specific variable selection procedure, selective inference can properly control for so-called selective type I error, which is a type I error conditional on a variable selection procedure, without imposing excessive additional computational costs. While selective inference can provide a valid hypothesis testing procedure, the main focus has hitherto been on Gaussian linear regression models. In this paper, we develop a selective inference framework for binary classification problem. We consider a logistic regression model after variable selection based on marginal screening, and derive the high dimensional statistical behavior of the post-selection estimator. This enables us to asymptotically control for selective type I error for the purposes of hypothesis testing after variable selection. We conduct several simulation studies to confirm the statistical power of the test, and compare our proposed method with data splitting and other methods.