Probability Calibration

AI generated predictions increasingly inform decision making in critical tasks, and therefore must be trustworthy. One widely used measure of trustworthiness is calibration, which requires that the predictions match the true frequencies and can be treated like real probabilities of a given outcome. However, defining calibration is subtle, and designing good measures of calibration error has been an active topic of recent research. The first goal is to find calibration measures that are actionable, meaning they can inform decision makers about their utility loss when predictions are treated as true probabilities, which is known as swap regret. The second goal is to find calibration measures that are testable, meaning that calibration error can be measured from a small sample of predictions and outcomes. Although these are very basic requirements, there is no existing calibration measure that fully satisfies both properties, and all existing measures relax actionability by bounding a weaker notion of swap regret, or relax testability by having suboptimal estimation error. We introduce a new calibration measure, Soft-Binned Calibration Decision Loss (SCDL), which we prove is fully actionable without weakening either requirement, and testable with nearly optimal error rate. In addition, SCDL satisfies other desired properties such as continuity and consistency. We also provide a set of experiments confirming that the theoretical advantages of SCDL compared to other measures lead to better performance in practice.

Probabilistic prediction systems often aggregate probability estimates from multiple models into a single decision. A common assumption is that if each model is individually calibrated, the aggregate prediction will also be well calibrated. We show that this assumption fails in multi-agent settings: individually calibrated predictors can become collectively miscalibrated when their predictions interact strategically, in the game-theoretic sense of Brier-optimal local response, even without deliberate coordination. This phenomenon arises naturally when agents are independently trained on overlapping data. We prove that under Brier-score-based aggregation with positively correlated beliefs, each agent's individually optimal report systematically underestimates the positive-class probability, yielding a Price of Anarchy greater than one whenever Cov(b_i, b_j) > 0. In a canonical setting (n = 5 agents, pairwise correlation = 0.5, base rate = 0.3), the empirically measured PoA in false-negative rate reaches 7.25x. In contrast, VCG-based aggregation aligns incentives by rewarding marginal contribution, achieving dominant-strategy incentive compatibility and near-optimal performance. Experiments on three real-world datasets (NSL-KDD, UNSW-NB15, Credit Card Fraud) show that VCG provides strong robustness while maintaining comparable accuracy. It performs particularly well in data-sparse and adversarial settings, and adaptive weighting further improves performance under distribution shift.

Fairness in toxicity classification involves three integrated axes: ranking, calibration, and abstention. Training-time interventions and post-hoc safety mechanisms cannot be evaluated independently because the former determines the efficacy of the latter. We compare Empirical Risk Minimization (ERM), instance-level reweighting, and Group DRO across these axes, combined with temperature scaling, confidence-based abstention, and per-identity threshold optimization. Evaluation uses subgroup AUC, BPSN/BNSP AUC, error gaps, and per-subgroup Expected Calibration Error (ECE) with bootstrap CIs ($n = 1000$). We report four findings. (1) Calibration disparity is a hidden fairness violation. ERM has near-perfect aggregate calibration ($0.013$) but is significantly miscalibrated across all identity subgroups ($+0.029$ to $+0.134$). (2) Training interventions reshape rather than eliminate disparity. Reweighted ERM improves ranking (BPSN AUC $+0.06$ to $+0.12$) but worsens the calibration-fairness gap by up to $+0.232$. Group DRO eliminates calibration disparity but only by becoming uniformly miscalibrated globally (ECE $0.118$). (3) Post-hoc methods inherit training failure modes. Temperature scaling fails because miscalibration is non-uniform. Confidence-based abstention works under ERM but breaks under DRO, where the risk-coverage curve rises with deferral. (4) Abstention itself is unfair. Confidence-based deferral helps background content far more than identity-mentioning content. We argue that SRAI fairness requires a multi-axis framework: methods that differ only in aggregate ranking can differ sharply in failure modes that determine real-world harm.

