# Information Geometrically Generalized Covariate Shift Adaptation

arXiv: https://arxiv.org/abs/2304.09387 · HTML: https://mlsanity.com/paper/2304.09387/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 51 references that are in the map.
- First posted on arXiv 19 Apr 2023.

## Builds on (most cited first, 9 of 9)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [How Does Batch Normalization Help Optimization?](https://mlsanity.com/paper/1805.11604/) (2018)
- [Evaluating Prediction-Time Batch Normalization for Robustness under Covariate Shift](https://mlsanity.com/paper/2006.10963/) (2020)
- [Rethinking Importance Weighting for Deep Learning under Distribution Shift](https://mlsanity.com/paper/2006.04662/) (2020)
- [A One-step Approach to Covariate Shift Adaptation](https://mlsanity.com/paper/2007.04043/) (2020)
- [Normalization Propagation: A Parametric Technique for Removing Internal Covariate Shift in Deep Networks](https://mlsanity.com/paper/1603.01431/) (2016)
- [α-Geodesical Skew Divergence](https://mlsanity.com/paper/2103.17060/) (2021)
- [An Internal Covariate Shift Bounding Algorithm for Deep Neural Networks by Unitizing Layers' Outputs](https://mlsanity.com/paper/2001.02814/) (2020)

## Built on by (most cited first, 6 of 6)

- [A Short Survey on Importance Weighting for Machine Learning](https://mlsanity.com/paper/2403.10175/) (2024)
- [On permutation-invariant neural networks](https://mlsanity.com/paper/2403.17410/) (2024)
- [Density Ratio Estimation via Sampling along Generalized Geodesics on Statistical Manifolds](https://mlsanity.com/paper/2406.18806/) (2024)
- [Graph-Smoothed Bayesian Black-Box Shift Estimator and Its Information Geometry](https://mlsanity.com/paper/2505.16251/) (2025)
- [Knowledge Distillation under Teacher Misspecification: An Order-Parameter Analysis of the Gap between Teacher Mimicry and Task Performance](https://mlsanity.com/paper/2608.29472/) (2026)
- [Higher-Order Asymptotics of Test-Time Adaptation for Batch Normalization Statistics](https://mlsanity.com/paper/2505.16257/) (2025)

## Abstract (arXiv)

Many machine learning methods assume that the training and test data follow the same distribution. However, in the real world, this assumption is very often violated. In particular, the phenomenon that the marginal distribution of the data changes is called covariate shift, one of the most important research topics in machine learning. We show that the well-known family of covariate shift adaptation methods is unified in the framework of information geometry. Furthermore, we show that parameter search for geometrically generalized covariate shift adaptation method can be achieved efficiently. Numerical experiments show that our generalization can achieve better performance than the existing methods it encompasses.