English
Related papers

Related papers: Tukey Depth Mechanisms for Practical Private Mean …

200 papers

Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…

Machine Learning · Statistics 2024-02-02 Bernardo Fichera , Viacheslav Borovitskiy , Andreas Krause , Aude Billard

One major impediment to the wider use of deep learning for clinical decision making is the difficulty of assigning a level of confidence to model predictions. Currently, deep Bayesian neural networks and sparse Gaussian processes are the…

We consider the problem of collaborative personalized mean estimation under a privacy constraint in an environment of several agents continuously receiving data according to arbitrary unknown agent-specific distributions. In particular, we…

Machine Learning · Computer Science 2024-12-02 Yauhen Yakimenka , Chung-Wei Weng , Hsuan-Yin Lin , Eirik Rosnes , Jörg Kliewer

We present a new algorithm for Tukey (halfspace) depth level sets and its implementation. Given $d$-dimensional data set for any $d\geq 2$, the algorithm is based on representation of level sets as intersections of balls in $R^d$, and can…

Computational Geometry · Computer Science 2016-11-16 Milica Bogicevic , Milan Merkle

Differential privacy (DP) is a rigorous notion of data privacy, used for private statistics. The canonical algorithm for differentially private mean estimation is to first clip the samples to a bounded range and then add noise to their…

Statistics Theory · Mathematics 2024-10-10 Gautam Kamath , Argyris Mouzakis , Matthew Regehr , Vikrant Singhal , Thomas Steinke , Jonathan Ullman

We consider the problem of distributedly estimating Gaussian processes in multi-agent frameworks. Each agent collects few measurements and aims to collaboratively reconstruct a common estimate based on all data. Agents are assumed with…

Multiagent Systems · Computer Science 2018-05-11 Gianluigi Pillonetto , Luca Schenato , Damiano Varagnolo

We study the task of differentially private clustering. For several basic clustering problems, including Euclidean DensestBall, 1-Cluster, k-means, and k-median, we give efficient differentially private algorithms that achieve essentially…

Machine Learning · Computer Science 2020-08-19 Badih Ghazi , Ravi Kumar , Pasin Manurangsi

We study distributed estimation of a Gaussian mean under communication constraints in a decision theoretical framework. Minimax rates of convergence, which characterize the tradeoff between the communication costs and statistical accuracy,…

Statistics Theory · Mathematics 2020-02-11 T. Tony Cai , Hongji Wei

We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…

Machine Learning · Statistics 2025-03-11 Gilles Blanchard , Jean-Baptiste Fermanian , Hannah Marienwald

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

Bayesian quantum estimation provides a robust framework for quantum technologies, especially in scenarios with limited data and minimal prior information. Yet, its application to continuous-variable Gaussian systems has remained limited and…

Quantum Physics · Physics 2026-05-19 Edward Gandar , Jesús Rubio

We study the sublinear multivariate mean estimation problem in $d$-dimensional Euclidean space. Specifically, we aim to find the mean $\mu$ of a ground point set $A$, which minimizes the sum of squared Euclidean distances of the points in…

Data Structures and Algorithms · Computer Science 2025-10-07 Beatrice Bertolotti , Matteo Russo , Chris Schwiegelshohn , Sudarshan Shyam

We initiate the study of differentially private (DP) estimation with access to a small amount of public data. For private estimation of d-dimensional Gaussians, we assume that the public data comes from a Gaussian that may have vanishing…

Machine Learning · Computer Science 2023-04-07 Alex Bie , Gautam Kamath , Vikrant Singhal

We introduce general tools for designing efficient private estimation algorithms, in the high-dimensional settings, whose statistical guarantees almost match those of the best known non-private algorithms. To illustrate our techniques, we…

Data Structures and Algorithms · Computer Science 2023-11-17 Hongjie Chen , Vincent Cohen-Addad , Tommaso d'Orsi , Alessandro Epasto , Jacob Imola , David Steurer , Stefan Tiegel

Tukey's $g$-and-$h$ distribution has been a powerful tool for data exploration and modeling since its introduction. However, two long standing challenges associated with this distribution family have remained unsolved until this day: how to…

Methodology · Statistics 2015-06-03 Ganggang Xu , Marc G. Genton

Many privacy mechanisms reveal high-level information about a data distribution through noisy measurements. It is common to use this information to estimate the answers to new queries. In this work, we provide an approach to solve this…

Machine Learning · Computer Science 2019-01-29 Ryan McKenna , Daniel Sheldon , Gerome Miklau

Bayesian optimization is a class of global optimization techniques. In Bayesian optimization, the underlying objective function is modeled as a realization of a Gaussian process. Although the Gaussian process assumption implies a random…

Statistics Theory · Mathematics 2023-05-08 Rui Tuo , Wenjia Wang

In statistical inference, we commonly assume that samples are independent and identically distributed from a probability distribution included in a pre-specified statistical model. However, such an assumption is often violated in practice.…

Machine Learning · Statistics 2024-10-29 Takafumi Kanamori , Kodai Yokoyama , Takayuki Kawashima

Classical multivariate statistics measures the outlyingness of a point by its Mahalanobis distance from the mean, which is based on the mean and the covariance matrix of the data. A multivariate depth function is a function which, given a…

Methodology · Statistics 2021-05-06 Karl Mosler , Pavlo Mozharovskyi

The Sampled Gaussian Mechanism (SGM)---a composition of subsampling and the additive Gaussian noise---has been successfully used in a number of machine learning applications. The mechanism's unexpected power is derived from privacy…

Machine Learning · Computer Science 2019-08-29 Ilya Mironov , Kunal Talwar , Li Zhang