Ask for More Than Bayes Optimal: A Theory of Indecisions for Classification

• URL: http://arxiv.org/abs/2412.12807v2
• Date: Sun, 13 Apr 2025 12:19:53 GMT
• Title: Ask for More Than Bayes Optimal: A Theory of Indecisions for Classification
• Authors: Mohamed Ndaoud, Peter Radchenko, Bradley Rava,
• Abstract summary: Selective classification is a powerful tool for automated decision-making in high-risk scenarios.<n>Our goal is to minimize the number of indecisions, which are observations that we do not automate.<n>By using indecisions, we are able to control the misclassification rate to any user-specified level, even below the Bayes optimal error rate.
• Score: 1.8434042562191815
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Selective classification is a powerful tool for automated decision-making in high-risk scenarios, allowing classifiers to make only highly confident decisions while abstaining when uncertainty is too high. Given a target classification accuracy, our goal is to minimize the number of indecisions, which are observations that we do not automate. For problems that are hard, the target accuracy may not be achievable without using indecisions. In contrast, by using indecisions, we are able to control the misclassification rate to any user-specified level, even below the Bayes optimal error rate, while minimizing the frequency of identifying an indecision. We provide a full characterization of the minimax risk in selective classification, proving key continuity and monotonicity properties that enable optimal indecision selection. Our results extend to hypothesis testing, where we control type II error given a fixed type I error, introducing a novel perspective in selective inference. We analyze the impact of estimating the regression function $\eta$, showing that plug-in classifiers remain consistent and that accuracy-based calibration effectively controls indecision levels. Additionally, we develop finite-sample calibration methods and identify cases where no training data is needed under the Monotone Likelihood Ratio (MLR) property. In the binary Gaussian mixture model, we establish sharp phase transition results, demonstrating that minimal indecisions can yield near-optimal accuracy even with suboptimal class separation. These findings highlight the potential of selective classification to significantly reduce misclassification rates with a relatively small cost in terms of indecisions.

