Isotonic Regression

Follow this topic Ask about this topic

Isotonic regression estimates a function that respects a known ordering in the data, often by minimizing prediction error subject to monotonicity constraints; the pool-adjacent-violators algorithm is a standard efficient solver. It is used for probability calibration, survival prediction, paired-comparison ranking, and correcting scores from models or benchmarks. Extensions include groupwise calibration and multidimensional methods that impose monotonicity through optimal transport, while theoretical analyses study finite-sample complexity and calibration guarantees. A central challenge is balancing flexible calibration against overfitting and loss of discrimination, with performance depending on sample size, operating conditions, and the metric used.

Latest papers

12 papers1 paper in the last four weeks, with none the four weeks before. 0.0% of all new papers.

Are You Sure Your LLM Is Sure? Repairing and Auditing Confidence
Oct 15, 2026Arijit Dey, Bhartendu Kumar, Ramya Hebbalaguppe +1Confidence Estimation in Language Models Language Model Calibration
MBZUAI · TCS Research Labs, India · IIT Delhi
TrustRoboReward: Preference-Ordered Isotonic Score Editing for Multi-Paradigm Robot Reward Models
Aug 9, 2026Yidong Wang, Yan Zhan, Ziteng Feng +16Reward Modeling Pairwise Preference Evaluation
Peking University · University of Science and Technology of China · Southeast University +6
Isotonic Bradley-Terry Model for Paired Comparison Data
Aug 3, 2026Ryoya YamasakiPairwise Preference Learning Pairwise Comparison
Hitotsubashi Institute for Advanced Study, Hitotsubashi University, 2-1 Naka, Kunitachi, 186-8601, Tokyo, Japan.
An analysis of binary isotonic regression: degrees of freedom and implications for calibration
Jul 29, 2026Raphael Rossellini, Rina Foygel Barber, Zhimei Ren +1Probability Calibration Model Calibration
Department of Statistics, University of Chicago · Department of Statistics and Data Science, University of Pennsylvania · Department of Statistics, University of Michigan
Isotonic Conformal Prediction
Jul 18, 2026Daniel Bensimon, Sean Xiang Yu, Eric D. Kolaczyk +1Conformal Prediction Uncertainty Calibration
Department of Mathematics and Statistics, McGill University; Mila · Eli Lilly and Company
Condition-Stratified Robustness Analysis of Post-Hoc Calibration Methods for Probabilistic Classifiers
Jul 13, 2026Gurdeep Singh VirdeePost-Hoc Calibration Probability Calibration
Fergana State Technical University, Uzbekistan
Why Not Hyperparameter-Friendly Optimisation? A Monotonic Adaptive Norm Rescaling Approach For Long-Tailed Recognition
Jun 1, 2026Shuo Zhang, Chenqi Li, Tingting ZhuLong-Tailed Classification Isotonic Regression
University of Oxford
Isotonic Survival Regression: Calibrated Survival Distributions from Deep Cox Models
May 15, 2026Anchit Jain, Kevin Zhang, Stephen BatesPost-Hoc Calibration Survival Analysis
EECS, MIT, Cambridge MA, USA.
Calibeating Prediction-Powered Inference
Apr 23, 2026Lars van der Laan, Mark Van Der LaanInverse Probability Weighting Parameter Estimation
Department of Statistics, University of Washington · Department of Statistics and Division of Biostatistics, Center for Targeted Machine Learning and Causal Inference, University of California, Berkeley
Calibrating Model-Based Evaluation Metrics for Summarization
Apr 19, 2026Hongye Liu, Dhanajit Brahma, Ricardo HenaoLanguage Model Calibration Summarization Evaluation
Duke University
Efficient Detection of Bad Benchmark Items with Novel Scalability Coefficients
Mar 26, 2026Michael Hardy, Joshua Gilbert, Benjamin DomingueBenchmark Auditing Psychometric Validation
Stanford University, CA, United States · Harvard University, MA, United States
Brenier Isotonic Regression
Mar 11, 2026Han Bao, Amirreza Eshraghi, Yutong WangIsotonic Regression Monotonicity Constraints
The Institute of Statistical Mathematics · Illinois Institute of Technology

Oct 15, 2026J/K move · Enter open · S save

Are You Sure Your LLM Is Sure? Repairing and Auditing Confidence

Arijit Dey, Bhartendu Kumar, Ramya Hebbalaguppe, Khuushi Maheshwari

MBZUAI · TCS Research Labs, India · IIT Delhi

Confidence Estimation in Language Models Language Model Calibration Confidence Estimation Probability Calibration LLM Auditing Isotonic Regression

Open paper AskPDF arXiv

Confidence scores determine whether an LLM answer is accepted, reviewed, or regenerated, yet scalar recalibration can only correct errors visible through the score itself. We introduce RADAR (Repair, Adopt, and Diagnose After Recalibration), a reliability framework that separates confidence repair from deciding whether to deploy the repair and auditing the errors that remain. Under squared loss, we decompose prediction risk into outcome noise, information hidden by the score, and mapping error; restricting repair to order-preserving maps additionally introduces a pooling gap. For repair, we propose Probe-Anchored Isotonic Calibration (PAIC), which learns a monotone map from correctness-probe predictions on unlabeled target prompts. PAIC's excess risk depends on the probe's score-conditional bias and fitting error rather than its overall accuracy. For adoption, we derive a paired procedure with finite-sample control of false improvements. For auditing, we develop a prompt-clustered kernel test that detects feature-aligned residual errors while accounting for dependent answers from the same prompt. Across multiple LLM checkpoints, benchmarks, and distribution shifts, richer predictors can improve confidence estimation, but projecting their information back to a scalar score can lose these gains, and lower prediction risk need not yield better review decisions. Across 47,400 replayed raw-score allocations, paired betting adopts candidates with lower held-out test risk in 42.95% of allocations, versus 15.09% for one-sided empirical Bernstein. RADAR thus provides a principled workflow to repair what a scalar score can express, adopt a repair only when supported by evidence, and diagnose systematic errors that recalibration leaves behind. Code and data will be released upon acceptance.