Differentially private Bayesian tests

• URL: http://arxiv.org/abs/2401.15502v2
• Date: Wed, 1 May 2024 20:32:44 GMT
• Title: Differentially private Bayesian tests
• Authors: Abhisek Chakraborty, Saptati Datta,
• Abstract summary: We present a novel differentially private Bayesian hypotheses testing framework that arise naturally under a principled data generative mechanism. By focusing on differentially private Bayes factors based on widely used test statistics, we circumvent the need to model the complete data generative mechanism.
• Score: 1.3127313002783776
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Differential privacy has emerged as an significant cornerstone in the realm of scientific hypothesis testing utilizing confidential data. In reporting scientific discoveries, Bayesian tests are widely adopted since they effectively circumnavigate the key criticisms of P-values, namely, lack of interpretability and inability to quantify evidence in support of the competing hypotheses. We present a novel differentially private Bayesian hypotheses testing framework that arise naturally under a principled data generative mechanism, inherently maintaining the interpretability of the resulting inferences. Furthermore, by focusing on differentially private Bayes factors based on widely used test statistics, we circumvent the need to model the complete data generative mechanism and ensure substantial computational benefits. We also provide a set of sufficient conditions to establish results on Bayes factor consistency under the proposed framework. The utility of the devised technology is showcased via several numerical experiments.

Related papers

• Seeing Unseen: Discover Novel Biomedical Concepts via Geometry-Constrained Probabilistic Modeling [53.7117640028211]
  We present a geometry-constrained probabilistic modeling treatment to resolve the identified issues. We incorporate a suite of critical geometric properties to impose proper constraints on the layout of constructed embedding space. A spectral graph-theoretic method is devised to estimate the number of potential novel classes.
  arXiv  Detail & Related papers  (2024-03-02T00:56:05Z)
• A unified Bayesian framework for interval hypothesis testing in clinical trials [4.911220423050305]
  The American Statistical Association (ASA) cautioned statisticians against making scientific decisions solely on the basis of traditional P-values. We demonstrate that the interval null hypothesis framework, when used in tandem with Bayes factor-based tests, is instrumental in circumnavigating the key issues of P-values.
  arXiv  Detail & Related papers  (2024-02-21T16:01:06Z)
• Device-independent certification of desirable properties with a confidence interval [0.0]
  We provide a versatile solution for rigorous device-independent certification. We show how the PBR protocol and the martingale-based protocol often offer similar performance. Our findings also show that the performance of the martingale-based protocol may be severely affected by one's choice of the witness.
  arXiv  Detail & Related papers  (2024-01-12T15:21:21Z)
• Differentially Private Permutation Tests: Applications to Kernel Methods [7.596498528060537]
  differential privacy has emerged as a rigorous framework for privacy protection, gaining widespread recognition in both academic and industrial circles. This paper aims to alleviate concerns in the context of hypothesis testing by introducing differentially private permutation tests. The proposed framework extends classical non-private permutation tests to private settings, maintaining both finite-sample validity and differential privacy in a rigorous manner.
  arXiv  Detail & Related papers  (2023-10-29T15:13:36Z)
• 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)
• A Double Machine Learning Approach to Combining Experimental and Observational Data [59.29868677652324]
  We propose a double machine learning approach to combine experimental and observational studies. Our framework tests for violations of external validity and ignorability under milder assumptions.
  arXiv  Detail & Related papers  (2023-07-04T02:53:11Z)
• Advancing Counterfactual Inference through Nonlinear Quantile Regression [77.28323341329461]
  We propose a framework for efficient and effective counterfactual inference implemented with neural networks. The proposed approach enhances the capacity to generalize estimated counterfactual outcomes to unseen data. Empirical results conducted on multiple datasets offer compelling support for our theoretical assertions.
  arXiv  Detail & Related papers  (2023-06-09T08:30:51Z)
• Empirical Bayesian Approaches for Robust Constraint-based Causal Discovery under Insufficient Data [38.883810061897094]
  Causal discovery methods assume data sufficiency, which may not be the case in many real world datasets. We propose Bayesian-augmented frequentist independence tests to improve the performance of constraint-based causal discovery methods under insufficient data. Experiments show significant performance improvement in terms of both accuracy and efficiency over SOTA methods.
  arXiv  Detail & Related papers  (2022-06-16T21:08:49Z)
• BaCaDI: Bayesian Causal Discovery with Unknown Interventions [118.93754590721173]
  BaCaDI operates in the continuous space of latent probabilistic representations of both causal structures and interventions. In experiments on synthetic causal discovery tasks and simulated gene-expression data, BaCaDI outperforms related methods in identifying causal structures and intervention targets.
  arXiv  Detail & Related papers  (2022-06-03T16:25:48Z)
• Private Sequential Hypothesis Testing for Statisticians: Privacy, Error Rates, and Sample Size [24.149533870085175]
  We study the sequential hypothesis testing problem under a slight variant of differential privacy, known as Renyi differential privacy. We present a new private algorithm based on Wald's Sequential Probability Ratio Test (SPRT) that also gives strong theoretical privacy guarantees.
  arXiv  Detail & Related papers  (2022-04-10T04:15:50Z)
• Balance-Subsampled Stable Prediction [55.13512328954456]
  We propose a novel balance-subsampled stable prediction (BSSP) algorithm based on the theory of fractional factorial design. A design-theoretic analysis shows that the proposed method can reduce the confounding effects among predictors induced by the distribution shift. Numerical experiments on both synthetic and real-world data sets demonstrate that our BSSP algorithm significantly outperforms the baseline methods for stable prediction across unknown test data.
  arXiv  Detail & Related papers  (2020-06-08T07:01:38Z)

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.