Related papers: Locally Private k-Means in One Round
Due to the progressive growth of the amount of data available in a wide variety of scientific fields, it has become more difficult to ma- nipulate and analyze such information. Even though datasets have grown in size, the K-means algorithm…
Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data…
Differential privacy (DP) provides robust privacy guarantees for statistical inference, but this can lead to unreliable results and biases in downstream applications. While several noise-aware approaches have been proposed which integrate…
We develop a theory of asymptotic efficiency in regular parametric models when data confidentiality is ensured by local differential privacy (LDP). Even though efficient parameter estimation is a classical and well-studied problem in…
Differential privacy (DP) techniques can be applied to the federated learning model to statistically guarantee data privacy against inference attacks to communication among the learning agents. While ensuring strong data privacy, however,…
We consider the approximability of center-based clustering problems where the points to be clustered lie in a metric space, and no candidate centers are specified. We call such problems "continuous", to distinguish from "discrete"…
In this paper, we propose an implicit gradient descent algorithm for the classic $k$-means problem. The implicit gradient step or backward Euler is solved via stochastic fixed-point iteration, in which we randomly sample a mini-batch…
Local differential privacy~(LDP) is an information-theoretic privacy definition suitable for statistical surveys that involve an untrusted data curator. An LDP version of quasi-maximum likelihood estimator~(QMLE) has been developed, but the…
Clustering is a hard discrete optimization problem. Nonconvex approaches such as low-rank semidefinite programming (SDP) have recently demonstrated promising statistical and local algorithmic guarantees for cluster recovery. Due to the…
We consider the privacy amplification properties of a sampling scheme in which a user's data is used in k steps chosen randomly and uniformly from a sequence (or set) of t steps. This sampling scheme has been recently applied in the context…
We introduce a notion of \emph{generic local algorithm} which strictly generalizes existing frameworks of local algorithms such as \emph{factors of i.i.d.} by capturing local \emph{quantum} algorithms such as the Quantum Approximate…
Prior work on differential privacy analysis of randomized SGD algorithms relies on composition theorems, where the implicit (unrealistic) assumption is that the internal state of the iterative algorithm is revealed to the adversary. As a…
We show a connection between sampling and optimization on discrete domains. For a family of distributions $\mu$ defined on size $k$ subsets of a ground set of elements that is closed under external fields, we show that rapid mixing of…
We consider the task of producing heatmaps from users' aggregated data while protecting their privacy. We give a differentially private (DP) algorithm for this task and demonstrate its advantages over previous algorithms on real-world…
We propose a new variant of the k-median problem, where the objective function models not only the cost of assigning data points to cluster representatives, but also a penalty term for disagreement among the representatives. We motivate…
Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…
We consider the minimax estimation problem of a discrete distribution with support size $k$ under privacy constraints. A privatization scheme is applied to each raw sample independently, and we need to estimate the distribution of the raw…
We study approximation algorithms for the socially fair $(\ell_p, k)$-clustering problem with $m$ groups, whose special cases include the socially fair $k$-median ($p=1$) and socially fair $k$-means ($p=2$) problems. We present (1) a…
Offline k-means clustering was studied extensively, and algorithms with a constant approximation are available. However, online clustering is still uncharted. New factors come into play: the ordering of the dataset and whether the number of…
Based on binary inquiries, we developed an algorithm to estimate population quantiles under Local Differential Privacy (LDP). By self-normalizing, our algorithm provides asymptotically normal estimation with valid inference, resulting in…