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We propose the weighted averaging method for smoothly bounding user contribution in differential privacy

Smoothly Bounding User Contributions in Differential Privacy

NIPS 2020, (2020)

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Abstract

A differentially private algorithm guarantees that the input of a single user won’t significantly change the output distribution of the algorithm. When a user contributes more data points, more information can be collected to improve the algorithm’s performance. But at the same time, more noise might need to be added to the algorithm in o...More

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Introduction
  • The notion of Differential Privacy, introduced by [DMNS06], aims to capture the requirement that the output of an algorithm should not reveal much about the information provided by a single user.
  • In many applications of differential privacy, a single user might contribute more than one data point.
  • While the standard definition of differential privacy can still capture such settings by defining a row as the collection of all data points belonging to the same user, an important and useful nuance is lost in this translation.
  • Most importantly, when a user contributes many data points, the algorithm designer must balance between the value of the information contained in these data points, and the added noise it will have to add to the output to make it private with respect to this user
Highlights
  • The notion of Differential Privacy, introduced by [DMNS06], aims to capture the requirement that the output of an algorithm should not reveal much about the information provided by a single user
  • While the standard definition of differential privacy can still capture such settings by defining a row as the collection of all data points belonging to the same user, an important and useful nuance is lost in this translation
  • We propose the weighted averaging method for smoothly bounding user contribution in differential privacy
  • Privacy is a fundamental concern in machine learning
  • Respecting the privacy of the users is a requirement of any real system and differential privacy allows to formalize such requirement
  • In this paper we provided algorithms with improved trade-offs of utility vs differential privacy
Methods
  • The authors perform an empirical evaluation of the algorithm and the authors compare it with the sample limiting algorithm for linear regression in the label-privacy case.
  • In Appendix E, the authors provide experimental results on logistic regression using the ERM algorithm of Setion 4.
  • Datasets The authors evaluated all methods on two publicly-available datasets containing real-world data as well as synthetic datasets with ground-truth generated with standard open-source libraries.
  • Synthetic data: The authors generated regression problem instances with sklearn’s make_regression (n ∈ [600, 3000] samples, d = 10 features, bias=0.0 and noise=20).
  • To model user contributions the authors used the Zipf’s distribution for the number of rows of a user.
Results
  • Results on the synthetic dataset

    The authors com-

    bers of samples n and different parameter α of the Zipf’s distribution.
  • Results on the synthetic dataset.
  • Bers of samples n and different parameter α of the Zipf’s distribution.
  • Lower α values correspond to more uneven distributions.
  • The results for α = 1.5, ε = 1, are plot in Figures 1.
  • Dataset ε The authors' method Sample limit h∗ Sample limit hmax 95.4 drugs 2 4862670.7 news 2.
  • The authors fix ε = 1 and n = 3000 samples and analyze the effect of the parameter α in Figure 2.
  • The authors' method is comparatively much better for low α, but it performs always better
Conclusion
  • The authors propose the weighted averaging method for smoothly bounding user contribution in differential privacy
  • The authors apply this method to estimating the mean and quantiles, empirical risk minimization, and linear regression.
  • Privacy requirements may negatively affect utility, and it is known that differential privacy potentially disparately impacts certain users [BPS19].
  • Such considerations are beyond the scope of the paper and the authors refer to the emerging literature on responsible machine learning for addressing them [KR19]
Tables
  • Table1: Average squared errors for our method, sample limit with best threshold (h∗), and using all data (hmax)
Download tables as Excel
Related work
  • Differential privacy is proposed by the seminal work of [DMNS06]. For a detailed survey on differential privacy, see [DR14].

    Differentially private linear regression and its general form, empirical risk minimization have been well-studied [CM08, CMS11, KST12, JKT12, TS13, SCS13, DJW13, JT14, BST14, Ull15, TTZ15, STU17, WLK+17, WYX17, ZZMW17, Wan18, She19a, She19b, INS+19, BFTT19, WX19, FKT20]. In particular, [WX19] studies label privacy which is similar to the setting we have in Section 5. These results are in the case when each user has only one data point.

    Motivated by federated learning, [AKMV19] initiates the study of bounding user contributions in differential privacy. [TAM19, PSY+19] study how to adaptively bound user contributions in differentially private stochastic gradient descent for federated learning. For a detailed survey on federated learning, see [KMA+19]. More broadly, our setting of each user having multiple data points can be considered as a special case of personalized/heterogeneous differential privacy [JYC15, SCS15, AGK17] and is very related to group privacy which is introduced in [Dwo06].
Study subjects and analysis
users with min 1 and max 63 samples: 502
To model user contributions we used the Zipf’s (power law) distribution for the number of rows of a user (users contributions are often heavy tailed [AH02]). Real-world datasets: We used also two UCI Machine Learning Datasets. drugs [GKMZ18] (n = 3107, d = 8, m = 502 users with min 1 and max 63 samples) and news [MT18] (n = 3452, d = 10, m = 297 users with min 1 and max 878 samples).

users with min 1 and max 63 samples: 502
To model user contributions we used the Zipf’s (power law) distribution for the number of rows of a user (users contributions are often heavy tailed [AH02]). Real-world datasets: We used also two UCI Machine Learning Datasets. drugs [GKMZ18] (n = 3107, d = 8, m = 502 users with min 1 and max 63 samples) and news [MT18] (n = 3452, d = 10, m = 297 users with min 1 and max 878 samples). Experimental set up Experiments are re-

samples: 3000
squared error, even orders of magnitude lower (notice the y-axis is in log scale). We now fix ε = 1 and n = 3000 samples and analyze the effect of the parameter α in Figure 2. Recall that α controls the inequality in the distribution of the user’s contributions

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