Probability Calibration

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18 papers in the last four weeks, up 260% on the four weeks before. 0.2% of all new papers.

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Oct 6, 2026cs.AI

Confidence Reasoning Graphs: Structured Confidence Estimation for LLM Agents

When using an LLM agent in a consequential domain, making an informed decision about whether to trust its output or intervene requires calibrated confidence in the agent's success. Confidence estimation for agents is difficult because evidence about success is distributed across heterogeneous, interdependent steps of an agent's trajectory. Practical agentic deployments introduce further challenges: frontier LLMs often provide limited access to internal signals, agent roll-outs are costly, and training data may be unavailable or quickly become outdated. To address these challenges, we introduce Confidence Reasoning Graphs (CRGs), an inference-time framework that estimates the probability an agent accomplished its task from a single trajectory, without privileged model access or training data. Rather than compressing an execution into a single holistic judgment, a CRG begins with the claim that the agent accomplished its task, decomposes it into contextualized sub-claims grounded in trajectory evidence, estimates confidence for each terminal claim, and finally aggregates these into an overall confidence estimate. Across three agentic benchmarks, three backbone models, and three agent frameworks, CRGs yield better-calibrated confidence and stronger risk-aware decision making than verbalized, sampling-based, and white-box surrogate baselines. We further find that calibration error alone can be misleading: a white-box surrogate baseline appears well calibrated while providing near-chance discrimination. Ablations attribute CRG's improvements to claim-level confidence estimation and aggregation rather than graph construction alone. Finally, a CRG exposes the claims and trajectory evidence underlying each confidence estimate, enabling it to be audited at decision time.

Brendan King, Farima Fatahi Bayat, Jean-Flavien Bussotti +2

University of California, Santa Cruz · Megagon Labs

Probability Calibration Confidence Estimation in Language Models LLM Agent Evaluation LLM Agent Reliability

Oct 6, 2026stat.ML

High-dimensional online calibration from harmonic weights

We study the online calibration of multidimensional forecasts over an arbitrary convex set

Y\subseteq\mathbb{R}^d

relative to an arbitrary error norm

\|\cdot\|_{L}

. For forecasting

d

binary outcomes simultaneously (

Y=[0,1]^d

), we give the first algorithm that achieves

\varepsilon

-calibration in a number of rounds that is polynomial in

d

for every fixed accuracy. It requires

d^{O(1/\varepsilon)}

rounds, exponentially improving the dimension dependence of previous bounds. For multi-class forecasting (

Y=Δ_d

), we obtain the same

d^{O(1/\varepsilon)}

rate, improving the

d^{\widetilde{O}(1/\varepsilon^2)}

bounds of Peng and Fishelson et al. Our algorithm is simple: on each round, it outputs a harmonically weighted distribution over harmonically smoothed past outcomes. The same algorithm works for every forecast set and norm. More generally, it achieves

\varepsilon

-calibration after

\exp(O(γ(Y,L)/\varepsilon))

rounds, where

γ(Y,L)

is a geometric parameter defined by a matrix discrepancy problem. The harmonic weights are motivated by the fact that the discrete Hilbert transform matrix achieves the optimal discrepancy up to a universal constant, simultaneously for every

L

. This optimality result may be of independent interest.

Maxwell Fishelson, Mehryar Mohri

Institute for Advanced Study. · Google Research and Courant Institute of Mathematical Sciences, New York.

Probability Calibration Model Calibration

Oct 6, 2026stat.ML

Explicit Asymptotic Bounds for Sequential Calibration Beyond $T^{2/3}$

Probability forecasts are calibrated when predicted probabilities match empirical outcome frequencies: among events assigned a probability

p

, we'd hope that the fraction of positive outcomes is close to

p

. We study the problem of sequential forecasting of binary outcomes. The classical

O(T^{2/3})

bound on expected cumulative

\ell_1

-calibration error established by Foster and Vohra stood for over two decades until Dagan et al. reduced the exponent

2/3

by an unspecified constant. We establish a new two-phase recursive labeling strategy for the sign-preservation-with-reuse game that yields the bound

O(n^αt^β)

for all choices of space and time. We then sharpen the reduction from upper bounds on sign preservation to calibration by modifying the equivalence of Dagan et al. to use only

O(\log T)

instances of the sign-preservation-with-reuse game. This lets us establish an explicit bound of

O(T^{0.662942288})

, the first explicit exponent below

2/3

for sequential calibration, by combining both improvements and choosing explicit feasible parameters.

Eric Dai, Maxwell Fishelson

Edison Academy Magnet School · Institute for Advanced Study

Probability Calibration Probabilistic Forecasting

Oct 5, 2026cs.CV

Certification of Real Images through Calibrated Content Authentication

Generative models can synthesize high-quality inauthentic multimedia content that is already being misused at scale. We evaluate twenty deepfake detectors against ten generators released in the last four years and find accuracy decreasing over time, from near-perfect 99.5% to 76%. Adversarial perturbations further reduce every baseline detector to below 2% accuracy, effectively inverting the detector's assigned label. We argue that this unreliability reflects a fundamental ambiguity: generators can reproduce authentic content exactly (e.g., through memorization), so content alone cannot reveal the true provenance label. For this reason, content produced by a generator must admit a faithful reconstruction by that same generator, and finding such a reconstruction makes synthetic provenance plausible and authenticity plausibly deniable. We therefore propose and evaluate a detection paradigm that outputs a calibrated prediction of whether authenticity is plausibly deniable: a faithful reconstruction by any known generator establishes plausible deniability, while calibration bounds how often content from known generators fails to be reproduced. Our evaluation shows that (i) our detector can be calibrated so that at most 1% of generated content is wrongly certified, an operating point at which most baseline detectors reach near-zero recall, including the strongest with 93% accuracy; (ii) calibrating a stricter security threshold on attacked samples preserves this bound against adaptive adversaries within the evaluated bounded-perturbation attack space, whose perturbations break every baseline, but does not cover arbitrary adversarial transformations; and (iii) post-hoc verifiability is eroding, as 1,116 of 3,000 Reddit images resist reproduction by a 2022 generator, but only 55 to 79 resist reproduction by 2024 generators.

