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pith:DTXDWKRR

pith:2026:DTXDWKRR22B45FA6FFKAZ224BL

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When to Trust Confidence Thresholding: Calibration Diagnostics for Pseudo-Labelled Regression

Marcell T. Kurbucz

The attenuation bias from thresholding confidence scores can be predicted exactly from residual score variance on unlabeled data.

arxiv:2605.12780 v1 · 2026-05-12 · stat.ME · cs.LG · stat.ML

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Claims

C1strongest claim

We derive a closed-form expression for the attenuation bias that confidence thresholding induces in the downstream regression coefficient, and show that the bias can be predicted, before any inference is run, from the residual score variance V^*=E[Var(p|X)] on the unlabelled set after partialling out the downstream controls X.

C2weakest assumption

The recent identification result for the underlying moment equation holds exactly, and calibration drift remains bounded; the structural separation X subset W is maintained so that V* is well-defined and observable.

C3one line summary

Attenuation bias from confidence thresholding in pseudo-labelled regression equals a closed-form function of residual score variance V* after partialling out controls X, yielding a (V*, κ) safety rule computable before inference.

References

29 extracted · 29 resolved · 1 Pith anchors

[1] N. Kallus, X. Mao, A. Zhou, Assessing algorithmic fairness with un- observed protected class using data combination, Management Science 68 (3) (2022) 1959–1981 2022

[2] Lee, Pseudo-label: The simple and efficient semi-supervised learn- ing method for deep neural networks, in: Workshop on challenges in representation learning, ICML, Vol 2013

[3] K. Sohn, D. Berthelot, C.-L. Li, Z. Zhang, N. Carlini, E. D. Cubuk, A.Kurakin, H.Zhang, C.Raffel, FixMatch: Simplifyingsemi-supervised learning with consistency and confidence, in: Advances in Neural 2020

[4] B. Zhang, Y. Wang, W. Hou, H. Wu, J. Wang, M. Okumura, T. Shi- nozaki, FlexMatch: Boosting semi-supervised learning with curriculum pseudo labeling, Advances in neural information processing systems 3 2021

[5] Y. Wang, H. Chen, Q. Heng, W. Hou, Y. Fan, Z. Wu, J. Wang, M. Sav- vides, T. Shinozaki, B. Raj, B. Schiele, X. Xie, FreeMatch: Self-adaptive thresholding for semi-supervised learning, International Co 2023

Receipt and verification

First computed	2026-05-18T03:09:13.160424Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1cee3b2a31d683ce941e29540ceb5c0aeda49fe3d3c5b1b2a031a3a28669c31c

Aliases

arxiv: 2605.12780 · arxiv_version: 2605.12780v1 · doi: 10.48550/arxiv.2605.12780 · pith_short_12: DTXDWKRR22B4 · pith_short_16: DTXDWKRR22B45FA6 · pith_short_8: DTXDWKRR

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/DTXDWKRR22B45FA6FFKAZ224BL \
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# expect: 1cee3b2a31d683ce941e29540ceb5c0aeda49fe3d3c5b1b2a031a3a28669c31c

Canonical record JSON

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