EMS Coreset: An Efficient Expectation-Maximization Algorithm for Sinkhorn Coreset

Coresets distill large datasets into small, representative subsets for efficient downstream learning. Yet Optimal Transport (OT)-based selection typically requires intensive computation of transport plans, limiting scalability. We introduce a scalable Sinkhorn coreset method that permits closed-form updates of the entropically regularized OT coupling by allowing non-uniform coreset weights. This produces centroids that generalize k-means via soft assignments. We establish asymptotic consistency of the selected measure and Lipschitz stability to data perturbations, providing accuracy and robustness guarantees. Across synthetic and real-world benchmarks, the proposed method achieves competitive or improved approximation quality while substantially reducing runtime compared to Wasserstein- and standard Sinkhorn-based coreset selection, especially at large scale.

Terminal Dimension Reduction for Time Series with Applications

Terminal embeddings have emerged as a powerful tool for dimension reduction. Given a set of points $P\subset \mathbb{R}^d$, a terminal embedding is a mapping $f:\mathbb{R}^d\rightarrow \mathbb{R}^t$ that preserves the pairwise distance between any pair of points $p\in P$ and $q\in \mathbb{R}^d$ up to small distortion under this mapping. Terminal embeddings have been particularly fruitful for constructing $k$-means and $k$-median coresets, where the objective is to find a typically weighted subset $Ω$ of $P$ such that for any candidate solution, the cost of the clustering objective on $Ω$ approximates the cost of the clustering objective on $P$ up to small distortion. Unfortunately, these techniques have not been extended to more complicated structures such as clustering time-series data under common straight-line interpolation between measurements. The main issue is that terminal embeddings, arguably the central technique in this line of research, cannot be linear and are thus not immediately suitable to preserve linear structures. In this work, we develop a generalization of terminal embeddings to affine line-segments that overcomes this issue. We showcase their applicability by using our lines-preserving terminal embeddings to obtain the first dimension-free coresets for clustering time-series under the Fréchet distance. The underlying dimension reduction uses Johnson-Lindenstrauss (JL) embeddings, and our experiments indicate that terminal embeddings perform similarly to JL and favorably against PCA for synthetic and real-world time-series, while only terminal embeddings extend pairwise distance preservation to the full ambient space.

Sensitivity Sampling with Predictions for k-Means Clustering

We study the problem of k-means clustering on large datasets. The state-of-the-art for the problem is given by coresets-based approaches, which build small weighted summaries of the input and derive approximate solutions with rigorous quality guarantees from them. One of the most popular and advanced approaches to derive coresets for k-means is sensitivity sampling. However, sensitivity sampling requires to compute the importance of each input point with respect to the whole dataset over all possible choices of centers. Since the exact computation of such quantities is unfeasible, current approaches work by approximating the sensitivity values. Nevertheless, the runtime of such approaches is still impractical for large datasets. In this work, we propose to reduce the runtime of sensitivity-based approaches for k-means by leveraging predictions to approximate the importance of input points. We first formally prove that current theoretical results on coresets construction via sensitivity sampling hold for coarser approximations of sensitivities compared to the one required by existing approaches. This implies that even fairly noisy predictors can be leveraged for sensitivity-sampling approaches. We then propose a natural predictor, which applies to the common scenario where clustering is performed (over time) on a sequence of datasets from the same problem. We prove that when the datasets in the sequence come from the same (unknown) distribution, centers resulting in a low error on one dataset can be used as predictions for sensitivity sampling in subsequent datasets, with guarantees on their quality. We perform an extensive experimental evaluation showing that our approach significantly improves, in terms of clustering cost vs runtime, over uniform sampling and state-of-the-art sensitivity sampling approaches when applied to sequences of datasets.

Provable Pruning for Efficient 3D Gaussian Splatting via Coresets

3D Gaussian Splatting (3DGS) enables high-quality real-time novel-view synthesis, but practical scenes often contain millions of Gaussians, making compression essential for deployment on limited hardware. Existing reduction methods are effective but mostly heuristic: they provide no multiplicative approximation guarantee for the rendered objective, and thus rely heavily on costly post-pruning finetuning to recover quality. We ask a basic question: can a 3DGS scene be provably replaced by a much smaller weighted subset (coreset) while preserving the objective of interest? We first show that, in the unrestricted setting, no non-trivial multiplicative 3DGS coreset exists. We then show that multiplicative guarantees are not impossible, but resolution-dependent. For a prescribed rendering resolution, such as representative views or grids of views/rays, we provide the first weighted coreset construction theorem for 3DGS. The construction samples Gaussians by sensitivity: provable importance scores measuring each Gaussian's role in the full-scene objective. Finally, under explicit validity and log-transmittance stability assumptions, we turn this objective guarantee into a rendering guarantee. Empirically, our method is strongest where deployment needs it most: aggressive compression with no or minimal recovery compute. In prune-only and very short finetuning regimes, it achieves state-of-the-art performance, showing that principled importance estimation can be both theoretically meaningful and practically useful. Open-source code is available at https://github.com/waseem-m/3dgs_provable_coresets.

Group-invariant Coresets for Data-efficient Active Learning

Active learning reduces labeling cost by querying the most informative unlabeled samples, but standard coreset methods ignore known data symmetries and can waste budget on transformed versions of the same instance. We propose GRINCO, a group-invariant coreset framework that performs acquisition in the quotient space induced by a transformation group, so that selection operates on orbits rather than raw samples. The method uses either canonical representatives or learned orbit-separating invariant embeddings to define practical quotient metrics, and combines quotient-space k-center selection with invariant training through an orbit-averaged loss. We further derive a generalization bound that relates excess orbit-averaged risk to quotient-space coverage, label uncertainty, and intra-orbit variability. Experiments on synthetic scale-invariant data and image benchmarks with rotation-induced redundancy show that GRINCO improves orbit coverage and achieves stronger label efficiency than conventional coreset baselines, especially when group-induced redundancy is substantial.

Active Learning with Low-Rank Structure for Data Selection

In the data selection problem, the objective is to choose a small, representative subset of data that can be used to efficiently train a machine learning model. Sener and Savarese [ICLR 2018] showed that, given an embedding representation of the data and suitable geometric assumptions, heuristics based on $k$-center clustering can be used to perform data selection. This perspective was further explored by Axiotis et. al. [ICML 2024], who proposed a data selection approach based on $k$-means clustering and sensitivity sampling. However, these methods rely on the assumption that the dataset exhibits intrinsic geometric structure that can be effectively captured by clustering, whereas many modern datasets instead possess global algebraic structure that is better exploited by low-rank approximation or principal component analysis. In this paper, we introduce a new data selection framework based on low-rank approximation and residual-based sampling, formulated through the lens of row subset selection and loss-preserving coreset construction. Given an embedding representation of the data satisfying mild regularity conditions, which can be interpreted as algebraic or angular notions of Lipschitz continuity, we show that it is possible to select a weighted subset of $\tilde{O}\left(k + \frac{1}{\varepsilon^2}\right)$ data points whose average loss approximates the average loss over the full dataset within a $(1+\varepsilon)$ relative error, up to an additive $\varepsilon Φ_k$ term, where $Φ_k$ denotes the optimal rank-$k$ approximation cost of the embedding matrix. We complement these theoretical guarantees with empirical evaluations, demonstrating that on a range of real-world datasets, our data selection approach achieves improved performance over prior strategies based on uniform sampling or clustering-based sensitivity sampling.