Sarim Hashmi, Abdelrahman Elsayed, Mohammed Talha Alam +2

Mohamed bin Zayed University of Artificial Intelligence Mabuhay, Abu Dhabi, UAE

Probability Calibration Digital Image Forensics Deepfake Detection

Oct 5, 2026cs.LG

Sharp Integrality Gaps in Calibration Distance

We study the offline gap between deterministic calibration distance C and its fractional relaxation L for binary unit-weight sequences under total absolute-change cost. We sharpen the offline comparison C <= L + O(sqrt(T)) (Qiao and Zheng, 2024, Theorem 2) to the sharp worst-case order Theta(T^(1/3)). If Delta_T is the supremum of C - L over length-T inputs, then T^(1/3)/1000 <= Delta_T <= 41T^(1/3) for T >= 216. The upper bound holds for every input, while each T >= 216 has a rational lower-bound input. For every input with m distinct forecasts, C <= L + m, and the unrestricted-sample worst-case sparse order is Theta(m). For rational forecasts and accuracy, with binary-encoded multiplicities of separately assignable unit identities, a grid-free polynomial-bit-time procedure returns B <= L <= U, U - B < eta, and an exactly calibrated compact repair of cost at most U + m <= L + m + eta.

Zinan Wang, Xinhao Yang

University of Manchester · University of Southern California

Probability Calibration Model Calibration

Oct 4, 2026cs.IR

SearchJev: A Fast and Calibrated System-1 Model for Search Agents

Search agents repeatedly make short decisions about relevance, evidence sufficiency, and search actions. Using generative language models for these decisions introduces latency and unreliable confidence. We present SearchJev, a fast and calibrated System-1 model that separates search decisions from System-2 reasoning and generation. Given a search state and a decision schema, SearchJev directly scores legal options without autoregressive output generation. We propose Soft-Label Learning for Calibrated Decisions (SLCD) to learn decision probabilities from uncertain supervision and calibrate their confidence. In a dual-system search agent, SearchJev handles short decisions and delegates uncertain judgments to System 2, which retains planning, query generation, and answer composition. We also introduce SearchDecision-Bench, a benchmark unifying six types of search decisions for training and evaluation. On SearchDecision-Bench, SEARCHJEV improves decision quality over same-size Qwen3.5 autoregressive models, achieves 5.2-5.3 times faster decisions, and reduces average expected calibration error by 41-74%. On BrowseComp-Plus, the dual-system agents achieve a 3.7-4.7 times speedup in active search time while improving answer accuracy from 45% to up to 54%.

Congfeng Cao, Lipeng Zuo, Konstantinos Papakostas +6

Huawei Technologies Co., Ltd. · Leiden University

Soft-Label Learning Probability Calibration Agentic Search Efficient Language Model Inference

Oct 1, 2026cs.AI

Beyond Answer Confidence: A Controlled Audit of Self-Knowledge in a Black-Box Decision Model

Decision models return probabilities intended for routing, abstention and automated action. Calibration makes those probabilities useful on average, but does not establish whether low confidence reflects chance or missing knowledge, nor whether confidence falls when a model moves beyond what it knows. We audit this distinction in Jev, a decision model, with over 15 public datasets and 6 generated task families, with paired interventions that vary the information supplied for a fixed item. Jev's confidence is calibrated on familiar closed-choice tasks but fails as an indicator of missing knowledge: with no answer-relevant information it assigns up to 0.80 to a salient option, and on news beyond an observed knowledge boundary it exceeds accuracy by 0.21--0.33, a gap that recalibration on earlier months does not close. Targeted yes/no questions give sharper readouts of the case: whether an outcome is settled (AUROC 1.00) and whether the evidence suffices (0.95, against 0.85 for confidence on the same items). Asking whether Jev knows the answer appears to flag fabricated entities and post-boundary news (0.91), but with realistic names or with dates removed it shows no advantage over answer uncertainty. Black-box knowledge audits therefore need explicit controls for surface cues. Code: https://github.com/Syntheme/beyond-answer-confidence.

Sharath M Shankaranarayana, Davor Runje, Jan Jannink

Probability Calibration Black-Box Model Auditing Epistemic Uncertainty

Sep 30, 2026cs.LG

Reliability-Aware Checkpoint Selection for Domain Generalization

Checkpoint selection in domain generalization often relies on source-validation accuracy, yet the selected checkpoint need not provide reliable probabilities on unseen target domains. Source-target distribution shifts can alter accuracy rankings, while accuracy alone does not measure predictive probability quality. We identify an empirical selection opportunity within fixed training trajectories: reselecting among checkpoints with near-optimal source accuracy can improve mean target probability quality with small observed changes in mean target accuracy. We study accuracy-constrained reliability selection (AC), which retains checkpoints within a tolerance of the best source-validation accuracy and ranks them by source reliability. Our reference rule aggregates within-set normalized negative log-likelihood (NLL) and class-wise calibration error (CwECE) using

D_\infty

. AC uses no target data and requires neither additional training nor weight averaging. We evaluate five domain generalization training algorithms on three benchmarks, using PACS to develop the objectives and a 0.5-percentage-point tolerance. In exploratory aggregation comparisons on 360 OfficeHome and TerraIncognita runs, the reference rule reduces mean target soft-bin squared-gap ECE and CwECE by 0.240% and 0.182%, respectively, and NLL by 0.030 relative to Source-Acc. Mean target accuracy changes by +0.213 percentage points. These results identify opportunities for reliability-aware reselection, while the additional benefit of joint over single-objective ranking remains unresolved.

