# Testing hypotheses via orthogonalization

arXiv: https://arxiv.org/abs/2606.29732 · HTML: https://mlsanity.com/paper/2606.29732/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 52 references that are in the map.
- First posted on arXiv 29 Jun 2026.

## Builds on (most cited first, 21 of 21)

- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Optimal Inference After Model Selection](https://mlsanity.com/paper/1410.2597/) (2014)
- [Selective Inference for Hierarchical Clustering](https://mlsanity.com/paper/2012.02936/) (2020)
- [Testing for a Change in Mean After Changepoint Detection](https://mlsanity.com/paper/1910.04291/) (2019)
- [Selective inference for k-means clustering](https://mlsanity.com/paper/2203.15267/) (2022)
- [Post-Selection Inference for Changepoint Detection Algorithms with Application to Copy Number Variation Data](https://mlsanity.com/paper/1812.03644/) (2018)
- [Splitting strategies for post-selection inference](https://mlsanity.com/paper/2102.02159/) (2021)
- [Data fission: splitting a single data point](https://mlsanity.com/paper/2112.11079/) (2021)
- [Data thinning for convolution-closed distributions](https://mlsanity.com/paper/2301.07276/) (2023)
- [Generalized Data Thinning Using Sufficient Statistics](https://mlsanity.com/paper/2303.12931/) (2023)
- [Exact Selective Inference with Randomization](https://mlsanity.com/paper/2212.12940/) (2022)
- [Selective inference for clustering with unknown variance](https://mlsanity.com/paper/2301.12999/) (2023)
- [Tailored inference for finite populations: conditional validity and transfer across distributions](https://mlsanity.com/paper/2104.04565/) (2021)
- [Imputation-Powered Inference](https://mlsanity.com/paper/2509.13778/) (2025)
- [Reconciling model-X and doubly robust approaches to conditional independence testing](https://mlsanity.com/paper/2211.14698/) (2022)
- [Decomposing Gaussians with Unknown Covariance](https://mlsanity.com/paper/2409.11497/) (2024)
- [Improving Power by Conditioning on Less in Post-selection Inference for Changepoints](https://mlsanity.com/paper/2301.05636/) (2023)
- [Discussion of "Data fission: splitting a single data point"](https://mlsanity.com/paper/2409.03069/) (2024)
- [Structure learning for zero-inflated counts, with an application to single-cell RNA sequencing data](https://mlsanity.com/paper/2011.12044/) (2020)
- [Distribution-free two-sample testing with blurred total variation distance](https://mlsanity.com/paper/2602.05862/) (2026)

## Abstract (arXiv)

Classical hypothesis testing frameworks break down in contemporary settings in which null hypotheses are increasingly abstract, the same data are used to both generate and test hypotheses, and minimal assumptions about the underlying data are made. In this work, we propose a new framework for conducting valid hypothesis tests in broad contexts. We propose to add and subtract external noise generated from a symmetric shift-family to our data, X, to partition it into two pieces, X(1) and X(2). We provide a generic strategy for orthogonalizing X(2) against X(1) under the null hypothesis H0, then show that testing whether the orthogonalization was successful provides a valid test of H0 under mild assumptions. Remarkably, this framework extends naturally to the post-selection inference setting: we simply select a hypothesis on X(1), then perform orthogonalization under the selected null. As our approach neither requires pre-specification of the selection mechanism, nor is restricted to a small class of data-generating distributions, it dramatically expands the settings for which valid post-selection inference can be conducted. We showcase the flexibility of our proposal in several case studies involving challenging pre-specified null hypotheses and post-selection inference scenarios.