# Augmented Inverse Hybrid Weighting: Robust Inference under Deterministic and Random Distribution Shifts

arXiv: https://arxiv.org/abs/2608.00701 · HTML: https://mlsanity.com/paper/2608.00701/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 36 references that are in the map.
- First posted on arXiv 1 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Diagnosing Model Performance Under Distribution Shift](https://mlsanity.com/paper/2303.02011/) (2023)
- [A Review of Generalizability and Transportability](https://mlsanity.com/paper/2102.11904/) (2021)
- [Generalizing causal inferences from individuals in randomized trials to all trial-eligible individuals](https://mlsanity.com/paper/1709.04589/) (2017)
- [Extending inferences from a randomized trial to a new target population](https://mlsanity.com/paper/1805.00550/) (2018)
- [Minimal Dispersion Approximately Balancing Weights: Asymptotic Properties and Practical Considerations](https://mlsanity.com/paper/1705.00998/) (2017)
- [Learning under random distributional shifts](https://mlsanity.com/paper/2306.02948/) (2023)
- [Calibrated inference: statistical inference that accounts for both sampling uncertainty and distributional uncertainty](https://mlsanity.com/paper/2202.11886/) (2022)
- [Out-of-distribution generalization under random, dense distributional shifts](https://mlsanity.com/paper/2404.18370/) (2024)
- [Covariate Selection for Generalizing Experimental Results: Application to Large-Scale Development Program in Uganda](https://mlsanity.com/paper/1909.02669/) (2019)
- [Beyond Reweighting: On the Predictive Role of Covariate Shift in Effect Generalization](https://mlsanity.com/paper/2412.08869/) (2024)
- [On the implied weights of linear regression for causal inference](https://mlsanity.com/paper/2104.06581/) (2021)
- [Predicting data value before collection: A coefficient for prioritizing sources under random distribution shift](https://mlsanity.com/paper/2504.06570/) (2025)

## Abstract (arXiv)

Reweighting source samples to match a target covariate distribution is a standard response to distribution shift when generalizing evidence from one population to another. This strategy is well suited to deterministic, learnable covariate discrepancies, but can be insufficient when source--target population differences also contain changes beyond covariate shift or when estimation of the density-ratio weights is unstable. To address this challenge, we introduce a new model that allows non-systematic changes between two population laws after systematic shifts are accounted for. Such residual shift is modeled as random perturbations to the probability space that cannot be represented in a learnable way. In this way, we separate systematic shifts, treated as bias and corrected by reweighting, from residual random perturbations, treated as distributional uncertainty and handled through dataset pooling. Under pure random perturbations, this principle yields Augmented Inverse Distance Weighting (AIDW), which uses regression augmentation and variance-optimal dataset-level pooling. For mixed shifts, we develop Augmented Inverse Hybrid Weighting (AIHW), which interpolates between AIDW and standard augmented importance weighting. Both methods trade off sampling uncertainty and distributional uncertainty via a distributional distance that describes the strength of random perturbations. We establish asymptotic properties of the methods, together with plug-in guidance for choosing tuning parameters and model diagnostic tools. Experiments on three real-world multi-site datasets demonstrate consistent reductions in mean-squared error compared with standard weighting baselines, along with substantially improved empirical coverage in settings where covariate-shift adjustment alone undercovers, showing the robustness of the proposed methods across diverse distribution shift scenarios.