11 accepted papers
Motivated by applications to classification problems on metric data, we study Weighted Metric Clustering problem: given a metric d over n points and a k x k symmetric matrix A with non-negative entries, the goal is to find a k-partition of these points into clusters C1,...,Ck, while minimizing the s…
We study the embedding dimension of distance comparison data in two settings: contrastive learning and $k$-nearest neighbors ($k$-NN). In both cases, the goal is to find the smallest dimension $d$ of an $\ell_p$-space in which a given dataset can be represented. We show that the arboricity of the as…
Contrastive learning is a highly successful technique for learning representations of data from labeled tuples, specifying the distance relations within the tuple. We study the sample complexity of contrastive learning, i.e. the minimum number of labeled tuples sufficient for getting high generaliza…
We give polynomial time algorithms for escaping from high-dimensional saddle points under a moderate number of constraints. Given gradient access to a smooth function, we show that (noisy) gradient descent methods can escape from saddle points under a logarithmic number of inequality constraints. Wh…
We study the problem of learning a hierarchical tree representation of data from labeled samples, taken from an arbitrary (and possibly adversarial) distribution. Consider a collection of data tuples labeled according to their hierarchical structure. The smallest number of such tuples required in or…
Stochastic gradient descent (SGD) is a prevalent optimization technique for large-scale distributed machine learning. While SGD computation can be efficiently divided between multiple machines, communication typically becomes a bottleneck in the distributed setting. Gradient compression methods can…
We initiate a comprehensive experimental study of objective-based hierarchical clustering methods on massive datasets consisting of deep embedding vectors from computer vision and NLP applications. This includes a large variety of image embedding (ImageNet, ImageNetV2, NaBirds), word embedding (Twit…
Hierarchical Clustering is an unsupervised data analysis method which has been widely used for decades. Despite its popularity, it had an underdeveloped analytical foundation and to address this, Dasgupta recently introduced an optimization viewpoint of hierarchical clustering with…
The problem of selecting a small-size representative summary of a large dataset is a cornerstone of machine learning, optimization and data science. Motivated by applications to recommendation systems and other scenarios with query-limited access to vast amounts of data, we propose a new rigorous al…
Recent works on Hierarchical Clustering (HC), a well-studied problem in exploratory data analysis, have focused on optimizing various objective functions for this problem under arbitrary similarity measures. In this paper we take the first step and give novel scalable algorithms for this problem tai…
We present first massively parallel (MPC) algorithms and hardness of approximation results for computing Single-Linkage Clustering of n input d-dimensional vectors under Hamming, $\ell_1, \ell_2$ and $\ell_\infty$ distances. All our algorithms run in O(log n) rounds of MPC for any fixed d and achiev…