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The Power of Localization for Efficiently Learning Linear Separators with Noise

This work provides the first polynomial-time active learning algorithm for learning linear separators in the presence of malicious noise or adversarial label noise, and achieves a label complexity whose dependence on the error parameter ϵ is polylogarithmic (and thus exponentially better than that of any passive algorithm).
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Center-based clustering under perturbation stability

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Relax, No Need to Round: Integrality of Clustering Formulations

We study exact recovery conditions for convex relaxations of point cloud clustering problems, focusing on two of the most common optimization problems for unsupervised clustering: k-means and…
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Guarantees for Spectral Clustering with Fairness Constraints

This work develops variants of both normalized and unnormalized constrained SC and shows that they help find fairer clusterings on both synthetic and real data and proves that their algorithms can recover this fair clustering with high probability.
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The Hardness of Approximation of Euclidean k-Means

The first hardness of approximation for the Euclidean $k-means problem is provided via an efficient reduction from the vertex cover problem on triangle-free graphs: given a triangle- free graph, the goal is to choose the fewest number of vertices which are incident on all the edges.
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Efficient Learning of Linear Separators under Bounded Noise

This work provides the first evidence that one can indeed design algorithms achieving arbitrarily small excess error in polynomial time under this realistic noise model and thus opens up a new and exciting line of research.
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Fair k-Center Clustering for Data Summarization

This paper provides a simple approximation algorithm for the $k$-center problem under the fairness constraint with running time linear in the size of the data set and $k$.
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Improved Spectral-Norm Bounds for Clustering

Aiming to unify known results about clustering mixtures of distributions under separation conditions, Kumar and Kannan [1] introduced a deterministic condition for clustering datasets. They showed…
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Stability Yields a PTAS for k-Median and k-Means Clustering

Improvements are made to the distance of the clustering found to the target from $O(\delta)$ to $\delta$ when all target clusters are large, and for $k-median the authors improve the ``largeness'' condition needed in the work of Balcan et al. to get exactly $delta-close from O(delta n) to $\Delta n$.
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Decision trees for entity identification: approximation algorithms and hardness results

A natural greedy algorithm is considered and an approximation guarantee of O(rK • log N) is proved, where N is the number of entities and K is the maximum number of distinct values of an attribute, which shows that it is NP-hard to approximate the problem within a factor of Ω(log N).
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