# Beyond Discrepancy: A Closer Look at the Theory of Distribution Shift

arXiv: https://arxiv.org/abs/2405.19156 · HTML: https://mlsanity.com/paper/2405.19156/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 24 references that are in the map.
- First posted on arXiv 29 May 2024.

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

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Return of Frustratingly Easy Domain Adaptation](https://mlsanity.com/paper/1511.05547/) (2015)
- [The Benefit of Multitask Representation Learning](https://mlsanity.com/paper/1505.06279/) (2015)
- [On the Value of Target Data in Transfer Learning](https://mlsanity.com/paper/2002.04747/) (2020)
- [Rates of Convergence for Nearest Neighbor Classification](https://mlsanity.com/paper/1407.0067/) (2014)
- [Iterative Feature Matching: Toward Provable Domain Generalization with Logarithmic Environments](https://mlsanity.com/paper/2106.09913/) (2021)
- [Multiple Source Domain Adaptation with Adversarial Training of Neural Networks](https://mlsanity.com/paper/1705.09684/) (2017)
- [Limits of Model Selection under Transfer Learning](https://mlsanity.com/paper/2305.00152/) (2023)

## Abstract (arXiv)

Many machine learning models appear to deploy effortlessly under distribution shift, and perform well on a target distribution that is considerably different from the training distribution. Yet, learning theory of distribution shift bounds performance on the target distribution as a function of the discrepancy between the source and target, rarely guaranteeing high target accuracy. Motivated by this gap, this work takes a closer look at the theory of distribution shift for a classifier from a source to a target distribution. Instead of relying on the discrepancy, we adopt an Invariant-Risk-Minimization (IRM)-like assumption connecting the distributions, and characterize conditions under which data from a source distribution is sufficient for accurate classification of the target. When these conditions are not met, we show when only unlabeled data from the target is sufficient, and when labeled target data is needed. In all cases, we provide rigorous theoretical guarantees in the large sample regime.