New algorithm finds k-centers from noisy distance estimates.
problem Finding k-centers in unknown metric spaces with noisy distance queries.
method Active algorithms using UCB, Thompson Sampling, and Track-and-Stop.
result Approximation ratio of two with high probability.
In data summarization we want to choose k prototypes in order to summarize a data set. We study a setting where the data set comprises several demographic groups and we are restricted to choose ki prototypes belonging to group i. A common approach to the problem without the fairness constraint is to optimize a c…
Replicable clustering algorithms for k-medians, k-means, and k-centers are proposed.
problem Designing clustering algorithms that produce the same partition on repeated runs under the same distribution.
method Utilizing approximation routines for combinatorial clustering problems in a black-box manner.
result Replicable algorithms for statistical k-medians, k-means, and k-centers with specified approximation and sample complexities. New algorithms for fair data summarization in massive data models.
problem Fair k-center problem in massive data. method Streaming and distributed algorithms with provable guarantees.
result First distributed algorithm with constant approximation ratio.
New clustering method ensures fairness and community preservation.
problem Fairness in clustering, especially for data points representing people.
method Developed an approach to extend k-center algorithms to satisfy pairwise fairness and community preservation. result Reasonable approximations of optimal clustering can be achieved while maintaining fairness.
Paper tackles noisy comparison oracle for robust clustering algorithms.
problem Finding robust clustering algorithms under noisy comparison oracle.
method Develops algorithms for k-center clustering and agglomerative hierarchical clustering using noisy comparison oracle.
result Proves robust algorithms achieve good approximation guarantees with high probability.
Unsupervised deep learning is one of the most powerful representation learning techniques. Restricted Boltzman machine, sparse coding, regularized auto-encoders, and convolutional neural networks are pioneering building blocks of deep learning. In this paper, we propose a new building block -- distributed random models…
Develops a fair clustering algorithm for datasets with outliers.
problem Fair clustering with outliers in datasets.
method Solves a linear program to identify and exclude outliers, then applies a rounding algorithm to find fair centers.
result Guaranteed approximation of fair radius and clustering cost.
DAMI uses interpretable regions to select informative samples for deep learning models.
problem Efficiently identifying informative samples for deep learning models with minimal annotation cost.
method Inspired by piece-wise linear interpretability in DNN, DAMI selects samples on different linearly separable regions.
result DAMI outperforms state-of-the-art approaches in tabular data.
A new algorithm finds optimal centers for sets in metric spaces.
problem Finding optimal centers for sets in metric spaces.
method Proved existence and computed an O(log2n)-size core-set for sets-k-means problem. result First PTAS for sets-k-means problem with near-linear time complexity. We extend the fair machine learning literature by considering the problem of proportional centroid clustering in a metric context. For clustering n points with k centers, we define fairness as proportionality to mean that any n/k points are entitled to form their own cluster if there is another center that is clo…
Fair clustering under the disparate impact doctrine requires that population of each protected group should be approximately equal in every cluster. Previous work investigated a difficult-to-scale pre-processing step for k-center and k-median style algorithms for the special case of this problem when the number of …
Suppose k centers are fit to m points by heuristically minimizing the k-means cost; what is the corresponding fit over the source distribution? This question is resolved here for distributions with p≥4 bounded moments; in particular, the difference between the sample cost and distribution cost decays with $…
We study the question of fair clustering under the {\em disparate impact} doctrine, where each protected class must have approximately equal representation in every cluster. We formulate the fair clustering problem under both the k-center and the k-median objectives, and show that even with two protected classes th…
The paper tackles fair correlation clustering with new algorithms and analysis.
problem Fair variants of correlation clustering under various constraints.
method Introducing a novel combinatorial optimization problem for fairlet decomposition.
result Approximation algorithms for fair correlation clustering under multiple fairness constraints.
Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately, kernel means are faced with scalability issues. A single point evaluation of the …
The study provides theoretical foundations for using smaller instances to predict algorithm performance on larger ones.
problem Scalability challenge in evaluating algorithms on large instances.
method Formalized size generalization, providing theoretical guarantees for predicting algorithm performance on large instances using smaller, representative instances.
result Characterized the subsample size sufficient to ensure performance on the subsample reflects performance on the full instance.
Improved approximation for socially fair clustering with ℓp-objective.
problem Finding a set of centers minimizing the maximum distance to all points in each group.
method Introduced a strengthened LP relaxation with an integrality gap of Θ(loglogℓlogℓ). result Improved approximation algorithm with (eO(p)loglogℓlogℓ)-approximation. A new framework improves fairness in clustering and Wasserstein Barycenter problems.
problem Fair clustering in datasets with multiple groups.
method Relax and Merge framework for (1+4ρ+O(ε))-approximate solutions. result Improved approximation guarantees for fairness constraints.
This paper introduces individual fairness in clustering using f-divergence.
problem Ensuring fair clustering by treating similar individuals similarly.
method Uses f-divergence to measure statistical similarity and assigns individuals to probability distributions over cluster centers. result Provides an algorithm with provable approximation guarantee for clustering with individual fairness constraints.
This paper finds the noise threshold for learning Gaussian mixture models equals channel capacity.
problem Learning Gaussian mixture models with noisy data.
method Bayesian formulation with uniformly distributed centers on a sphere, analyzing the large system limit.
result The maximal noise level σ2 for which GMM learning is as easy as labeled observations is the channel capacity. New method clusters non-spherical Gaussian mixtures with fewer samples and time.
problem Clustering non-spherical Gaussian mixtures with arbitrary component covariances.
method Sum-of-Squares method for finding low-dimensional projections.
result Improved clustering algorithms with fewer samples and time complexity.