Search Results for author:
Found 9 papers, 3 papers with code
Settling Time vs. Accuracy Tradeoffs for Clustering Big Data
We study the theoretical and practical runtime limits of k-means and k-median clustering on large datasets.
Data-Efficient Learning via Clustering-Based Sensitivity Sampling: Foundation Models and Beyond
We study the data selection problem, whose aim is to select a small representative subset of data that can be used to efficiently train a machine learning model.
Differential Privacy for Clustering Under Continual Observation
We consider the problem of clustering privately a dataset in $\mathbb{R}^d$ that undergoes both insertion and deletion of points.
Improved Coresets for Euclidean $k$-Means
the Euclidean $k$-median problem) consists of finding $k$ centers such that the sum of squared distances (resp.
Scalable Differentially Private Clustering via Hierarchically Separated Trees
We study the private $k$-median and $k$-means clustering problem in $d$ dimensional Euclidean space.
Towards Optimal Lower Bounds for k-median and k-means Coresets
Given a set of points in a metric space, the $(k, z)$-clustering problem consists of finding a set of $k$ points called centers, such that the sum of distances raised to the power of $z$ of every data point to its closest center is minimized.
Improved Coresets and Sublinear Algorithms for Power Means in Euclidean Spaces
Special cases of problem include the well-known Fermat-Weber problem -- or geometric median problem -- where $z = 1$, the mean or centroid where $z=2$, and the Minimum Enclosing Ball problem, where $z = \infty$. We consider these problem in the big data regime. Here, we are interested in sampling as few points as possible such that we can accurately estimate $m$. More specifically, we consider sublinear algorithms as well as coresets for these problems. Sublinear algorithms have a random query access to the $A$ and the goal is to minimize the number of queries. Here, we show that $\tilde{O}(\varepsilon^{-z-3})$ samples are sufficient to achieve a $(1+\varepsilon)$ approximation, generalizing the results from Cohen, Lee, Miller, Pachocki, and Sidford [STOC '16] and Inaba, Katoh, and Imai [SoCG '94] to arbitrary $z$.
On the Power of Louvain in the Stochastic Block Model
A classic problem in machine learning and data analysis is to partition the vertices of a network in such a way that vertices in the same set are densely connected and vertices in different sets are loosely connected.
Fully Dynamic Consistent Facility Location
This improves over the naive algorithm which consists in recomputing a solution at each time step and that can take up to $O(n^2)$ update time, and $O(n^2)$ total recourse.