Jinshi Liu, Jiahao Li, Pan Liu +5

Shenzhen University · Xiamen University · The Hong Kong University of Science and Technology (Guangzhou) +3

Probability Calibration Domain Generalization Cross-Domain Generalization

Sep 30, 2026cs.LG

OmniMed-Jev: Calibrating LVLM Confidence for Trustworthy Medical Multimodal Decisions via System One

Medical models are judged not only on correctness, but on whether reported confidence matches actual accuracy. Generalist multimodal medical models have expanded what a single model can perceive, yet they still express bounded decisions such as diagnoses, findings or cell counts as generated text, so the reported probability reflects the next token rather than the decision itself. Motivated by decision-native interfaces such as Jev, we introduce OmniMed-Jev, which represents each medical decision as a Choice, Noul or Score decision over a runtime-supplied candidate set and returns a full distribution over that set: mutually exclusive classes, binary presence of a finding, or a bounded ordered value. The design is omni in three respects: it accepts diverse imaging modalities, covers different prediction tasks, and expresses them through one candidate-conditioned probability model, so heterogeneous outputs become comparable probabilities rather than task-specific strings. In an interface-controlled comparison against a generative baseline trained on the same backbone, data and schedule, OmniMed-Jev's reported probabilities track observed correctness far more closely, reducing calibration error by up to an order of magnitude and reliability error by up to two, while point-prediction performance remains comparable; counting is the one family where the generative baseline stays ahead. Making the decision distribution the model's output is not a format change but what turns reported numbers into probabilities that mean what they say. These results support explicit decision modeling as a way to make reported confidence meaningful within the evaluated tasks, and they are not evidence of clinical readiness: the comparison cannot separate the interface from associated training differences, which we state alongside the results. Code is available at github.com/lytang63/OmniMed-Jev.

Luyao Tang, Cheng Chen

Department of Electrical and Computer Engineering The University of Hong Kong, Hong Kong SAR, China

Probability Calibration Multimodal Classification Medical VLMs Multimodal Model Evaluation

Sep 30, 2026cs.AI

How Much Can Reliability Drift Under a Fixed Confidence Distribution?

A classifier's conditional accuracy can change while its confidence distribution stays exactly the same. We study the worst-case movement of the reliability relation under covariate shifts that preserve the distribution of the confidence score, constraining the reweighting within each confidence level by a

χ^2

budget; the resulting worst case, as a function of the budget, is a fragility profile. On an interval of budgets that can be computed from the source distribution, the profile equals exactly the square root of the budget times the within-level variance of the correctness propensity -- the grouping-loss term of calibration-refinement decompositions. Beyond this interval the profile is governed by the tails of the propensity law, and the entire upward profile determines the centred within-level law; consequently, calibration residual and grouping variance do not determine fragility in general, though they do when labels and predictions are deterministic. Since the propensity is not observed, we restrict reweightings to a learned finite readout within confidence bins, bound the part the restriction misses by the grouping variance remaining inside readout cells, estimate the restricted profile with role-separated labels, and provide a separate split-sample lower confidence bound. On ImageNet this bound is positive in both splits for four of six primary classifiers and nine of twelve additional ones as released, and for three of eighteen after temperature scaling. Held-out drift under optimised reweightings fitted without evaluation labels tracks the estimated profile; an exploratory label-permutation diagnostic yields near-zero agreement for this statistic while largely reproducing the correlation observed for unsigned random reweightings.

Wenhao Liang, Lin Yue, Wei Emma Zhang +3

Adelaide University

Distribution Shift Robustness Probability Calibration Distributionally Robust Optimization Covariate Shift Model Calibration

Sep 28, 2026cs.AI

Jev thinks "I don't know'', but doesn't say it: Introducing Sys1Cal-v1 Dataset for Probability Calibration

The appearance of Jev marked the era of System One Models, foundation models that return structured decisions with probability distributions rather than text. Aside from low cost and great speed, Jev's central promise is that these probabilities are calibrated: such claim is not backed by any public test and available external benchmarks evaluate confidence calibration, not whether every returned option probability has the right numerical meaning. To tackle this issue, we introduce Sys1Cal-v1, a dataset of True/False questions about a proposition

A

for which the exact probability

P(A)

is known by construction. Each item is queried through the three Jev primitives - Noul, Choice and Score - and evaluated by total variation distance from the ground-truth distribution, which can be used to estimate a soft accuracy of System One Models. We showcase the utility of Sys1Cal-v1 as a benchmark dataset by evaluating Jev and SemIf, an open-source Choice-style baseline. In this work, however, we focus even more deeply on Jev, by studying the calibration of its Score and Choice answers. In particular, we discover a peculiar behaviour that can be explained by assuming that Jev suppresses a third truth value, going beyond True and False. In other words, in \texttt{Choice} answers,

P(A)

and

P(\neg A)

are presented as if

P(A)+P(\neg A)=1

, while a term

P(U)\neq0

is missing in the sum. Recovering

P(U)

leads to an improvement of median soft accuracy in \texttt{Choice} answers from

0.771

to

0.978

, suggesting that, even in binary decisions, Jev wants to answer with a third option:``I don't know''.

Riccardo Porcedda

Department of Excellence L’EMbeDS, Sant’Anna School of Advanced Studies, Italy · Department of Computer Science, University of Pisa, Italy

Probability Calibration Uncertainty Calibration

Sep 27, 2026cs.LG

Posterior Regimes and Latent Deception: Variational Bayesian Inference in Hidden Markov Models for Sequential Fraud Detection in Financial Transactions

We present a three-tier progression of Hidden Markov Models: maximum-likelihood (Baum-Welch), variational Bayesian (VBEM), and a neural variational extension (Neural VBEM), that model each customer's transaction history as a trajectory through a small number of latent behavioural regimes, one of which is empirically identified as fraud-associated. The Neural VBEM HMM replaces the fixed Gaussian-multinomial emission family with a learned encoder, compressing a 741-dimensional transaction representation into a 64-dimensional latent space in which the VBEM HMM's posterior operates; a UMAP projection of this space reveals that the discovered regimes are not discrete clusters but ordered segments of a single continuous behavioural manifold, with confirmed fraud concentrated at its extreme. We show that the model's natural output, that is, the posterior probability of regime membership, is routinely mistaken for a fraud probability, and quantify the resulting miscalibration (the regime-membership interpretation error, MRIE); a corrected posterior-predictive score, closes most of this gap. We further distinguish batch (smoothed) inference, which uses look-ahead unavailable at deployment time, from filtered (forward-only) inference, and report both. On IEEE-CIS transaction data, the neural tier achieves a 14.4

\times

fraud enrichment in its identified regime; while its AUPRC trails a discriminative XGBoost baseline, we show this gap is structural and not incidental, and argue the model is best positioned as a calibrated triage and interpretability layer rather than a drop-in ranking replacement.

