Related papers: Locally Private k-Means in One Round
The K-means algorithm is arguably the most popular data clustering method, commonly applied to processed datasets in some "feature spaces", as is in spectral clustering. Highly sensitive to initializations, however, K-means encounters a…
The problem of estimating a parameter in the drift coefficient is addressed for $N$ discretely observed independent and identically distributed stochastic differential equations (SDEs). This is done considering additional constraints,…
Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work,…
We consider a setup in which confidential i.i.d. samples $X_1,\dotsc,X_n$ from an unknown finite-support distribution $\boldsymbol{p}$ are passed through $n$ copies of a discrete privatization channel (a.k.a. mechanism) producing outputs…
In this paper, we show that the popular K-means clustering problem can equivalently be reformulated as a conic program of polynomial size. The arising convex optimization problem is NP-hard, but amenable to a tractable semidefinite…
Compressing the output of \epsilon-locally differentially private (LDP) randomizers naively leads to suboptimal utility. In this work, we demonstrate the benefits of using schemes that jointly compress and privatize the data using shared…
Privacy concerns with sensitive data are receiving increasing attention. In this paper, we study local differential privacy (LDP) in interactive decentralized optimization. By constructing random local aggregators, we propose a framework to…
In this work, we study local minimax convergence estimation rates subject to $\epsilon$-differential privacy. Unlike worst-case rates, which may be conservative, algorithms that are locally minimax optimal must adapt to easy instances of…
Local differential privacy is a promising privacy-preserving model for statistical aggregation of user data that prevents user privacy leakage from the data aggregator. This paper focuses on the problem of estimating the distribution of…
$K$-means clustering is a widely used machine learning method for identifying patterns in large datasets. Recently, semidefinite programming (SDP) relaxations have been proposed for solving the $K$-means optimization problem, which enjoy…
We consider the problem of estimating sparse discrete distributions under local differential privacy (LDP) and communication constraints. We characterize the sample complexity for sparse estimation under LDP constraints up to a constant…
Clustering is a basic task in data analysis and machine learning, and the optimization of clustering objectives are well-studied optimization problems; amongst these, the $k$-Means objective is arguably the most well known. Given a…
Over the last three decades, researchers have intensively explored various clustering tools for categorical data analysis. Despite the proposal of various clustering algorithms, the classical k-modes algorithm remains a popular choice for…
The $K$-nearest neighbors is a basic problem in machine learning with numerous applications. In this problem, given a (training) set of $n$ data points with labels and a query point $p$, we want to assign a label to $p$ based on the labels…
We present new algorithms for estimating and testing \emph{collision probability}, a fundamental measure of the spread of a discrete distribution that is widely used in many scientific fields. We describe an algorithm that satisfies…
Conformal prediction (CP) provides sets of candidate classes with a guaranteed probability of containing the true class. However, it typically relies on a calibration set with clean labels. We address privacy-sensitive scenarios where the…
This paper presents a practical global optimization algorithm for the K-center clustering problem, which aims to select K samples as the cluster centers to minimize the maximum within-cluster distance. This algorithm is based on a…
The central question studied in this paper is Renyi Differential Privacy (RDP) guarantees for general discrete local mechanisms in the shuffle privacy model. In the shuffle model, each of the $n$ clients randomizes its response using a…
Clustering is one of the most important tools for analysis of large datasets, and perhaps the most popular clustering algorithm is Lloyd's algorithm for $k$-means. This algorithm takes $n$ vectors $V=[v_1,\dots,v_n]\in\mathbb{R}^{d\times…
In this paper, we address the challenge of differential privacy in the context of graph cuts, specifically focusing on the multiway cut and the minimum $k$-cut. We introduce edge-differentially private algorithms that achieve nearly optimal…