Calibrated probability outputs of trained classifiers are increasingly used as inputs to downstream regression estimands such as effects, prevalences, or disparities for a latent group observed only on a small labelled subset. A standard practice is to threshold the calibrated score at a confidence cutoff and treat the hard label as the truth. Building on a recent identification result for the underlying moment equation, we develop a calibration-aware diagnostic apparatus for pseudo-labelling pipelines. 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 $V^{*}=\mathbb{E}[\operatorname{Var}(p\mid X)]$ on the unlabelled set after partialling out the downstream controls $X$. We further obtain a sharp sensitivity bound under bounded calibration drift, and identify the boundary $V^{*}=0$, which holds iff $p$ is a deterministic function of $X$; this motivates a structural separation between classifier features $W$ and downstream controls $X\subsetneq W$. Five controlled simulations and a UCI Adult illustration trace the predictions. The contribution is operational: a $(V^{*}, κ)$ decision rule that practitioners can compute from any classifier output to decide whether confidence thresholding is safe.

Automated ASD screening tools remain limited by single-architecture evaluations, axis-restricted assessment, and near-exclusive focus on adult cohorts, obscuring age-specific diagnostic patterns critical for early intervention. We introduce ASD-Bench, a systematic tabular benchmark evaluating ML, deep learning, and foundation model configurations across three age cohorts (children 1-11 yr, adolescents 12-16 yr, adults 17-64 yr) on four axes: predictive performance, calibration, interpretability, and adversarial robustness. Applied to a curated v3 dataset of 4,068 AQ-10 records, our benchmark spans classical models (XGBoost, AdaBoost, Random Forest, Logistic Regression), neural networks (MLP), deep tabular transformers (TabNet, TabTransformer, FT-Transformer), and TabPFN v2. We introduce the Heuristic Aggregate Penalty (HAP): a cost-sensitive metric penalising false negatives more heavily and incorporating cross-validation variance for deployment stability. Adult classification yields high performance (10/17 models achieve perfect F1 and AUC), while adolescents present a harder task (F1 ceiling 0.837 vs. 0.915 for children). Feature hierarchies shift across cohorts: A9 (social motivation) dominates for children, A5 (pattern recognition) leads for adolescents, and adults exhibit a flatter importance profile consistent with developmental social masking. Accuracy and calibration are dissociated: AdaBoost achieves F1=1.000 on adults with ECE=0.302, confirming single-metric evaluation is insufficient for clinical AI. Cohort-specific deployment recommendations are provided. All findings should be interpreted as proof-of-concept evidence on questionnaire-derived labels rather than clinically validated diagnostic performance.

We study online multicalibration beyond the worst-case. We give a single, efficient algorithm which dynamically interpolates between benign and worst-case sequences by adaptively refining a dyadic grid of prediction values. Its error is controlled by the number of leaves in the refinement tree. Our analysis recovers the known $\widetilde O(T^{2/3})$ worst-case-optimal rate for online multicalibration, while simultaneously automatically adapting to easier instances: in the marginal stochastic setting it obtains a rate of $\widetilde O(\sqrt T)$, and for piecewise-stationary means with $J$ segments its rate is $\widetilde O(\sqrt{JT})$. More generally, the rate depends on a threshold-complexity measure of the predictable mean process relative to the group family. We show that this dependence is tight up to logarithmic factors.

