# Coarsening Latent-Class Probabilities: Directional Distortion and Coverage Loss

arXiv: https://arxiv.org/abs/2608.11784 · HTML: https://mlsanity.com/paper/2608.11784/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 43 references that are in the map.
- First posted on arXiv 12 Aug 2026.

## Builds on (most cited first, 11 of 11)

- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [Fairness Under Unawareness: Assessing Disparity When Protected Class Is Unobserved](https://mlsanity.com/paper/1811.11154/) (2018)
- [Assessing Algorithmic Fairness with Unobserved Protected Class Using Data Combination](https://mlsanity.com/paper/1906.00285/) (2019)
- [Assumption-Lean and Data-Adaptive Post-Prediction Inference](https://mlsanity.com/paper/2311.14220/) (2023)
- [Inference for Regression with Variables Generated by AI or Machine Learning](https://mlsanity.com/paper/2402.15585/) (2024)
- [Estimating Racial Disparities When Race is Not Observed](https://mlsanity.com/paper/2303.02580/) (2023)
- [Addressing Discretization-Induced Bias in Demographic Prediction](https://mlsanity.com/paper/2405.16762/) (2024)
- [Sensitivity Analysis using Approximate Moment Condition Models](https://mlsanity.com/paper/1808.07387/) (2018)
- [Identification of Latent Group Effects under Conditional Calibration](https://mlsanity.com/paper/2604.08798/) (2026)
- [When to Trust Confidence Thresholding: Calibration Diagnostics for Pseudo-Labelled Regression](https://mlsanity.com/paper/2605.12780/) (2026)

## Abstract (arXiv)

Outcomes are regressed on a calibrated probability vector for unobserved class membership. Under a structural conditional mean excluding the score and conditional calibration, the observed-data model reduces to a partially linear regression. The probability vector is a Berkson-type surrogate for membership, so the effect vector τ is identified without attenuation. In practice the vector is often coarsened to a hard label - an argmax, a confidence threshold - and that label need not retain the Berkson property. For any coarsening the plug-in estimator converges to Aτ, where A-I is determined by the regression of the discarded part of the score on the retained part. Coarsening therefore leaves τ undistorted exactly when that regression vanishes, and otherwise distorts some contrasts far more than others. The same operator determines the bias that drives coverage loss. Where that bias is of the order of the standard error, the Wald interval has limiting coverage Phi(z-nu)-Phi(-z-nu), with nu their ratio. A fixed bias sends coverage to zero. Operator, standard error, and - through the uncoarsened estimator - the bias are estimable from observed data, so the implied coverage can be approximated before the interval is reported. Simulations show severe coverage loss after argmax coarsening. Three real-data audits exhibit the direction-specific distortion.