Joseph Uririoghene Obukofe, Anthony O'Hare, Chioma Sandra Dike

Computing Science and Mathematics, Faculty of Natural Sciences, University of Stirling, Stirling FK9 4LA, Scotland, United Kingdom · University of Nottingham, Nottingham, NG7 2RD, United Kingdom

Probability Calibration Financial Fraud Detection Hidden Markov Models

Sep 27, 2026cs.LG

A Free Knob: Decoupling Calibration and Predictive Skill in Threshold-Based Evaluation

Many dense-prediction benchmarks evaluate rare events by pooling prediction and target over spatial blocks, thresholding each, and scoring the contingency table. At a fixed rare operating point, the max-pooled Critical Success Index (CSI) confounds spatial discrimination with amplitude calibration: sharp observations promote many blocks above threshold, while attenuated predictions from squared-error regression leave the same blocks below it. We repurpose classical monotone calibration as a symmetric audit: a post-hoc transform fitted on held-out data and applied separately to each system. The transform cannot reverse pixel ordering, so any contrast it reproduces cannot establish improved spatial ranking. On SEVIR, two released checkpoints of one architecture differ by -29.5% in extreme-threshold CSI before the control and by +5.3% after it. Across 450 pairwise contrasts among 6 systems, the difference in pooled frequency-bias deviation is associated with how far the CSI contrast moves under the control (r = +0.796), and 51 contrasts reverse sign. At CasCast's published extreme-event operating point, the cascade-over-backbone CSI gap falls from 0.1601 to 0.0339, a 78.8% reduction; the remaining gap stays positive. The effect persists when the transform is fitted on a window before the test period, and calibration also reveals advantages hidden by a better-calibrated baseline. On geostationary infrared imagery the relative gain grows as events become rarer, crowd counting reproduces the bias-gain relationship under patch-sum pooling, and semantic segmentation, where frequency bias is already near one, shows little average change. The confound therefore requires both a fixed operating point and a training regime that leaves the output miscalibrated there. We recommend reporting pooled frequency bias and a symmetric held-out FreeKnob Audit alongside rare-event pool-and-threshold scores.

Md Tanveer Hossain Munim, Bijoy Ahmed Saiem, Al-Amin Sany +1

Regional Integrated Multi-Hazard Early Warning System (RIMES) · Bangladesh University of Engineering and Technology (BUET)

Post-Hoc Calibration Probability Calibration Remote Sensing Benchmarks Rare-Event Estimation

Sep 27, 2026cs.CR

Evaluating System One Models for Agent Security Decisions: Reliability, Calibration, and Selective Automation

Model-based judges support agent security by detecting prompt injections, assessing interaction risks, and screening harmful requests. System One models select from predefined answers and report probabilities that software can use to allow, block, or review inputs, but the reliability of these automated decisions remains unclear. We evaluate Jev, Laya, Decider, and Bespoke Nimble against specialized classifiers and language-model judges, examining decision accuracy, probability calibration, and selective automation. We draw the following conclusions. (1) Strong overall performance and favorable aggregate calibration can hide failures concentrated in particular attack groups, including attacks classified as safe with high confidence. (2) The evaluated adapted configurations do not consistently improve classification over their base models across tasks. (3) Under the strictest evaluated error limits, the policies allow few inputs automatically, and separate allow and block thresholds increase automation mainly through more blocks. Passing confirmation does not ensure that these limits hold on test. (4) Judges can detect attacks missed by another model, but may also falsely flag more benign inputs and share the other model's high-confidence errors. These findings support evaluating model accuracy, probability calibration, and the resulting allow/block/review decisions together.

Yixuan Liu

TraceStone and Nanyang Technological University, Singapore

Probability Calibration Selective Prediction AI Agent Evaluation AI Agent Security Prompt Injection Detection LLM Agent Reliability

Sep 24, 2026cs.CR

Calibrated Decision Models for Autonomous Penetration-Testing Harnesses: JEV and Laya as System One Decision Layers for LLM-Driven Pentest Agents

Autonomous penetration-testing harnesses use large language models (LLMs) for reconnaissance, exploitation, and reporting, but often rely on those same models to confirm findings, grade severity, and select agents. This can lead to false positives, inflated severity, and wasted compute. We examine how System One decision models, lightweight non-generative classifiers that return typed, calibrated verdicts, can support these decisions. We make five contributions. First, we define four decision points: finding adjudication, severity recalibration, agent pruning, and confirmation loops. Second, we present an exploratory NeuroSploit case study comparing one run with TypeSafe System One (Jev) and one without it against a web target containing 13 vulnerabilities. Differences in severity distribution, runtime, and grading by exposed data type motivate the architecture but do not establish statistical significance. Third, we review published specifications for Jev, Jev-Ultrafast, and the open-source Laya without assuming that results from other benchmarks transfer to penetration testing. Fourth, we discuss RLHF, RLAIF, RLCD, and RLHV as training approaches and their implications for trust in security decisions. Finally, we propose Rave, a domain-adapted System One model, and outline its training data, evaluation protocol, and potential effect on harness assurance.

