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1 code implementation • 16 Jun 2023 • Joel Daniel Andersson, Rasmus Pagh

We address the efficiency problem by presenting a simple alternative to the binary mechanism in which 1) generating the noise takes constant average time per value, 2) the variance is reduced by a factor about 4 compared to the binary mechanism, and 3) the noise distribution at each step is identical.

no code implementations • 14 Jun 2023 • Martin Aumüller, Christian Janos Lebeda, Boel Nelson, Rasmus Pagh

Under a concentration assumption on $\mathcal{D}$, we show how to exploit skew in the vector $\boldsymbol{\sigma}$, obtaining a (zero-concentrated) differentially private mean estimate with $\ell_2$ error proportional to $\|\boldsymbol{\sigma}\|_1$.

no code implementations • 30 May 2022 • Ioana O. Bercea, Jakob Bæk Tejs Houen, Rasmus Pagh

We refer to our parameterization of the weighted Bloom filter as a $\textit{Daisy Bloom filter}$.

1 code implementation • 13 Oct 2021 • Rasmus Pagh, Nina Mesing Stausholm

Federated learning, in which training data is distributed among users and never shared, has emerged as a popular approach to privacy-preserving machine learning.

1 code implementation • 6 Jul 2021 • Matti Karppa, Martin Aumüller, Rasmus Pagh

We present an algorithm called Density Estimation from Approximate Nearest Neighbors (DEANN) where we apply Approximate Nearest Neighbor (ANN) algorithms as a black box subroutine to compute an unbiased KDE.

no code implementations • 3 Feb 2021 • Kasper Green Larsen, Rasmus Pagh, Jakub Tětek

For $t > 1$, the estimator takes the median of $2t-1$ independent estimates, and the probability that the estimate is off by more than $2 \|v\|_2/\sqrt{s}$ is exponentially small in $t$.

1 code implementation • 26 Jan 2021 • Martin Aumüller, Sariel Har-Peled, Sepideh Mahabadi, Rasmus Pagh, Francesco Silvestri

Given a set of points $S$ and a radius parameter $r>0$, the $r$-near neighbor ($r$-NN) problem asks for a data structure that, given any query point $q$, returns a point $p$ within distance at most $r$ from $q$.

no code implementations • NeurIPS 2020 • Edith Cohen, Rasmus Pagh, David P. Woodruff

We design novel composable sketches for WOR $\ell_p$ sampling, weighted sampling of keys according to a power $p\in[0, 2]$ of their frequency (or for signed data, sum of updates).

8 code implementations • 10 Dec 2019 • Peter Kairouz, H. Brendan McMahan, Brendan Avent, Aurélien Bellet, Mehdi Bennis, Arjun Nitin Bhagoji, Kallista Bonawitz, Zachary Charles, Graham Cormode, Rachel Cummings, Rafael G. L. D'Oliveira, Hubert Eichner, Salim El Rouayheb, David Evans, Josh Gardner, Zachary Garrett, Adrià Gascón, Badih Ghazi, Phillip B. Gibbons, Marco Gruteser, Zaid Harchaoui, Chaoyang He, Lie He, Zhouyuan Huo, Ben Hutchinson, Justin Hsu, Martin Jaggi, Tara Javidi, Gauri Joshi, Mikhail Khodak, Jakub Konečný, Aleksandra Korolova, Farinaz Koushanfar, Sanmi Koyejo, Tancrède Lepoint, Yang Liu, Prateek Mittal, Mehryar Mohri, Richard Nock, Ayfer Özgür, Rasmus Pagh, Mariana Raykova, Hang Qi, Daniel Ramage, Ramesh Raskar, Dawn Song, Weikang Song, Sebastian U. Stich, Ziteng Sun, Ananda Theertha Suresh, Florian Tramèr, Praneeth Vepakomma, Jianyu Wang, Li Xiong, Zheng Xu, Qiang Yang, Felix X. Yu, Han Yu, Sen Zhao

FL embodies the principles of focused data collection and minimization, and can mitigate many of the systemic privacy risks and costs resulting from traditional, centralized machine learning and data science approaches.

no code implementations • 24 Sep 2019 • Badih Ghazi, Pasin Manurangsi, Rasmus Pagh, Ameya Velingker

Using a reduction of Balle et al. (2019), our improved analysis of the protocol of Ishai et al. yields, in the same model, an $\left(\varepsilon, \delta\right)$-differentially private protocol for aggregation that, for any constant $\varepsilon > 0$ and any $\delta = \frac{1}{\mathrm{poly}(n)}$, incurs only a constant error and requires only a constant number of messages per party.

Cryptography and Security Data Structures and Algorithms

no code implementations • 24 Sep 2019 • Rasmus Pagh, Johan Sivertsen

Motivated by the problem of filtering candidate pairs in inner product similarity joins we study the following inner product estimation problem: Given parameters $d\in {\bf N}$, $\alpha>\beta\geq 0$ and unit vectors $x, y\in {\bf R}^{d}$ consider the task of distinguishing between the cases $\langle x, y\rangle\leq\beta$ and $\langle x, y\rangle\geq \alpha$ where $\langle x, y\rangle = \sum_{i=1}^d x_i y_i$ is the inner product of vectors $x$ and $y$.

1 code implementation • 3 Sep 2019 • Thomas D. Ahle, Michael Kapralov, Jakob B. T. Knudsen, Rasmus Pagh, Ameya Velingker, David Woodruff, Amir Zandieh

Oblivious sketching has emerged as a powerful approach to speeding up numerical linear algebra over the past decade, but our understanding of oblivious sketching solutions for kernel matrices has remained quite limited, suffering from the aforementioned exponential dependence on input parameters.

Data Structures and Algorithms

no code implementations • 29 Aug 2019 • Badih Ghazi, Noah Golowich, Ravi Kumar, Rasmus Pagh, Ameya Velingker

- Protocols in the multi-message shuffled model with $poly(\log{B}, \log{n})$ bits of communication per user and $poly\log{B}$ error, which provide an exponential improvement on the error compared to what is possible with single-message algorithms.

2 code implementations • 28 Jun 2019 • Martin Aumüller, Tobias Christiani, Rasmus Pagh, Michael Vesterli

We describe a novel synthetic data set that is difficult to solve for almost all existing nearest neighbor search approaches, and for which PUFFINN significantly outperform previous methods.

Data Structures and Algorithms Computational Geometry

no code implementations • 19 Jun 2019 • Badih Ghazi, Rasmus Pagh, Ameya Velingker

Federated learning promises to make machine learning feasible on distributed, private datasets by implementing gradient descent using secure aggregation methods.

1 code implementation • 5 Jun 2019 • Martin Aumüller, Rasmus Pagh, Francesco Silvestri

There are several variants of the similarity search problem, and one of the most relevant is the $r$-near neighbor ($r$-NN) problem: given a radius $r>0$ and a set of points $S$, construct a data structure that, for any given query point $q$, returns a point $p$ within distance at most $r$ from $q$.

no code implementations • 18 Feb 2018 • Yasuo Tabei, Yoshihiro Yamanishi, Rasmus Pagh

We present novel space-efficient feature maps (SFMs) of RFFs for a space reduction from O(dD) of the original FMs to O(d) of SFMs with a theoretical guarantee with respect to concentration bounds.

no code implementations • 9 Oct 2015 • Thomas D. Ahle, Rasmus Pagh, Ilya Razenshteyn, Francesco Silvestri

* New upper and lower bounds for (A)LSH-based algorithms.

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