The Brier score conflates two distinct properties of probabilistic predictions: reliability (calibration error) and resolution (discriminatory power). We introduce the Manokhin Probability Matrix, a BCG-style two-dimensional diagnostic framework that separates them. Classifiers are placed on a 2x2 grid by Spiegelhalter Z-statistic and AUC-ROC expected rank, then assigned to one of four archetypes: Eagle (good on both axes), Bull (strong discrimination, poor calibration), Sloth (well-calibrated, weak discriminator), and Mole (poor on both). Each archetype carries a distinct prescription. We populate the matrix from a large-scale empirical study spanning 21 classifiers, 5 post-hoc calibrators, and 30 real-world binary classification tasks from the TabArena-v0.1 suite. The assignment is unambiguous. CatBoost, TabICL, EBM, TabPFN, GBC, and Random Forest are Eagles. XGBoost, LightGBM, and HGB are Bulls; Venn-Abers calibration cuts log-loss by 6.5 to 12.6% on Bulls but degrades Eagles by 2.1%. SVM, LR, LDA, and the empirical base-rate predictor are Sloths. MLP, KNN, Naive Bayes, and ExtraTrees are Moles. A theoretical asymmetry follows: no order-preserving post-hoc calibrator can add discriminatory power (Proposition 1), so calibration is the fixable part and discrimination is the hard part. The practical rule is direct: do not optimise aggregate Brier score without first decomposing it; optimise discrimination first, then fix calibration post-hoc. Code and raw experimental data are available at https://github.com/valeman/classifier_calibration.

Conformal prediction provides distribution-free predictive intervals with finite-sample marginal coverage. However, achieving conditional validity and interval efficiency (in terms of short interval length) remains challenging, particularly in complex settings with heteroskedasticity, skewed responses, or estimation errors. We propose a conformal-style calibration method for responses obtained by the probability integral transform (PIT) of the conditional cumulative distribution function (CDF) estimated via neural networks to construct a finite-sample-adjusted percentile interval with the shortest length determined by the estimated conditional CDF. Calibrating in PIT space is effective because PIT values are asymptotically feature-independent when the CDF estimator is accurate, which mitigates feature-dependent miscoverage and improves conditional calibration. On the other hand, our percentile calibration adapts to the empirical PIT distribution, which is robust against a possibly imperfect estimation of the conditional CDF. We prove the finite-sample marginal coverage property of the proposed method and show its asymptotic conditional coverage under mild consistency conditions. Experiments on diverse synthetic and real-world benchmarks demonstrate better conditional calibration and substantially shorter intervals than existing methods.

Objective: Accurate probability estimates are essential for the safe deployment of medical image segmentation models in clinical decision-making. However, modern deep segmentation networks are often poorly calibrated, a problem exacerbated when multiple expert annotations exhibit substantial disagreement. While inter-rater variability is typically treated as noise, it provides valuable information about intrinsic annotation ambiguity that must be reflected in model confidence. Methods: We improve the probabilistic calibration of medical image segmentation models by reformulating multi-rater supervision as an ordinal learning problem. Voxel-wise annotator agreement is treated as an ordered target, linking predictive confidence to the empirical variability in training data. This formulation allows the use of ordinal-aware scoring rules, such as the Ranked Probability Score ordinal loss, combined with a standard binary objective to preserve discriminative performance. Results: We evaluated the proposed approach across four public segmentation benchmarks spanning ophthalmology, histopathology, and thoracic imaging. Calibration was assessed using a multi-rater extension of expected calibration error. Results consistently show that ordinal-aware training yields substantially improved calibration with respect to inter-rater agreement without degrading segmentation accuracy. Conclusions: Treating multi-rater annotations as ordered information provides a principled and architecture-agnostic route to more reliable probabilistic segmentation models.

Confidence calibration has been dominated by the Expected Calibration Error (ECE), a linear metric that counts calibration offset equally regardless of the confidence level at which it occurs. We show that ECE can remain small even under arbitrarily large overconfidence risk, so we propose Calibrated Size Ratio (CSR) instead, an interpretable metric that equals 1 under perfect calibration, from which we derive the risk probability $P_{\mathrm{risk}}$ that quantifies the statistical evidence for overconfidence. We further argue that overconfidence risk assessment must be complemented by a measure of discriminative value: whether the assigned confidences actively distinguish correct from incorrect predictions. We show that confidence-weighted accuracy $\mathrm{cwA}$ is the natural such complement, and that confidence-weighting extends to all standard classification metrics. In particular, we prove that the confidence-weighted AUC (cwAUC) captures the information about calibration while the classical AUC cannot. We validate the proposed indicators on several synthetic confidence distributions under multiple controlled calibration profiles and find that CSR separates risky from non-risky assignments. We also test the metrics on fifteen real datasets, with and without post-hoc calibration, and find that standard methods can yield risky confidence profiles.