Joas Antonio dos Santos Barbosa

Independent Researcher — AI and Offensive Security S˜ao Paulo, SP, Brazil

Probability Calibration Cybersecurity LLM Agent Security Automated Penetration Testing

Sep 22, 2026stat.ML

A Practical Guide on Graphical Model Validation

This manuscript formalizes the most popular model validation tools used in general insurance actuarial modeling. These include graphical tools like calibration plots, actual-vs-expected plots, lift charts, Murphy diagrams, as well as classical statistical tools such as Bregman losses, deviance losses, elementary losses, Murphy's decomposition and Gini scores. Particular emphasis is placed on whether calibration and discrimination are studied under a policy-weighted or an exposure-weighted population measure. This distinction is crucial in ensuring that premium schemes are calibrated on the correct scale.

Mario V. Wüthrich

Department of Mathematics, ETH Zurich

Probability Calibration Model Calibration

Sep 22, 2026cs.LG

Certified Against Which Oracle? Execution Labels Set the Reported Risk of Conformal Abstention for Text-to-SQL

A conformal abstention certificate for text-to-SQL is only as truthful as the correctness labels it is calibrated on. The uncertainty pipelines that read confidence off execution consistency take those labels from the single database a benchmark ships, an oracle known to be lenient. We run a preregistered intervention on Spider-Realistic, swapping that database for the benchmark's distilled multi-instance test suite. Across four SQL-specialist checkpoints and two split schemes, the swap raises the certificate's held-out risk 2.73 to 10.23 points above the risk its own labels report. Neither oracle reports the risk experts assign. Under blinded labels from two SQL experts, a certificate calibrated at a nominal 0.10 carries 20.0 and 17.2 points of risk on two checkpoints. The stricter oracle errs in both directions: most of the answers it rejects are not judged wrong, and some of those it accepts are. An AI-assigned census of what it rejects finds a semantic error in a quarter to a third of them, depending on the population. It attributes most of the rest to underspecified questions, synthetic instances or suspected reference-query defects, a flag supported by a preregistered blinded expert audit. The oracle also decides how a confidence score is judged. Every execution-consistency score looks better under the labels of the oracle that built its clusters, in 16 of 16 combinations. Under expert labels, building such a score on suite clusters instead of shipped-database clusters raises its area under the ROC curve (AUROC) by 6.96 points on one checkpoint and 1.53 on the other. On the second, the expert interval excludes the 8.3 points the suite labels report. A certificate should be reported with both oracles, and an oracle-relative difference read as semantic risk only after the benchmark is audited. A consistency score should be evaluated under an oracle that did not build it.

Jiamiao Liu, Dewen Qiao, Yu Zhang +1

Department of Information, Xinqiao Hospital Army Medical University (Third Military Medical University) Chongqing 400037, China

Probability Calibration Benchmark Auditing Conformal Prediction Text-to-SQL Conformal Risk Control Benchmark Validity

Sep 22, 2026cs.RO

You Should Be Properly Scoring Your Odometry

When we evaluate the performance of our odometry, it is common practice to score the estimated track against a ground truth. Unfortunately, scoring uses point metrics, such as the root mean square error, that ignore the covariance matrix which estimators like filters and smoothers already report. Using the covariance matters for two reasons. First, the covariance encodes the estimator's uncertainty, so it tells us whether the estimator trusts its own output. An overconfident estimator will not report itself lost. Second, the covariance weights the error in each direction of the estimate. Without the covariance, an estimator is unduly penalized for a high error in an uncertain direction. Instead of point metrics, we should use strictly proper scoring rules. These rules score the estimate together with its reported uncertainty. Strictly proper scoring rules recover the point metrics when no covariance is reported, and they diagnose covariance inconsistency when covariance is reported. Using a one-sided pairwise test, we show that two estimators can expose overconfidence in at least one of them without a ground truth. Strictly proper scoring rules and our pairwise test are available in our open-source framework smfeval. As a case study, we use smfeval to assess the uncertainty quality of the translational component of ground-based LiDAR-inertial odometry. Across four filters we find overconfidence - the worst case reports centimeter certainty with kilometer error. Knowing the filters are overconfident, we investigate the mechanism. The investigation traces overconfidence to filters crediting LiDAR measurements with more new information than they carry.

Ola Rønning, Usama Saqib, Andrzej Wąsowski

Software Quality Research Group, IT University of Copenhagen, Denmark

Probability Calibration Proper Scoring Rules Uncertainty Calibration

Sep 21, 2026stat.ML

PICPIs: Prediction-Interval-Conditional Prediction Intervals

A classical question in statistics is which observable quantities to condition on when drawing inferences about unobservable targets. For conformal prediction in nonparametric uncertainty quantification, standard marginal validity offers limited resolution at the prediction values on which decisions are based, and fully conditional guarantees with respect to the covariates are provably unattainable. We address this gap by introducing a prediction-based conditioning framework that we refer to as Prediction-Interval-Conditional Prediction Intervals (PICPIs). Formally, a PICPI is an interval

I

satisfying a self-consistency condition:

\mathbb{E} [Y \mid p(X) \in I] \in I,

for predictive model

p

, contextual covariate

X

, and outcome

Y

. Thus, an interval simultaneously defines a stratum of prediction values and certifies that the mean outcome in that stratum lies in the same interval. This self-consistency condition yields data-adaptive strata without altering the original prediction. Such intervals can be constructed using practical algorithms. Under regularity of the prediction distribution, the constructed intervals cover all but an arbitrarily small fraction of prediction values and have widths that decrease at rate

n^{-1/3}

, up to logarithmic factors and the prediction error. Moreover, identifying these locally calibrated intervals can, in turn, inform downstream decision-making. We derive inference procedures for PICPIs in probabilistic prediction and multi-class classification, accompanied by theoretical guarantees. Empirical results are provided that compare PICPIs with existing interval-based baselines.

