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Found 16 papers, 4 papers with code
A Tight VC-Dimension Analysis of Clustering Coresets with Applications
We consider coresets for $k$-clustering problems, where the goal is to assign points to centers minimizing powers of distances.
On Approximability of $\ell_2^2$ Min-Sum Clustering
In this paper, we give the first hardness-of-approximation result for the $\ell_2^2$ min-sum $k$-clustering problem.
Distributed Differentially Private Data Analytics via Secure Sketching
We explore the use of distributed differentially private computations across multiple servers, balancing the tradeoff between the error introduced by the differentially private mechanism and the computational efficiency of the resulting distributed algorithm.
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.
Optimal Sketching Bounds for Sparse Linear Regression
For this problem, under the $\ell_2$ norm, we observe an upper bound of $O(k \log (d)/\varepsilon + k\log(k/\varepsilon)/\varepsilon^2)$ rows, showing that sparse recovery is strictly easier to sketch than sparse regression.
Sparse Dimensionality Reduction Revisited
In this work, we revisit sparse embeddings and identify a loophole in the lower bound.
Improved Coresets for Euclidean $k$-Means
the Euclidean $k$-median problem) consists of finding $k$ centers such that the sum of squared distances (resp.
An Empirical Evaluation of $k$-Means Coresets
Using this benchmark and real-world data sets, we conduct an exhaustive evaluation of the most commonly used coreset algorithms from theory and practice.
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 $z$.
Algorithms for Fair Team Formation in Online Labour Marketplaces
In this short paper, we define the Fair Team Formation problem in the following way: given an online labour marketplace where each worker possesses one or more skills, and where all workers are divided into two or more not overlapping classes (for examples, men and women), we want to design an algorithm that is able to find a team with all the skills needed to complete a given task, and that has the same number of people from all classes.
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.
Principal Fairness: Removing Bias via Projections
Reducing hidden bias in the data and ensuring fairness in algorithmic data analysis has recently received significant attention.
On Coresets for Logistic Regression
For data sets with bounded $\mu(X)$-complexity, we show that a novel sensitivity sampling scheme produces the first provably sublinear $(1\pm\varepsilon)$-coreset.
On the Local Structure of Stable Clustering Instances
We study the classic $k$-median and $k$-means clustering objectives in the beyond-worst-case scenario.
