Differentially Private Conditional Independence Testing

• URL: http://arxiv.org/abs/2306.06721v3
• Date: Fri, 22 Mar 2024 19:40:59 GMT
• Title: Differentially Private Conditional Independence Testing
• Authors: Iden Kalemaj, Shiva Prasad Kasiviswanathan, Aaditya Ramdas,
• Abstract summary: Conditional independence (CI) tests are widely used in statistical data analysis. In this work, we investigate conditional independence testing under the constraint of differential privacy.
• Score: 35.376975903797444
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Conditional independence (CI) tests are widely used in statistical data analysis, e.g., they are the building block of many algorithms for causal graph discovery. The goal of a CI test is to accept or reject the null hypothesis that $X \perp \!\!\! \perp Y \mid Z$, where $X \in \mathbb{R}, Y \in \mathbb{R}, Z \in \mathbb{R}^d$. In this work, we investigate conditional independence testing under the constraint of differential privacy. We design two private CI testing procedures: one based on the generalized covariance measure of Shah and Peters (2020) and another based on the conditional randomization test of Cand\`es et al. (2016) (under the model-X assumption). We provide theoretical guarantees on the performance of our tests and validate them empirically. These are the first private CI tests with rigorous theoretical guarantees that work for the general case when $Z$ is continuous.

Related papers

• A Conditional Independence Test in the Presence of Discretization [14.917729593550199]
  Existing test methods can't work when only discretized observations are available. We propose a conditional independence test specifically designed to accommodate the presence of such discretization.
  arXiv  Detail & Related papers  (2024-04-26T18:08:15Z)
• Collaborative non-parametric two-sample testing [55.98760097296213]
  The goal is to identify nodes where the null hypothesis $p_v = q_v$ should be rejected. We propose the non-parametric collaborative two-sample testing (CTST) framework that efficiently leverages the graph structure. Our methodology integrates elements from f-divergence estimation, Kernel Methods, and Multitask Learning.
  arXiv  Detail & Related papers  (2024-02-08T14:43:56Z)
• A Permutation-Free Kernel Independence Test [36.50719125230106]
  In nonparametric independence testing, we observe i.i.d. data $(X_i,Y_i)_i=1n$, where $X in mathcalX, Y in mathcalY$ lie in any general spaces. Modern test statistics such as the kernel Hilbert-Schmidt Independence Criterion (HSIC) and Distance Covariance (dCov) have intractable null distributions due to the degeneracy of the underlying U-statistics. This paper provides a simple but nontrivial modification of HSIC
  arXiv  Detail & Related papers  (2022-12-18T15:28:16Z)
• Sequential Kernelized Independence Testing [101.22966794822084]
  We design sequential kernelized independence tests inspired by kernelized dependence measures. We demonstrate the power of our approaches on both simulated and real data.
  arXiv  Detail & Related papers  (2022-12-14T18:08:42Z)
• Sharp Constants in Uniformity Testing via the Huber Statistic [16.384142529375435]
  Uniformity testing is one of the most well-studied problems in property testing. It is known that the optimal sample complexity to distinguish the uniform distribution on $m$ elements from any $epsilon$-far distribution with $1-delta probability is $n. We show that the collisions tester achieves a sharp maximal constant in the number of standard deviations of separation between uniform and non-uniform inputs.
  arXiv  Detail & Related papers  (2022-06-21T20:43:53Z)
• Nonparametric extensions of randomized response for private confidence sets [51.75485869914048]
  This work derives methods for performing nonparametric, nonasymptotic statistical inference for population means under the constraint of local differential privacy (LDP) We present confidence intervals (CI) and time-uniform confidence sequences (CS) for $mustar$ when only given access to the privatized data.
  arXiv  Detail & Related papers  (2022-02-17T16:04:49Z)
• A Kernel Test for Causal Association via Noise Contrastive Backdoor Adjustment [18.791409397894835]
  We develop a non-parametric method to test the textitdo-null hypothesis $H_0:; p(y|textit do(X=x))=p(y)$ against the general alternative. We demonstrate that backdoor-HSIC (bd-HSIC) is calibrated and has power for both binary and continuous treatments under a large number of confounders.
  arXiv  Detail & Related papers  (2021-11-25T19:12:37Z)
• Optimal Testing of Discrete Distributions with High Probability [49.19942805582874]
  We study the problem of testing discrete distributions with a focus on the high probability regime. We provide the first algorithms for closeness and independence testing that are sample-optimal, within constant factors.
  arXiv  Detail & Related papers  (2020-09-14T16:09:17Z)
• Locally Private Hypothesis Selection [96.06118559817057]
  We output a distribution from $mathcalQ$ whose total variation distance to $p$ is comparable to the best such distribution. We show that the constraint of local differential privacy incurs an exponential increase in cost. Our algorithms result in exponential improvements on the round complexity of previous methods.
  arXiv  Detail & Related papers  (2020-02-21T18:30:48Z)
• Optimal rates for independence testing via $U$-statistic permutation tests [7.090165638014331]
  We study the problem of independence testing given independent and identically distributed pairs taking values in a $sigma$-finite, separable measure space. We first show that there is no valid test of independence that is uniformly consistent against alternatives of the form $f: D(f) geq rho2 $.
  arXiv  Detail & Related papers  (2020-01-15T19:04:23Z)

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.