Credal Two-Sample Tests of Epistemic Ignorance

• URL: http://arxiv.org/abs/2410.12921v1
• Date: Wed, 16 Oct 2024 18:09:09 GMT
• Title: Credal Two-Sample Tests of Epistemic Ignorance
• Authors: Siu Lun Chau, Antonin Schrab, Arthur Gretton, Dino Sejdinovic, Krikamol Muandet,
• Abstract summary: We introduce credal two-sample testing, a new hypothesis testing framework for comparing credal sets. We generalise two-sample tests to compare credal sets, enabling reasoning for equality, inclusion, intersection, and mutual exclusivity.
• Score: 34.42566984003255
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce credal two-sample testing, a new hypothesis testing framework for comparing credal sets -- convex sets of probability measures where each element captures aleatoric uncertainty and the set itself represents epistemic uncertainty that arises from the modeller's partial ignorance. Classical two-sample tests, which rely on comparing precise distributions, fail to address epistemic uncertainty due to partial ignorance. To bridge this gap, we generalise two-sample tests to compare credal sets, enabling reasoning for equality, inclusion, intersection, and mutual exclusivity, each offering unique insights into the modeller's epistemic beliefs. We formalise these tests as two-sample tests with nuisance parameters and introduce the first permutation-based solution for this class of problems, significantly improving upon existing methods. Our approach properly incorporates the modeller's epistemic uncertainty into hypothesis testing, leading to more robust and credible conclusions, with kernel-based implementations for real-world applications.