Tree ensembles provide strong classification performance but usually behave as black-box models. Post-hoc interpretability techniques such as RuleCOSI+ extract a small ruleset that approximates the ensemble, but this simplification can leave the probabilities attached to the extracted rules unreliable. In particular, RuleCOSI+ assigns empirical class probabilities to the extracted rules and repeatedly uses those rule statistics during its greedy combination and simplification procedure. We present RCProb, a probabilistic extension that uses smoothed atomic class-conditional evidence for the expensive search stages and a support-adaptive mixture with an ensemble-informed m-estimate for the final rule probabilities. The method is evaluated on 18 binary and 5 multiclass datasets using random forest (RF) and gradient boosting machine (GBM) ensembles. Relative to RuleCOSI+, the median paired log-loss reduction is 71.9% for RF and 62.5% for GBM, with both differences remaining significant after Holm correction. The number of rules decreases by 38.7% for RF and 38.5% for GBM, while the primary tests do not detect a macro-F1 difference. Confidence-ECE also decreases for both ensembles, with statistical support for RF after correction. A separate controlled experiment with dedicated calibration data shows that native RCProb probabilities are competitive with RuleCOSI+ followed by temperature scaling, although additional post-hoc calibration can still improve RCProb. The results show that probability estimation is an important part of rule extraction and not only a post-processing step.

Conventional object detectors typically operate under a closed-set assumption, limiting recognition to a predefined set of base classes seen during training. Open-vocabulary object detection (OVD) addresses this limitation by leveraging vision-language models (VLMs) to generate pseudo labels for novel object classes. However, existing OVD methods suffer from two critical drawbacks: (1) inaccurate class label assignments, as VLMs are optimized for image-level predictions rather than the region-level predictions required for pseudo labeling, and (2) unreliable objectness scores from region proposal networks (RPNs) trained exclusively on base object classes. To address these issues, we propose a novel pseudo labeling framework for OVD. Our approach introduces a hierarchical confidence calibration (HCC) technique, which ensures reliable class label estimation by assessing consistency across hierarchical semantic levels (class, super- and sub-category). We also present LoCLIP, a parameter-efficient adaptation of CLIP that incorporates an objectness token to mitigate base class bias problem of RPNs and provide reliable objectness estimations for novel object classes. Extensive experiments on standard OVD benchmarks, including COCO and LVIS, demonstrate that our approach clearly sets a new state of the art, validating the effectiveness of our approach. Project site: https://cvlab.yonsei.ac.kr/projects/HCC

We study the minimax sample complexity of multicalibration in the batch setting. A learner observes $n$ i.i.d. samples from an unknown distribution and must output a (possibly randomized) predictor whose population multicalibration error, measured by Expected Calibration Error (ECE), is at most $\varepsilon$ with respect to a given family of groups. For every fixed $κ> 0$, in the regime $|G|\le \varepsilon^{-κ}$, we prove that $\widetildeΘ(\varepsilon^{-3})$ samples are necessary and sufficient, up to polylogarithmic factors. The lower bound holds even for randomized predictors, and the upper bound is realized by a randomized predictor obtained via an online-to-batch reduction. This separates the sample complexity of multicalibration from that of marginal calibration, which scales as $\widetildeΘ(\varepsilon^{-2})$, and shows that mean-ECE multicalibration is as difficult in the batch setting as it is in the online setting, in contrast to marginal calibration which is strictly more difficult in the online setting. In contrast we observe that for $κ= 0$, the sample complexity of multicalibration remains $\widetildeΘ(\varepsilon^{-2})$ exhibiting a sharp threshold phenomenon. More generally, we establish matching upper and lower bounds, up to polylogarithmic factors, for a weighted $L_p$ multicalibration metric for all $1 \le p \le 2$, with optimal exponent $3/p$. We also extend the lower-bound template to a regular class of elicitable properties, and combine it with the online upper bounds of Hu et al. (2025) to obtain matching bounds for calibrating properties including expectiles and bounded-density quantiles.