Xuelin Yang, Baihe Huang, Yilong Hou +2

University of California, Berkeley · Stanford University · Inria Paris

Probability Calibration Conformal Prediction Model Calibration Regression Prediction Intervals

Sep 20, 2026cs.LG

CSC: Calibrated Simplicity for Conflict-Aware Social Bot Detection in the LLM Era

Social bot detection is essential for protecting online platforms from misinformation amplification, coordinated manipulation, and distorted public discourse. However, large language models have made social bots much harder to detect from text alone because semantic camouflage is now cheap, fluent, and scalable. The resulting challenge is modality conflict: an account may look human-like in semantics while remaining suspicious in graph structure, profile attributes, or cross-modal consistency. Recent graph-based detectors tackle this limitation by adding graph-side complexity, such as sparse prototype selection, adaptive gating, or architecture-specific control logic, yet our experiments suggest that complexity alone is not the most reliable way to resolve such conflict. We therefore propose CSC, a calibrated-simplicity framework for conflict-aware LLM-era social bot detection. The framework combines three design choices: a simplified prototype-guided graph expert that retains useful structural biases while removing unstable graph-side heuristics, calibrated simplex-constrained fusion that aligns heterogeneous confidence spaces before late fusion, and a lightweight inconsistency expert that models cross-modal disagreement. Experiments on TwiBot-22, TwiBot-20, and MGStBot-large show that \textsc{CSC} improves calibrated operating-point decision quality while remaining competitive across external benchmarks. Further analyses show that calibration improves confidence reliability, the inconsistency expert mainly provides localized corrections in high-conflict or near-threshold regions, and simplified graph-side control yields a better stability-cost trade-off. A targeted semantic-camouflage stress test further shows that replacing selected bot text with matched human text sharply degrades the standalone text expert while leaving graph and fused evidence stable on a balanced challenge set.

Yipeng Qian, Pengjie Zhao, Chaoxi Niu

Minzu University of China Beijing, China · City University of Macau Macau, China

Social Media Analysis Probability Calibration Multimodal Fusion

Sep 14, 2026stat.ME

A Ranking Approach for Measuring Calibration

When providing forecasted probabilities with a predictive model, the ideal model offers perfect calibration: the true probability of the outcome (i.e., the probability that

Y=1

) exactly matches the forecasted probability

f(X)

. In practice, models inevitably exhibit calibration error, and it is therefore important to be able to measure this miscalibration to assess a model's reliability. The Expected Calibration Error (ECE) is the most widely used measure of miscalibration, but is known to be impossible to estimate the ECE with guaranteed accuracy in an assumption-free setting. In this work, we propose an alternative measure, the rankECE, that is based on comparing points with neighboring values of the predicted probability

f(X)

. Our theoretical guarantees and empirical results establish that rankECE provides a better proxy for ECE as compared to binned approximations to ECE, which are the most commonly-used approximations in practice.

Anirban Chatterjee, Rina Foygel Barber

Department of Mathematics and Statistics Boston University · Department of Statistics University of Chicago

Probability Calibration Model Calibration

Sep 9, 2026stat.ML

A Unifying Perspective on Probabilities as Model Predictions

Although probabilistic statements are ubiquitous, foundational disagreements persist about their understanding, as exemplified by debates between Bayesians and frequentists; moreover, it is unclear when and why acting on them actually leads to desirable outcomes. Here, we argue that every probability is the output of a \emph{prediction method}, that is, it depends on both a particular way of constructing abstractions and a way of transforming them into predictions. Through this, we provide a unifying perspective on supposedly different kinds of probabilities and show that even supposedly objective ones are model-dependent. We demonstrate that when a finite calibration criterion is met, one can anticipate the distribution of utilities for a given policy and inform successful decision-making on finite sets of events. Based on the notion of prediction methods, inductive arguments, and the probability calculus, we explain the feasibility of the calibration criterion in many settings. Overall, we develop a coherent perspective on probabilities and their use, connecting key intuitions behind other interpretations along the way.

Benedikt Höltgen

Hasso Plattner Institute, University of Potsdam

Probability Calibration Decision-Making under Uncertainty

Sep 7, 2026cs.LG

The Accuracy Paradox: Empirical Diagnostic of Default Decision Thresholds in Multi-Label Enzyme Commission Prediction [With Code]

Automated prediction of Enzyme Commission (EC) numbers plays a central role in functional annotation and computational drug discovery. However, standard multi-label machine learning pipelines frequently rely on default decision thresholds (t=0.50), assuming balanced prior distributions across target heads. In this study, we present a systematic empirical diagnostic of uncalibrated fixed decision boundaries operating under severe class imbalance across N = 14,096 annotated compounds categorized into six primary EC classes (EC1-EC6). Our results highlight a pronounced Accuracy Paradox: while the multi-label system achieves a deceivingly high mean accuracy of 77.16%, the macro F1-score (0.3976) and macro recall (0.3872) reveal severe predictive breakdown. Majority target classes suffer from hyper-sensitivity and over-prediction, whereas minority classes exhibit sharp recall decay, culminating in a total decision boundary collapse for EC6 (Recall = 0.00%) despite underlying discriminative power (ROC-AUC = 0.5857). Feature correlation analysis further reveals high linear redundancy among topological indices relative to fingerprint density metrics. Ultimately, this diagnostic study demonstrates that standard point predictions mask critical errors in bioinformatics workflows. We establish target-specific threshold optimization and post-hoc conformal calibration as essential, open-source post-processing safeguards for reliable applied machine learning and deep learning architectures.

