On Computationally Efficient Multi-Class Calibration

• URL: http://arxiv.org/abs/2402.07821v2
• Date: Sat, 8 Jun 2024 04:27:46 GMT
• Title: On Computationally Efficient Multi-Class Calibration
• Authors: Parikshit Gopalan, Lunjia Hu, Guy N. Rothblum,
• Abstract summary: Project calibration gives strong guarantees for all downstream decision makers. It ensures that the probabilities predicted by summing the probabilities assigned to labels in $T$ are close to some perfectly calibrated binary predictor.
• Score: 9.032290717007065
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Consider a multi-class labelling problem, where the labels can take values in $[k]$, and a predictor predicts a distribution over the labels. In this work, we study the following foundational question: Are there notions of multi-class calibration that give strong guarantees of meaningful predictions and can be achieved in time and sample complexities polynomial in $k$? Prior notions of calibration exhibit a tradeoff between computational efficiency and expressivity: they either suffer from having sample complexity exponential in $k$, or needing to solve computationally intractable problems, or give rather weak guarantees. Our main contribution is a notion of calibration that achieves all these desiderata: we formulate a robust notion of projected smooth calibration for multi-class predictions, and give new recalibration algorithms for efficiently calibrating predictors under this definition with complexity polynomial in $k$. Projected smooth calibration gives strong guarantees for all downstream decision makers who want to use the predictor for binary classification problems of the form: does the label belong to a subset $T \subseteq [k]$: e.g. is this an image of an animal? It ensures that the probabilities predicted by summing the probabilities assigned to labels in $T$ are close to some perfectly calibrated binary predictor for that task. We also show that natural strengthenings of our definition are computationally hard to achieve: they run into information theoretic barriers or computational intractability. Underlying both our upper and lower bounds is a tight connection that we prove between multi-class calibration and the well-studied problem of agnostic learning in the (standard) binary prediction setting.

Related papers

• Dirichlet-Based Prediction Calibration for Learning with Noisy Labels [40.78497779769083]
  Learning with noisy labels can significantly hinder the generalization performance of deep neural networks (DNNs) Existing approaches address this issue through loss correction or example selection methods. We propose the textitDirichlet-based Prediction (DPC) method as a solution.
  arXiv  Detail & Related papers  (2024-01-13T12:33:04Z)
• Generating Unbiased Pseudo-labels via a Theoretically Guaranteed Chebyshev Constraint to Unify Semi-supervised Classification and Regression [57.17120203327993]
  threshold-to-pseudo label process (T2L) in classification uses confidence to determine the quality of label. In nature, regression also requires unbiased methods to generate high-quality labels. We propose a theoretically guaranteed constraint for generating unbiased labels based on Chebyshev's inequality.
  arXiv  Detail & Related papers  (2023-11-03T08:39:35Z)
• 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)
• A Consistent and Differentiable Lp Canonical Calibration Error Estimator [21.67616079217758]
  Deep neural networks are poorly calibrated and tend to output overconfident predictions. We propose a low-bias, trainable calibration error estimator based on Dirichlet kernel density estimates. Our method has a natural choice of kernel, and can be used to generate consistent estimates of other quantities.
  arXiv  Detail & Related papers  (2022-10-13T15:11:11Z)
• T-Cal: An optimal test for the calibration of predictive models [49.11538724574202]
  We consider detecting mis-calibration of predictive models using a finite validation dataset as a hypothesis testing problem. detecting mis-calibration is only possible when the conditional probabilities of the classes are sufficiently smooth functions of the predictions. We propose T-Cal, a minimax test for calibration based on a de-biased plug-in estimator of the $ell$-Expected Error (ECE)
  arXiv  Detail & Related papers  (2022-03-03T16:58:54Z)
• 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)
• Distribution-Free, Risk-Controlling Prediction Sets [112.9186453405701]
  We show how to generate set-valued predictions from a black-box predictor that control the expected loss on future test points at a user-specified level. Our approach provides explicit finite-sample guarantees for any dataset by using a holdout set to calibrate the size of the prediction sets.
  arXiv  Detail & Related papers  (2021-01-07T18:59:33Z)
• Online Multivalid Learning: Means, Moments, and Prediction Intervals [16.75129633574157]
  We present a technique for providing contextual predictions that are "multivalid" in various senses. The resulting estimates correctly predict various statistics of the labels $y$ not just marginally. Because our algorithms handle adversarially chosen examples, they can equally well be used to predict statistics of the residuals of arbitrary point prediction methods.
  arXiv  Detail & Related papers  (2021-01-05T19:08:11Z)
• Almost Tight L0-norm Certified Robustness of Top-k Predictions against Adversarial Perturbations [78.23408201652984]
  Top-k predictions are used in many real-world applications such as machine learning as a service, recommender systems, and web searches. Our work is based on randomized smoothing, which builds a provably robust classifier via randomizing an input. For instance, our method can build a classifier that achieves a certified top-3 accuracy of 69.2% on ImageNet when an attacker can arbitrarily perturb 5 pixels of a testing image.
  arXiv  Detail & Related papers  (2020-11-15T21:34:44Z)
• 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.