Estimating the prevalence of a category in a population using imperfect measurement devices (diagnostic tests, classifiers, or large language models) is fundamental to science, public health, and online trust and safety. Standard approaches correct for known device error rates but assume these rates remain stable across populations. We show this assumption fails under covariate shift and that multicalibration, which enforces calibration conditional on the input features rather than just on average, is sufficient for unbiased prevalence estimation under such shift. Standard calibration and quantification methods fail to provide this guarantee. Our work connects recent theoretical work on fairness to a longstanding measurement problem spanning nearly all academic disciplines. A simulation confirms that standard methods exhibit bias growing with shift magnitude, while a multicalibrated estimator maintains near-zero bias. While we focus the discussion mostly on LLMs, our theoretical results apply to any classification model. Two empirical applications -- estimating employment prevalence across U.S. states using the American Community Survey, and classifying political texts across four countries using an LLM -- demonstrate that multicalibration substantially reduces bias in practice, while highlighting that calibration data should cover the key feature dimensions along which target populations may differ.

Multi-modal test-time adaptation (TTA) enhances the resilience of benchmark multi-modal models against distribution shifts by leveraging the unlabeled target data during inference. Despite the documented success, the advancement of multi-modal TTA methodologies has been impeded by a persistent limitation, i.e., the lack of explicit modeling of category-conditional distributions, which is crucial for yielding accurate predictions and reliable decision boundaries. Canonical Gaussian discriminant analysis (GDA) provides a vanilla modeling of category-conditional distributions and achieves moderate advancement in uni-modal contexts. However, in multi-modal TTA scenario, the inherent modality distribution asymmetry undermines the effectiveness of modeling the category-conditional distribution via the canonical GDA. To this end, we introduce a tailored probabilistic Gaussian model for multi-modal TTA to explicitly model the category-conditional distributions, and further propose an adaptive contrastive asymmetry rectification technique to counteract the adverse effects arising from modality asymmetry, thereby deriving calibrated predictions and reliable decision boundaries. Extensive experiments across diverse benchmarks demonstrate that our method achieves state-of-the-art performance under a wide range of distribution shifts. The code is available at https://github.com/XuJinglinn/AdaPGC.

We introduce Unified Multimodal Uncertain Inference (UMUI), a multimodal inference task spanning text, audio, and video, where models must produce calibrated probability estimates of hypotheses conditioned on a premise in any modality or combination. While uncertain inference has been explored in text, extension to other modalities has been limited to single-modality binary entailment judgments, leaving no framework for fine-grained probabilistic reasoning in or across other modalities. To address this, we curate a human-annotated evaluation set with scalar probability judgments across audio, visual, and audiovisual settings, and additionally evaluate on existing text and audio benchmarks. We introduce CLUE (Calibrated Latent Uncertainty Estimation), which combines self-consistent teacher calibration and distribution-based confidence probing to produce calibrated predictions. We demonstrate that our 3B-parameter model achieves equivalent or stronger performance than zero-shot baselines up to 32B parameters across all modalities.

Machine learning forecast systems are moving beyond point predictions to full predictive distributions for future outcomes y conditional on complex inputs x. However, these distributions are often locally miscalibrated, especially for high-stakes tail events where accurate uncertainty quantification is most needed to establish trust in models. Local miscalibration occurs because training data often lack examples of low-frequency events. The goal of this paper is to describe a simple, yet flexible framework that, at deployment, produces interpretable diagnostics and a robust correction mechanism of predictive distributions when train examples are limited. With this goal in mind, we introduce a semiparametric version of the Local Amortized Diagnostic and Reshaping (LADaR) framework that posits a covariate-dependent parametric model for a diagnostic transport map regressed nonparametrically on inputs to describe how to correct tail probabilities across the feature space to match calibration data. These maps provide the user with local, real-time diagnostics and a reshaped predictive distribution that can be related back to physical processes in the input space. We apply these semiparametric diagnostic transport maps to short-term tropical cyclone intensity forecasting to detect evolutionary modes linked to local miscalibration in the National Hurricane Center's forecasts and improve predictions for severe weather hazards.

