Related papers: A Statistical Perspective on Coreset Density Estim…

Subsampling algorithms are a natural approach to reduce data size before fitting models on massive datasets. In recent years, several works have proposed methods for subsampling rows from a data matrix while maintaining relevant information…

In this paper, we provide a novel perspective on the underlying structure of real-world data with ground-truth clusters via characterization of an abundantly observed yet often overlooked density-geometry correlation, that manifests itself…

The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of…

Reusing existing datasets is of considerable significance to researchers and developers. Dataset search engines help a user find relevant datasets for reuse. They can present a snippet for each retrieved dataset to explain its relevance to…

For two decades, reproducing kernels and their associated discrepancies have facilitated elegant theoretical analyses in the setting of quasi Monte Carlo. These same tools are now receiving interest in statistics and related fields, as…

This study proposes a data condensation method for multivariate kernel density estimation by genetic algorithm. First, our proposed algorithm generates multiple subsamples of a given size with replacement from the original sample. The…

Clustering algorithms are of fundamental importance when dealing with large unstructured datasets and discovering new patterns and correlations therein, with applications ranging from scientific research to medical imaging and marketing…

We study the problem of constructing coresets for $(k, z)$-clustering when the input dataset is corrupted by stochastic noise drawn from a known distribution. In this setting, evaluating the quality of a coreset is inherently challenging,…

Recently, the field of machine learning has undergone a transition from model-centric to data-centric. The advancements in diverse learning tasks have been propelled by the accumulation of more extensive datasets, subsequently facilitating…

Nonparametric kernel density and local polynomial regression estimators are very popular in Statistics, Economics, and many other disciplines. They are routinely employed in applied work, either as part of the main empirical analysis or as…

Kernel density estimation is a technique for approximating probability distributions. Here, it is applied to the calculation of mutual information on a metric space. This is motivated by the problem in neuroscience of calculating the mutual…

We propose a way of transforming the problem of conditional density estimation into a single nonparametric regression task via the introduction of auxiliary samples. This allows leveraging regression methods that work well in high…

Active learning enables the efficient construction of a labeled dataset by labeling informative samples from an unlabeled dataset. In a real-world active learning scenario, considering the diversity of the selected samples is crucial…

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…

In this paper we study the problem of pointwise density estimation from observations with multiplicative measurement errors. We elucidate the main feature of this problem: the influence of the estimation point on the estimation accuracy. In…

Coresets for $k$-means and $k$-median problems yield a small summary of the data, which preserve the clustering cost with respect to any set of $k$ centers. Recently coresets have also been constructed for constrained $k$-means and…

Dataset Condensation is a newly emerging technique aiming at learning a tiny dataset that captures the rich information encoded in the original dataset. As the size of datasets contemporary machine learning models rely on becomes…

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…

Coresets are arguably the most popular compression paradigm for center-based clustering objectives such as $k$-means. Given a point set $P$, a coreset $\Omega$ is a small, weighted summary that preserves the cost of all candidate solutions…

The goal of coreset selection is to identify representative subsets of datasets for efficient model training. Yet, existing approaches paradoxically require expensive training-based signals, e.g., gradients, decision boundary estimates or…