Related papers

• Uncertainty Weighted Gradients for Model Calibration [22.39558434131574]
  Deep networks often produce over-confident or under-confident predictions, leading to miscalibration. We propose a unified loss framework for focal loss and its variants, where we mainly attribute their superiority in model calibration to the loss weighting factor. Our method achieves state-of-the-art (SOTA) performance.
  arXiv  Detail & Related papers  (2025-03-26T04:16:05Z)
• Improving Predictor Reliability with Selective Recalibration [15.319277333431318]
  Recalibration is one of the most effective ways to produce reliable confidence estimates with a pre-trained model. We propose textitselective recalibration, where a selection model learns to reject some user-chosen proportion of the data. Our results show that selective recalibration consistently leads to significantly lower calibration error than a wide range of selection and recalibration baselines.
  arXiv  Detail & Related papers  (2024-10-07T18:17:31Z)
• On support vector machines under a multiple-cost scenario [1.743685428161914]
  Support Vector Machine (SVM) is a powerful tool in binary classification. We propose a novel SVM model in which misclassification costs are considered by incorporating performance constraints.
  arXiv  Detail & Related papers  (2023-12-22T16:12:25Z)
• Calibration by Distribution Matching: Trainable Kernel Calibration Metrics [56.629245030893685]
  We introduce kernel-based calibration metrics that unify and generalize popular forms of calibration for both classification and regression. These metrics admit differentiable sample estimates, making it easy to incorporate a calibration objective into empirical risk minimization. We provide intuitive mechanisms to tailor calibration metrics to a decision task, and enforce accurate loss estimation and no regret decisions.
  arXiv  Detail & Related papers  (2023-10-31T06:19:40Z)
• Fair Classifiers that Abstain without Harm [24.90899074869189]
  In critical applications, it is vital for classifiers to defer decision-making to humans. We propose a post-hoc method that makes existing classifiers selectively abstain from predicting certain samples. Our framework outperforms existing methods in terms of fairness disparity without sacrificing accuracy at similar abstention rates.
  arXiv  Detail & Related papers  (2023-10-09T23:07:28Z)
• Model Calibration in Dense Classification with Adaptive Label Perturbation [44.62722402349157]
  Existing dense binary classification models are prone to being over-confident. We propose Adaptive Label Perturbation (ASLP) which learns a unique label perturbation level for each training image. ASLP can significantly improve calibration degrees of dense binary classification models on both in-distribution and out-of-distribution data.
  arXiv  Detail & Related papers  (2023-07-25T14:40:11Z)
• Improving Selective Visual Question Answering by Learning from Your Peers [74.20167944693424]
  Visual Question Answering (VQA) models can have difficulties abstaining from answering when they are wrong. We propose Learning from Your Peers (LYP) approach for training multimodal selection functions for making abstention decisions. Our approach uses predictions from models trained on distinct subsets of the training data as targets for optimizing a Selective VQA model.
  arXiv  Detail & Related papers  (2023-06-14T21:22:01Z)
• Minimum-Risk Recalibration of Classifiers [9.31067660373791]
  We introduce the concept of minimum-risk recalibration within the framework of mean-squared-error decomposition. We show that transferring a calibrated classifier requires significantly fewer target samples compared to recalibrating from scratch.
  arXiv  Detail & Related papers  (2023-05-18T11:27:02Z)
• Minimax-Bayes Reinforcement Learning [2.7456483236562437]
  This paper studies (sometimes approximate) minimax-Bayes solutions for various reinforcement learning problems. We find that while the worst-case prior depends on the setting, the corresponding minimax policies are more robust than those that assume a standard (i.e. uniform) prior.
  arXiv  Detail & Related papers  (2023-02-21T17:10:21Z)
• Training Normalizing Flows with the Precision-Recall Divergence [73.92251251511199]
  We show that achieving a specified precision-recall trade-off corresponds to minimising -divergences from a family we call the em PR-divergences We propose a novel generative model that is able to train a normalizing flow to minimise any -divergence, and in particular, achieve a given precision-recall trade-off.
  arXiv  Detail & Related papers  (2023-02-01T17:46:47Z)
• Arbitrariness and Social Prediction: The Confounding Role of Variance in Fair Classification [31.392067805022414]
  Variance in predictions across different trained models is a significant, under-explored source of error in fair binary classification. In practice, the variance on some data examples is so large that decisions can be effectively arbitrary. We develop an ensembling algorithm that abstains from classification when a prediction would be arbitrary.
  arXiv  Detail & Related papers  (2023-01-27T06:52:04Z)
• On Calibrating Semantic Segmentation Models: Analyses and An Algorithm [51.85289816613351]
  We study the problem of semantic segmentation calibration. Model capacity, crop size, multi-scale testing, and prediction correctness have impact on calibration. We propose a simple, unifying, and effective approach, namely selective scaling.
  arXiv  Detail & Related papers  (2022-12-22T22:05:16Z)
• Calibrated Selective Classification [34.08454890436067]
  We develop a new approach to selective classification in which we propose a method for rejecting examples with "uncertain" uncertainties. We present a framework for learning selectively calibrated models, where a separate selector network is trained to improve the selective calibration error of a given base model. We demonstrate the empirical effectiveness of our approach on multiple image classification and lung cancer risk assessment tasks.
  arXiv  Detail & Related papers  (2022-08-25T13:31:09Z)
• Is the Performance of My Deep Network Too Good to Be True? A Direct Approach to Estimating the Bayes Error in Binary Classification [86.32752788233913]
  In classification problems, the Bayes error can be used as a criterion to evaluate classifiers with state-of-the-art performance. We propose a simple and direct Bayes error estimator, where we just take the mean of the labels that show emphuncertainty of the classes. Our flexible approach enables us to perform Bayes error estimation even for weakly supervised data.
  arXiv  Detail & Related papers  (2022-02-01T13:22:26Z)
• Online Selective Classification with Limited Feedback [82.68009460301585]
  We study selective classification in the online learning model, wherein a predictor may abstain from classifying an instance. Two salient aspects of the setting we consider are that the data may be non-realisable, due to which abstention may be a valid long-term action. We construct simple versioning-based schemes for any $mu in (0,1],$ that make most $Tmu$ mistakes while incurring smash$tildeO(T1-mu)$ excess abstention against adaptive adversaries.
  arXiv  Detail & Related papers  (2021-10-27T08:00:53Z)
• Calibrating Predictions to Decisions: A Novel Approach to Multi-Class Calibration [118.26862029820447]
  We introduce a new notion -- emphdecision calibration -- that requires the predicted distribution and true distribution to be indistinguishable'' to a set of downstream decision-makers. Decision calibration improves decision-making on skin lesions and ImageNet classification with modern neural network.
  arXiv  Detail & Related papers  (2021-07-12T20:17:28Z)
• Modularity in Reinforcement Learning via Algorithmic Independence in Credit Assignment [79.5678820246642]
  We show that certain action-value methods are more sample efficient than policy-gradient methods on transfer problems that require only sparse changes to a sequence of previously optimal decisions. We generalize the recently proposed societal decision-making framework as a more granular formalism than the Markov decision process.
  arXiv  Detail & Related papers  (2021-06-28T21:29:13Z)
• Scalable Marginal Likelihood Estimation for Model Selection in Deep Learning [78.83598532168256]
  Marginal-likelihood based model-selection is rarely used in deep learning due to estimation difficulties. Our work shows that marginal likelihoods can improve generalization and be useful when validation data is unavailable.
  arXiv  Detail & Related papers  (2021-04-11T09:50:24Z)
• Provable tradeoffs in adversarially robust classification [96.48180210364893]
  We develop and leverage new tools, including recent breakthroughs from probability theory on robust isoperimetry. Our results reveal fundamental tradeoffs between standard and robust accuracy that grow when data is imbalanced.
  arXiv  Detail & Related papers  (2020-06-09T09:58:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.