# Distribution Shift Inversion for Out-of-Distribution Prediction

**Authors:** Runpeng Yu, Songhua Liu, Xingyi Yang, Xinchao Wang  
**arXiv:** [2306.08328](https://arxiv.org/abs/2306.08328)  
**Date:** 2023-06-14  
**Summary page:** https://www.summarizepaper.com/en/paper/2306.08328v1/

## Key points

- Development of numerous algorithms in machine learning to address distribution shift between training and testing data
- Mitigating distribution shift in unseen testing sets is rarely investigated due to unavailability of testing data during training
- Proposal of portable Distribution Shift Inversion (DSI) algorithm that bypasses requirement of testing data for distribution translator training
- DSI algorithm combines OoD testing samples with additional Gaussian noise and transfers them back towards the training distribution using a diffusion model trained only on the source distribution
- Effectiveness of DSI method supported by theoretical analysis and experimental results
- Integration of DSI into commonly used OoD algorithms demonstrated
- Cost analyses and practical suggestions provided for inference and training processes.

## Summary

The field of machine learning has seen the development of numerous algorithms that address the distribution shift between training and testing data in order to improve out-of-distribution (OoD) prediction. However, mitigating the distribution shift in unseen testing sets is rarely investigated due to the unavailability of testing data during training. To tackle this issue, the authors propose a portable Distribution Shift Inversion (DSI) algorithm that bypasses the requirement of testing data for distribution translator training. The algorithm combines OoD testing samples with additional Gaussian noise and transfers them back towards the training distribution using a diffusion model trained only on the source distribution. The effectiveness of this method is supported by theoretical analysis and experimental results which demonstrate its integration into commonly used OoD algorithms. Furthermore, cost analyses and practical suggestions are provided for inference and training processes.