Related papers

• SConU: Selective Conformal Uncertainty in Large Language Models [59.25881667640868]
  We propose a novel approach termed Selective Conformal Uncertainty (SConU) We develop two conformal p-values that are instrumental in determining whether a given sample deviates from the uncertainty distribution of the calibration set at a specific manageable risk level. Our approach not only facilitates rigorous management of miscoverage rates across both single-domain and interdisciplinary contexts, but also enhances the efficiency of predictions.
  arXiv  Detail & Related papers  (2025-04-19T03:01:45Z)
• FactTest: Factuality Testing in Large Language Models with Finite-Sample and Distribution-Free Guarantees [41.78390564658645]
  Large Language Models (LLMs) to generate hallucinations and non-factual content undermines their reliability in high-stakes domains. We introduce FactTest, a novel framework that statistically assesses whether a LLM can confidently provide correct answers to given questions. We show that FactTest effectively detects hallucinations and improves the model's ability to abstain from answering unknown questions, leading to an over 40% accuracy improvement.
  arXiv  Detail & Related papers  (2024-11-04T20:53:04Z)
• General Frameworks for Conditional Two-Sample Testing [3.3317825075368908]
  We study the problem of conditional two-sample testing, which aims to determine whether two populations have the same distribution after accounting for confounding factors. This problem commonly arises in various applications, such as domain adaptation and algorithmic fairness. We introduce two general frameworks that implicitly or explicitly target specific classes of distributions for their validity and power.
  arXiv  Detail & Related papers  (2024-10-22T02:27:32Z)
• Non-Convex Robust Hypothesis Testing using Sinkhorn Uncertainty Sets [18.46110328123008]
  We present a new framework to address the non-robust hypothesis testing problem. The goal is to seek the optimal detector that minimizes the maximum numerical risk.
  arXiv  Detail & Related papers  (2024-03-21T20:29:43Z)
• Deep anytime-valid hypothesis testing [29.273915933729057]
  We propose a general framework for constructing powerful, sequential hypothesis tests for nonparametric testing problems. We develop a principled approach of leveraging the representation capability of machine learning models within the testing-by-betting framework. Empirical results on synthetic and real-world datasets demonstrate that tests instantiated using our general framework are competitive against specialized baselines.
  arXiv  Detail & Related papers  (2023-10-30T09:46:19Z)
• Prototype-based Aleatoric Uncertainty Quantification for Cross-modal Retrieval [139.21955930418815]
  Cross-modal Retrieval methods build similarity relations between vision and language modalities by jointly learning a common representation space. However, the predictions are often unreliable due to the Aleatoric uncertainty, which is induced by low-quality data, e.g., corrupt images, fast-paced videos, and non-detailed texts. We propose a novel Prototype-based Aleatoric Uncertainty Quantification (PAU) framework to provide trustworthy predictions by quantifying the uncertainty arisen from the inherent data ambiguity.
  arXiv  Detail & Related papers  (2023-09-29T09:41:19Z)
• Selective Nonparametric Regression via Testing [54.20569354303575]
  We develop an abstention procedure via testing the hypothesis on the value of the conditional variance at a given point. Unlike existing methods, the proposed one allows to account not only for the value of the variance itself but also for the uncertainty of the corresponding variance predictor.
  arXiv  Detail & Related papers  (2023-09-28T13:04:11Z)
• Sequential Predictive Two-Sample and Independence Testing [114.4130718687858]
  We study the problems of sequential nonparametric two-sample and independence testing. We build upon the principle of (nonparametric) testing by betting.
  arXiv  Detail & Related papers  (2023-04-29T01:30:33Z)
• Bootstrapped Edge Count Tests for Nonparametric Two-Sample Inference Under Heterogeneity [5.8010446129208155]
  We develop a new nonparametric testing procedure that accurately detects differences between the two samples. A comprehensive simulation study and an application to detecting user behaviors in online games demonstrates the excellent non-asymptotic performance of the proposed test.
  arXiv  Detail & Related papers  (2023-04-26T22:25:44Z)
• Shortcomings of Top-Down Randomization-Based Sanity Checks for Evaluations of Deep Neural Network Explanations [67.40641255908443]
  We identify limitations of model-randomization-based sanity checks for the purpose of evaluating explanations. Top-down model randomization preserves scales of forward pass activations with high probability.
  arXiv  Detail & Related papers  (2022-11-22T18:52:38Z)
• Statistical and Computational Phase Transitions in Group Testing [73.55361918807883]
  We study the group testing problem where the goal is to identify a set of k infected individuals carrying a rare disease. We consider two different simple random procedures for assigning individuals tests.
  arXiv  Detail & Related papers  (2022-06-15T16:38:50Z)
• A Data-Driven Approach to Robust Hypothesis Testing Using Sinkhorn Uncertainty Sets [12.061662346636645]
  We seek the worst-case detector over distributional uncertainty sets centered around the empirical distribution from samples using Sinkhorn distance. Compared with the Wasserstein robust test, the corresponding least favorable distributions are supported beyond the training samples, which provides a more flexible detector.
  arXiv  Detail & Related papers  (2022-02-09T03:26:15Z)
• A One-step Approach to Covariate Shift Adaptation [82.01909503235385]
  A default assumption in many machine learning scenarios is that the training and test samples are drawn from the same probability distribution. We propose a novel one-step approach that jointly learns the predictive model and the associated weights in one optimization.
  arXiv  Detail & Related papers  (2020-07-08T11:35:47Z)
• Good Classifiers are Abundant in the Interpolating Regime [64.72044662855612]
  We develop a methodology to compute precisely the full distribution of test errors among interpolating classifiers. We find that test errors tend to concentrate around a small typical value $varepsilon*$, which deviates substantially from the test error of worst-case interpolating model. Our results show that the usual style of analysis in statistical learning theory may not be fine-grained enough to capture the good generalization performance observed in practice.
  arXiv  Detail & Related papers  (2020-06-22T21:12:31Z)
• Achieving Equalized Odds by Resampling Sensitive Attributes [13.114114427206678]
  We present a flexible framework for learning predictive models that approximately satisfy the equalized odds notion of fairness. This differentiable functional is used as a penalty driving the model parameters towards equalized odds. We develop a formal hypothesis test to detect whether a prediction rule violates this property, the first such test in the literature.
  arXiv  Detail & Related papers  (2020-06-08T00:18:34Z)

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.