Bilal Ahmad, Rajed Mehmood

The Department of Electrical, Electronics and Telecommunication Engineering, UET Lahore, Pakistan · Department of Computer Science and Engineering, Jiangsu University, Jiangsu, China

Class-Imbalanced Learning Multi-Label Classification Probability Calibration

Sep 1, 2026cs.LG

Let Confidence Change, Not the Prediction: Prediction-Preserving Repair for Post-hoc Calibration

Post-hoc calibration corrects reported confidence, yet a multiclass calibrator can also change the associated top-1 prediction. Accuracy captures only the net effect of these changes on correctness, not how often predictions change; the Top-1 Prediction Change Rate (TPCR) instead measures this frequency. We propose Calibrator-Output Repair for Top-1 Decision Preservation (CORD), the first post-fit adapter to impose exact prediction preservation by repairing the full calibrated probability vector. From the original and calibrated outputs alone, CORD determines the mass assigned to the original top-1. The calibrated conditional distribution allocates the remaining mass over the other classes, yielding a repaired vector whose own argmax recovers the original prediction. On the calibration split, CORD coordinates the repaired masses to retain the calibrated outputs' mean mass on original predictions whenever attainable. The adapter alters neither the fitted calibrator nor its direct output, fits no additional supervised map, and requires no user- or validation-tuned hyperparameter. Across CIFAR-10/100 and ImageNet-1K, CORD attains zero TPCR by construction and lowers mean ECE, NLL, and Brier relative to the corresponding direct outputs in every dataset; paired gains persist under distribution shift and across calibration-set sizes. CORD thus removes the preservation constraint from calibrator fitting and assigns exact recovery of the original decision to subsequent output repair. Our code is available at https://github.com/labhai/CORD.

Daehwan Kim, Haejun Chung, Ikbeom Jang

Hanyang University, Seoul, Republic of Korea · Hankuk University of Foreign Studies, Yongin, Republic of Korea

Post-Hoc Calibration Probability Calibration Model Calibration

Aug 28, 2026cs.AI

Timing-Aware Repurchase Prediction for Web-Scale E-Commerce: Survival Models for Multi-Surface Grocery Recommendation

Repurchase recommenders in e-commerce are commonly framed as a binary question asking "will this customer buy this item within W days", a formulation that requires a separately trained model for every horizon of interest. We replace this stack with survival models that predict time-to-repurchase directly, and evaluate them on millions of customers from a major grocery e-commerce platform across more than thirty ablation configurations. Our study makes three contributions. First, an empirical hazard analysis reveals a slightly decreasing marginal hazard (k ~ 0.9), differing from the common intuition that grocery items become more likely to be repurchased the longer since the last purchase (increasing hazard, k > 1). Log-Normal achieves the best marginal fit (R^2 = 0.998) and the best ranking, despite Weibull providing the best conditional residual fit, revealing an apparent discrepancy we analyze in detail. Second, a single Accelerated Failure Time (AFT) model replaces three per-horizon binary classifiers, matching or exceeding each at its own horizon while using roughly 3x fewer total trees. Feature importance reshuffles under the survival objective: channel-cadence and recency signals rise while aggregate frequency counts fall. Third, a 4-parameter parametric calibration maps raw survival CDFs to per-horizon probabilities with zero cross-horizon monotonicity violations. Calibration quality varies by an order of magnitude across the AFT family: Exponential AFT (Weibull k=1) achieves expected calibration error (ECE) ~1e-4, roughly 10x lower than Log-Normal, while ranking metrics agree within 0.3% relative. We adopt Exponential AFT for probability-consuming surfaces and Log-Normal for pure ranking, exposing a principled calibration-ranking trade-off within a single AFT family.

Akshay Kekuda, Shreeranjani Srirangamsridharan, Ishan Bhatt +5

Walmart Global Tech · Bellevue, WA, USA · Sunnyvale, CA, USA

Probability Calibration Survival Analysis Recommender Systems E-Commerce

Aug 11, 2026cs.LG

Hierarchical Empirical-Bayes Naive Bayes: Minimax Smoothing and Calibration with AODE Extension

The Naive Bayes (NB) classifier remains a standard choice for categorical data, yet its widely used smoothing rules, such as Laplace, Lidstone, Krichevsky-Trofimov, and the

m

-estimate, all prescribe a fixed smoothing strength that ignores feature cardinality, sample size, and class imbalance, inducing a non-vanishing bias on modern high-cardinality tabular data. We propose hierarchical empirical-Bayes Naive Bayes (HEB-NB), in which each class-feature conditional probability is smoothed by a Dirichlet prior whose concentration is learned data-adaptively via Type-II maximum likelihood, enabling principled information sharing across classes while retaining closed-form inference. We further introduce HEB average one-dependence estimators (HEB-AODE), showing that the adaptive smoothing transfers cleanly to structural relaxations of NB. Theoretically, we establish a non-asymptotic

\ell_1

error bound for HEB-NB matching the empirical-distribution minimax rate plus a vanishing data-adaptive bias, together with a matching Laplace-tight lower bound that yields a finite-sample, risk-level strict separation from Laplace. We further derive a plug-in excess Bayes-risk bound via total-variation tensorization and a population top-1 expected calibration error (ECE) corollary. Empirically, across 31 UCI and OpenML benchmarks, HEB-NB attains the best average Friedman rank on probabilistic metrics, with up to 22.1% log-loss reductions on high-cardinality datasets and consistent improvements of HEB-AODE over vanilla AODE. Combining HEB-NB with mutual-information weighting reduces top-1 ECE by 41%-70%, demonstrating substantial gains in probabilistic accuracy and calibration.

Nguyen Thai Anh, Truong Viet Vu, Tran Thien Thanh +2

Faculty of Information Technology, Van Lang School of Technology, Van Lang University, Ho Chi Minh City, 70000, Vietnam · Institute of Information Technology and Electrical-Electronics Engineering, Ho Chi Minh City University of Transport, Ho Chi Minh City, 700000, Vietnam

Probability Calibration Empirical Bayes Hierarchical Bayesian Modeling Minimax Estimation

