Differentially private multivariate medians

• URL: http://arxiv.org/abs/2210.06459v2
• Date: Tue, 26 Mar 2024 16:49:11 GMT
• Title: Differentially private multivariate medians
• Authors: Kelly Ramsay, Aukosh Jagannath, Shoja'eddin Chenouri,
• Abstract summary: We develop novel finite-sample performance guarantees for differentially private depth-based medians. We show that under Cauchy marginals, the cost of heavy-tailed location estimation outweighs the cost of privacy.
• Score: 4.588028371034407
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Statistical tools which satisfy rigorous privacy guarantees are necessary for modern data analysis. It is well-known that robustness against contamination is linked to differential privacy. Despite this fact, using multivariate medians for differentially private and robust multivariate location estimation has not been systematically studied. We develop novel finite-sample performance guarantees for differentially private multivariate depth-based medians, which are essentially sharp. Our results cover commonly used depth functions, such as the halfspace (or Tukey) depth, spatial depth, and the integrated dual depth. We show that under Cauchy marginals, the cost of heavy-tailed location estimation outweighs the cost of privacy. We demonstrate our results numerically using a Gaussian contamination model in dimensions up to d = 100, and compare them to a state-of-the-art private mean estimation algorithm. As a by-product of our investigation, we prove concentration inequalities for the output of the exponential mechanism about the maximizer of the population objective function. This bound applies to objective functions that satisfy a mild regularity condition.

Related papers

• Differentially private projection-depth-based medians [0.0]
  We develop $(epsilon,delta)$-differentially private projection-depth-based medians using the propose-test-release (PTR) and exponential mechanisms. We quantify the probability the test in PTR fails, as well as the cost of privacy via finite sample deviation bounds.
  arXiv  Detail & Related papers  (2023-12-12T23:17:29Z)
• Bounded and Unbiased Composite Differential Privacy [25.427802467876248]
  The objective of differential privacy (DP) is to protect privacy by producing an output distribution that is indistinguishable between two neighboring databases. Existing solutions attempt to address this issue by employing post-processing or truncation techniques. We propose a novel differentially private mechanism which uses a composite probability density function to generate bounded and unbiased outputs.
  arXiv  Detail & Related papers  (2023-11-04T04:43:47Z)
• Initialization Matters: Privacy-Utility Analysis of Overparameterized Neural Networks [72.51255282371805]
  We prove a privacy bound for the KL divergence between model distributions on worst-case neighboring datasets. We find that this KL privacy bound is largely determined by the expected squared gradient norm relative to model parameters during training.
  arXiv  Detail & Related papers  (2023-10-31T16:13:22Z)
• On the Privacy-Robustness-Utility Trilemma in Distributed Learning [7.778461949427662]
  We present the first tight analysis of the error incurred by any algorithm ensuring robustness against a fraction of adversarial machines. Our analysis exhibits a fundamental trade-off between privacy, robustness, and utility.
  arXiv  Detail & Related papers  (2023-02-09T17:24:18Z)
• General Gaussian Noise Mechanisms and Their Optimality for Unbiased Mean Estimation [58.03500081540042]
  A classical approach to private mean estimation is to compute the true mean and add unbiased, but possibly correlated, Gaussian noise to it. We show that for every input dataset, an unbiased mean estimator satisfying concentrated differential privacy introduces approximately at least as much error.
  arXiv  Detail & Related papers  (2023-01-31T18:47:42Z)
• Optimal Algorithms for Mean Estimation under Local Differential Privacy [55.32262879188817]
  We show that PrivUnit achieves the optimal variance among a large family of locally private randomizers. We also develop a new variant of PrivUnit based on the Gaussian distribution which is more amenable to mathematical analysis and enjoys the same optimality guarantees.
  arXiv  Detail & Related papers  (2022-05-05T06:43:46Z)
• Featurized Density Ratio Estimation [82.40706152910292]
  In our work, we propose to leverage an invertible generative model to map the two distributions into a common feature space prior to estimation. This featurization brings the densities closer together in latent space, sidestepping pathological scenarios where the learned density ratios in input space can be arbitrarily inaccurate. At the same time, the invertibility of our feature map guarantees that the ratios computed in feature space are equivalent to those in input space.
  arXiv  Detail & Related papers  (2021-07-05T18:30:26Z)
• Robust and Differentially Private Mean Estimation [40.323756738056616]
  Differential privacy has emerged as a standard requirement in a variety of applications ranging from the U.S. Census to data collected in commercial devices. An increasing number of such databases consist of data from multiple sources, not all of which can be trusted. This leaves existing private analyses vulnerable to attacks by an adversary who injects corrupted data.
  arXiv  Detail & Related papers  (2021-02-18T05:02:49Z)
• Graph-Homomorphic Perturbations for Private Decentralized Learning [64.26238893241322]
  Local exchange of estimates allows inference of data based on private data. perturbations chosen independently at every agent, resulting in a significant performance loss. We propose an alternative scheme, which constructs perturbations according to a particular nullspace condition, allowing them to be invisible.
  arXiv  Detail & Related papers  (2020-10-23T10:35:35Z)
• A One-Pass Private Sketch for Most Machine Learning Tasks [48.17461258268463]
  Differential privacy (DP) is a compelling privacy definition that explains the privacy-utility tradeoff via formal, provable guarantees. We propose a private sketch that supports a multitude of machine learning tasks including regression, classification, density estimation, and more. Our sketch consists of randomized contingency tables that are indexed with locality-sensitive hashing and constructed with an efficient one-pass algorithm.
  arXiv  Detail & Related papers  (2020-06-16T17:47:48Z)
• Designing Differentially Private Estimators in High Dimensions [0.0]
  We study differentially private mean estimation in a high-dimensional setting. Recent work in high-dimensional robust statistics has identified computationally tractable mean estimation algorithms.
  arXiv  Detail & Related papers  (2020-06-02T21:17:30Z)

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.