Multivariate density estimation from privatised data: universal consistency and minimax rates

Györfi, László; Kroll, Martin

doi:10.1080/10485252.2022.2163634

Cited by 2 publications

(3 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For a privacy parameter α ∈ [0, ∞], any non-interactive privacy mechanism is said to be an α-locally differentially private mechanism if the con- , 2018;Berrett and Butucea, 2019;Butucea et al, 2020;Berrett et al, 2021;Györfi and Kroll, 2023). In order to define the privatized data, we first choose a closed Euclidean ball B = {x ∈ R d : x ≤ r} of radius r > 0 centred at the origin.…”

Section: Anonymization Of the Raw Datamentioning

confidence: 99%

See 1 more Smart Citation

On Rate Optimal Private Regression Under Local Differential Privacy

Györfi¹,

Kroll²

2025

STAT SINICA

View full text Add to dashboard Cite

We consider the problem of estimating a regression function from anonymized data in the framework of local differential privacy. We propose a novel partitioning estimate of the regression function, derive a rate of convergence for the excess prediction risk over Hölder classes, and prove a matching lower bound. In contrast to the existing literature on the problem the so-called strong density assumption on the design distribution is obsolete.

show abstract

Section: Anonymization Of the Raw Datamentioning

confidence: 99%

“…(5.19) has turned out to be essential for proving lower bounds in the density estimation problem before (Butucea et al, 2020;Györfi and Kroll, 2023).…”

Section: Proof Of Theorem 3 (Lower Bound)mentioning

confidence: 99%

On Rate Optimal Private Regression Under Local Differential Privacy

Györfi¹,

Kroll²

2025

STAT SINICA

View full text Add to dashboard Cite

show abstract

“…In the literature, different estimation methods have been proposed. We may cite histogram estimators [WZ10,GK21], projection estimators [WZ10,DJW18], Kernel estimators [HRW13,Kro21] and wavelets estimators [BDKS20]. We focus here on density estimation but other topics have been explored in the private setup.…”

Section: Introductionmentioning

confidence: 99%

Density estimation under local differential privacy and Hellinger loss

Sart

2023

Bernoulli

View full text Add to dashboard Cite

In this paper, we carry out a piecewise constant estimator of the density for privatised data. We establish a non-asymptotic oracle inequality for the Hellinger loss and deduce that our estimator is adaptive and (almost) rate optimal over a wide range of Besov classes. In particular, we show that a lower bound condition improves the convergence rates. This is in contrast to what happens with the L 2 loss where the rates can differ depending on whether the density is bounded or not.

show abstract

Multivariate density estimation from privatised data: universal consistency and minimax rates

Cited by 2 publications

References 16 publications

On Rate Optimal Private Regression Under Local Differential Privacy

On Rate Optimal Private Regression Under Local Differential Privacy

Density estimation under local differential privacy and Hellinger loss

Contact Info

Product

Resources

About