Proper scoring rules are essential for evaluating probabilistic forecasts. We propose a simple algebraic rearrangement of the Yates covariance decomposition of the Brier score into three independently non-negative terms: a variance mismatch term, a correlation deficit term, and a calibration-in-the-large term. This rearrangement makes the optimality conditions for perfect forecasting transparent: the optimal forecast must simultaneously match the variance of outcomes, achieve perfect positive correlation with outcomes, and match the mean of outcomes. Any deviation from these conditions results in a positive contribution to the Brier score.

Visual corruptions can change vision--language model (VLM) behavior in ways that top-1 accuracy does not capture. A model may keep the same answer while losing distributional support, or improve accuracy through unstable wrong-to-correct changes. We introduce Bench-C, a controlled multiple-choice testbed for studying these effects. It selects semantically diverse samples whose predictions respond to corruption, and evaluates them under 19 corruption types and five severity levels. To measure how corruption changes the option distribution, we introduce the Robustness Alignment Score (RAS), which combines confidence-correctness alignment with uncertainty direction. We further separate originally correct samples from originally wrong samples, and track whether changes are temporary or persistent across severity. Experiments across 13 VLMs reveal a counterintuitive pattern: mild corruptions can improve top-1 accuracy while degrading prediction structure. These failures include silent degradation, erroneous overconfidence, and severity-dependent persistence. Bench-C therefore supports robustness evaluation that goes beyond final answers and attributes where reliability changes occur. Code and data are available at https://github.com/xiangjieSui/Bench-C.

[Corrected v2: an audit found that the score, threshold, and latency descriptions below are not what the shared codebase implements, and that the evaluation streams are assembled constructions. See the correction note on the title page and the corrected companion work, arXiv:2605.24696 (corrected v3), artifact doi:10.5281/zenodo.22673735.] We present a risk-calibrated approach to streaming intrusion detection that couples Bayesian Online Changepoint Detection (BOCPD) with decision thresholds aligned to Site Reliability Engineering (SRE) error budgets. BOCPD provides run-length posteriors that adapt to distribution shift and concept drift; we map these posteriors to alert decisions by optimizing expected operational cost under false-positive and false-negative budgets. We detail the hazard model, conjugate updates, and an O(1)-per-event implementation. A concrete SRE example shows how a 99.9% availability SLO (43.2 minutes per month error budget) yields a probability threshold near 0.91 when missed incidents are 10x more costly than false alarms. We evaluate on the full UNSW-NB15 and CIC-IDS2017 benchmarks with chronological splits, comparing against strong unsupervised baselines (ECOD, COPOD, and LOF). Metrics include PR-AUC, ROC-AUC, Brier score, calibration reliability diagrams, and detection latency measured in events. Results indicate improved precision-recall at mid to high recall and better probability calibration relative to baselines. We release implementation details, hyperparameters, and ablations for hazard sensitivity and computational footprint. Code and reproducibility materials will be made available upon publication; datasets and implementation are available from the corresponding author upon reasonable request.

We study the fundamental problem of calibrating a linear binary classifier of the form $σ(\hat{w}^\top x)$, where the feature vector $x$ is Gaussian, $σ$ is a link function, and $\hat{w}$ is an estimator of the true linear weight $w^\star$. By interpolating with a noninformative $\textit{chance classifier}$, we construct a well-calibrated predictor whose interpolation weight depends on the angle $\angle(\hat{w}, w_\star)$ between the estimator $\hat{w}$ and the true linear weight $w_\star$. We establish that this angular calibration approach is provably well-calibrated in a high-dimensional regime where the number of samples and features both diverge, at a comparable rate. The angle $\angle(\hat{w}, w_\star)$ can be consistently estimated. Furthermore, the resulting predictor is uniquely $\textit{Bregman-optimal}$, minimizing the Bregman divergence to the true label distribution within a suitable class of calibrated predictors. Our work is the first to provide a calibration strategy that satisfies both calibration and optimality properties provably in high dimensions. Additionally, we identify conditions under which a classical Platt-scaling predictor converges to our Bregman-optimal calibrated solution. Thus, Platt-scaling also inherits these desirable properties provably in high dimensions.