Aug 11, 2026cs.LG

MARCO: Click-Intent Decomposition for Calibrated Ads Conversion Prediction

Not all clicks are equal. Industrial ads ranking decouples conversion probability into click-through rate (CTR) and post-click conversion rate (CVR), yet treats every click as the same event. In reality, users provide a free, self-generated signal of intent through their physical UI interactions. Different click types on the same ad exhibit a 4-fold difference in actual conversion rates. By conflating these signals, the standard CVR model under-predicts high-intent clicks and over-predicts low-intent ones, which is a bias masked by near-perfect aggregate calibration. We propose MARCO (Multi-intent Ads Ranking Composition Optimization), a framework that resolves this bias by decomposing each click by intent. Using the logged click type as a free behavioral label, MARCO trains per-intent CVR heads on homogeneous populations, and at serving time composes their per-intent CVR estimates under a predicted distribution over intents. Theoretically, we prove that decomposition never raises population risk, give the exact headroom under squared loss and non-negativity under the deployed loss, and show through a routing-efficiency dial how much of it reaches serving. Because the population-optimal score is unchanged, any gain is a finite-capacity estimation and calibration effect that we validated both offline and online. For deployment at scale, we further cast multi-impression, multi-click attribution as credit assignment with a bias-variance tradeoff analogous to RL return estimation, showing last-impression, first-click attribution is the low-bias, low-variance, deterministic choice under production constraints, and derive three consistency conditions enforced end-to-end at scale. Deployed at binary intent granularity, MARCO corrects per-intent calibration to approximately 100%, lifts conversions per click by +2.80%, and drives +0.98% cumulative improvement in topline metrics.

Shiwen Shen, Xiru Huang, Liang Luo +32

Meta AI, Menlo Park, California, USA

Probability Calibration Online Advertising

Aug 10, 2026cs.LG

Multimodal Federated Learning under Dual-Axis Modality Missingness

Multimodal federated learning (FL) supports collaborative modeling in privacy-sensitive health-sensing and medical settings, but realistic deployments often exhibit dual-axis modality missingness: clients have different modality sets, and individual samples may contain only subsets of the modalities available locally. Existing methods typically address these two axes separately. We propose Flux, a multimodal federated learning framework built around two complementary components. First, modality-aware confidence tempering learns sample-specific confidence for each modality through mask-aware unimodal supervision and fuses the confidence estimates from observed modalities into a sample-adaptive temperature that adjusts predictive sharpness according to evidence quality and completeness. Second, gradient-decoupled private adaptation applies this temperature only to a client-private prediction pathway, while training the shared federated model with a standard, untempered objective. This enables sample-specific, client-local confidence adaptation without allowing confidence-dependent gradients to perturb shared representation learning. Across four multimodal datasets, Flux achieves the highest average macro-F1 on every dataset, outperforming the strongest dataset-specific baseline by 0.8~2.2 points and by 1.6 points on average. Additional analyses demonstrate favorable calibration, temperature sensitivity to both modality missingness and input corruption, and more stable shared optimization under private-only tempering. Our code is available at https://github.com/AdibaOrz/Flux.

Adiba Orzikulova, Jaehyun Kwak, Jaemin Shin +5

1KAIST · 2CUHK · 3HKUST

Multimodal Federated Learning Missing-Modality Learning Probability Calibration Federated Learning Heterogeneous Federated Learning

Jul 29, 2026stat.ML

An analysis of binary isotonic regression: degrees of freedom and implications for calibration

Isotonic regression is a canonical tool for estimating monotone functions and calibrating probabilistic predictors. We provide a fully sharp finite-sample characterization of its worst-case degrees of freedom on binary samples. Specifically, we identify the binary sequences that maximize the number of distinct fitted values produced by isotonic regression. We develop a sharp bound on the degrees of freedom with a leading term of

\frac{3}{(4π^2)^{1/3}} n^{2/3}

using analytic number theory, improving on previous bounds. We then apply this result to calibration. Calibration is a central requirement for probabilistic prediction, and isotonic regression is a widely used post-processing method for improving calibration. Building on deterministic degrees-of-freedom bounds, we derive, to our knowledge, the first nontrivial distribution-free guarantee on the Expected Calibration Error (ECE) of isotonic regression. This ECE bound is fully model-free and distribution-free, only assuming

Y \in \{0,1\}

.

Raphael Rossellini, Rina Foygel Barber, Zhimei Ren +1

Department of Statistics, University of Chicago · Department of Statistics and Data Science, University of Pennsylvania · Department of Statistics, University of Michigan

Probability Calibration Model Calibration Statistical Learning Theory Isotonic Regression

Jul 25, 2026cs.LG

Bayesian Complete-Pooling in Cross-Subject Classification for Motor Imagery Electroencephalogram

Brain-computer interfaces (BCIs) have long sought calibration-free operation, but classifiers are typically benchmarked by discrimination alone, blind to whether predicted probabilities are well calibrated - a meaningful gap given nonstationary electroencephalogram (EEG) signals and the risk of overconfident point-estimate classifiers under distribution shift. We conducted a large-scale study contrasting Bayesian complete-pooling models against frequentist baselines for cross-subject, left-hand versus right-hand motor imagery EEG classification across 20 datasets. Six frequentist pipelines were each paired with an analogous Bayesian pipeline sharing identical feature engineering, fit via Markov chain Monte Carlo posterior sampling. Our primary metric was the Brier score, decomposed into reliability and resolution, alongside AUROC for discrimination and Shannon entropy for sharpness. Each metric was analyzed via random-effects meta-analysis (REML, Knapp-Hartung adjustment), verified by leave-one-out influence analysis. Bayesian complete-pooling produced statistically but not practically significant improvements in reliability and increases in predictive uncertainty (lower sharpness); Brier score, resolution, and discrimination showed no significant differences. Between-study heterogeneity was low across all metrics, though the reliability result was sensitive to leave-one-out removal. We additionally profiled computational cost, finding that Bayesian pipelines consumed roughly thirteen times more energy than their frequentist counterparts, a cost that remains modest relative to common household appliances. These results suggest that Bayesian complete-pooling alone offers limited practical benefit for cross-subject motor imagery classification, and that partial-pooling across subjects and sessions is a more promising direction for future work.

Ethan Davis

University of Washington, USA

Cross-Subject EEG Decoding MI Classification Brain-Computer Interfaces Probability Calibration Bayesian Inference Classification