Debarghya Ghoshdastidar

arXiv2026

Explainable Clustering of Mixture Models

The explainable clustering problem was first posed by Moshkovitz et al. (ICML 2020) and studies how well an axis-aligned decision tree with $K$ leaves can approximate a given clustering. The performance of the tree is measured via the \textit{price of explainability}, defined as the ratio between the clustering cost of the tree (where every leaf is a cluster) and the optimal cost. Several recent works have given worst-case characterizations of the price of explainability for different cost functions. However, these guarantees are data-agnostic and therefore notoriously pessimistic in practical clustering settings. In this paper, we study explainable clustering from the point of view of mixture models, which allows us to give the first data-dependent bounds on the price of explainability. First, we focus on $K$-medians clustering of mixture models with subexponential tails. We propose an algorithm that leverages information about the distribution of the data to find better cuts, and prove new upper and lower bounds. Second, we extend our algorithm and the theoretical guarantees it provides to kernel clustering, thereby refining the existing worst-case analysis.

cs.LG↗

arXiv2026

An Analysis of Self-supervised Pre-training with Dependent Samples

Self-supervised learning relies on so-called data augmentations $ϕ(x)$ of unlabeled datapoints $x$ --- for example, masking random pixels in an image $x$ --- that should leave the label of $x$ invariant and are often used to learn a lower-complexity invariant subspace $\cal V$ for downstream tasks. In practice, such augmentations $\{ ϕ_l(x_i) \}$ are pooled together to learn $\cal V$, despite obvious inter-dependencies between different augmentations $ϕ_l(x), ϕ_k(x)$ of the same datapoint $x$. However, theoretical works on the subject typically consider procedures that avoid such dependencies, and are therefore limited to operate on smaller subsets of independent data. We show in this work that pooling augmentations together, despite inter-dependencies, is a better alternative than the baseline of partitioning the data into subsets of independent data. More precisely, in the context of estimating $\cal V$, the statistical estimation error bounds for pooling are never worse than the partitioning baseline, and in some cases --- such as masking or noise injection-based augmentations over a shallow neural network --- naive pooling leads to faster rates in terms of the number of augmentations. The benefits of pooling are particularly prominent when the correlations between different augmentations $ϕ_l(x), ϕ_k(x)$ have mild effects on estimation or help decrease the estimation variance. The analysis, therefore, yields new insights into the success of pooling augmented samples in self-supervised pre-training, and provides an intuition behind the practical preference towards using many augmentations.

stat.ML↗