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The proliferation of large data sets and Bayesian inference techniques motivates demand for better data sparsification. Coresets provide a principled way of summarizing a large dataset via a smaller one that is guaranteed to match the…

Uniform sampling is a highly efficient method for data summarization. However, its effectiveness in producing coresets for clustering problems is not yet well understood, primarily because it generally does not yield a strong coreset, which…

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…

With the dramatic growth in the number of application domains that generate probabilistic, noisy and uncertain data, there has been an increasing interest in designing algorithms for geometric or combinatorial optimization problems over…

Efficient and scalable non-parametric or semi-parametric regression analysis and density estimation are of crucial importance to the fields of statistics and machine learning. However, available methods are limited in their ability to…

Coreset selection, which aims to select a subset of the most informative training samples, is a long-standing learning problem that can benefit many downstream tasks such as data-efficient learning, continual learning, neural architecture…

In real world, our datasets often contain outliers. Moreover, the outliers can seriously affect the final machine learning result. Most existing algorithms for handling outliers take high time complexities (e.g. quadratic or cubic…

The present paper constructs coresets for weight-constrained anisotropic assignment and clustering. In contrast to the well-studied unconstrained least-squares clustering problem, approximating the centroids of the clusters no longer…

In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…

Model compression is crucial for deployment of neural networks on devices with limited computational and memory resources. Many different methods show comparable accuracy of the compressed model and similar compression rates. However, the…

Geometric data summarization has become an essential tool in both geometric approximation algorithms and where geometry intersects with big data problems. In linear or near-linear time large data sets can be compressed into a summary, and…

A Bayesian pseudocoreset is a compact synthetic dataset summarizing essential information of a large-scale dataset and thus can be used as a proxy dataset for scalable Bayesian inference. Typically, a Bayesian pseudocoreset is constructed…

Quantum computing is anticipated to offer immense computational capabilities which could provide efficient solutions to many data science problems. However, the current generation of quantum devices are small and noisy, which makes it…

Measuring similarity between two objects is the core operation in existing clustering algorithms in grouping similar objects into clusters. This paper introduces a new similarity measure called point-set kernel which computes the similarity…

Bayesian coresets approximate a posterior distribution by building a small weighted subset of the data points. Any inference procedure that is too computationally expensive to be run on the full posterior can instead be run inexpensively on…

The fuzzy $K$-means problem is a popular generalization of the well-known $K$-means problem to soft clusterings. We present the first coresets for fuzzy $K$-means with size linear in the dimension, polynomial in the number of clusters, and…

The success of deep learning hinges on enormous data and large models, which require labor-intensive annotations and heavy computation costs. Subset selection is a fundamental problem that can play a key role in identifying smaller portions…

Data distillation and coresets have emerged as popular approaches to generate a smaller representative set of samples for downstream learning tasks to handle large-scale datasets. At the same time, machine learning is being increasingly…

We obtain the first strong coresets for the $k$-median and subspace approximation problems with sum of distances objective function, on $n$ points in $d$ dimensions, with a number of weighted points that is independent of both $n$ and $d$;…

A $k$-decision tree $t$ (or $k$-tree) is a recursive partition of a matrix (2D-signal) into $k\geq 1$ block matrices (axis-parallel rectangles, leaves) where each rectangle is assigned a real label. Its regression or classification loss to…