A set of probabilistic forecasts is calibrated if each prediction of the forecaster closely approximates the empirical distribution of outcomes on the subset of timesteps where that prediction was made. We study the fundamental problem of online calibrated forecasting of binary sequences under the standard $\ell_1$ calibration error metric, which was initially studied by Foster & Vohra (1998). They derived an algorithm with $O(T^{2/3})$ calibration error after $T$ time steps, and showed a lower bound of $Ω(T^{1/2})$. These bounds remained stagnant for two decades, until Qiao & Valiant (2021) improved the lower bound to $Ω(T^{0.528})$ by introducing a combinatorial game called sign preservation and showing that lower bounds for this game imply lower bounds for calibration. In this paper, we give the first improvement to the $O(T^{2/3})$ upper bound on calibration error of Foster & Vohra. We do this by introducing a variant of Qiao & Valiant's game that we call sign preservation with reuse (SPR). We prove that the relationship between SPR and calibrated forecasting is bidirectional: not only do lower bounds for SPR translate into lower bounds for calibration, but algorithms for SPR also translate into new algorithms for calibrated forecasting. We then give an improved upper bound for the SPR game, which implies, via our equivalence, a forecasting algorithm with calibration error $O(T^{2/3 - \varepsilon})$ for some $\varepsilon > 0$, improving Foster & Vohra's upper bound for the first time. Using similar ideas, we then prove a slightly stronger lower bound than that of Qiao & Valiant, namely $Ω(T^{0.54389})$. Our lower bound is obtained by an oblivious adversary, marking the first $ω(T^{1/2})$ calibration lower bound for oblivious adversaries.

Open-set recognition refers to the problem in which classes that were not seen during training appear at inference time. This requires the ability to identify instances of novel classes while maintaining discriminative capability for closed-set classification. OpenMax was the first deep neural network-based approach to address open-set recognition by calibrating the predictive scores of a standard closed-set classification network. In this paper we present MetaMax, a more effective post-processing technique that improves upon contemporary methods by directly modeling class activation vectors. MetaMax removes the need for computing class mean activation vectors (MAVs) and distances between a query image and a class MAV as required in OpenMax. Experimental results show that MetaMax outperforms OpenMax and is comparable in performance to other state-of-the-art approaches.

Feed-forward 3D reconstruction models output a per-pixel confidence that is used by downstream systems as an uncertainty signal. The confidence is trained to serve as a weight in the training loss of models. Whether the confidence can be used as an uncertainty magnitude has not been measured. We audit seven backbones on 13 datasets and score the confidence on four properties, i.e., ranking of error, ratio of error to uncertainty on average, slope of this ratio across the confidence range, and coverage of the implied error distribution. Although the confidence ranks error quite well, the uncertainty decoded from the confidence is too small compared to the actual error. The uncertainty has the right size only under the exact training conditions. The median case is off by at least 2.4x across all seven models, while the uncertainty is further off the more confident the model is. Our work shows that the overconfidence appears on unseen scenes even when the model reaches its loss's optimum. As a post-hoc repair we fit a power law on the confidence with two constants per backbone--dataset pair. The repair brings all four audited properties to target at the dataset level, while leaving ranking untouched. Fitted with the target dataset held out, the constants bring the median case from 2.4x off to 1.35x. The repair does not hold below the dataset level, where two-thirds of held-out scenes are still more than five points off in coverage. We attribute what the repair cannot reach to the model, which carries neither the scale of the error nor the shape of its distribution across predictions. We release the audit protocol, its results, and the fitted constants per backbone-dataset pair.