Maedeh Zarvandi

Maximilian Fleissner, Maedeh Zarvandi, Debarghya Ghoshdastidar

We study the explainable clustering problem first posed by Moshkovitz, Dasgupta, Rashtchian, and Frost (ICML 2020). The goal of explainable clustering is to fit an axis-aligned decision tree with $K$ leaves and minimal clustering cost (where every leaf is a cluster). The fundamental theoretical question in this line of work is the \textit{price of explainability}, defined as the ratio between the clustering cost of the tree and the optimal cost. Numerous papers have provided worst-case guarantees on this quantity. For $K$-medians, it has recently been shown that the worst-case price of explainability is $Θ(\log K)$. While this settles the matter from a data-agnostic point of view, two important questions remain unanswered: Are tighter guarantees possible for well-clustered data? And can we trust decision trees to recover underlying cluster structures? In this paper, we place ourselves in a statistical setting of mixture models to answer both questions. We prove that better guarantees are indeed feasible for well-clustered data. Our algorithm takes as input a mixture model and constructs a tree in data-independent time. We then extend our analysis to kernel clustering, deriving new guarantees that significantly improve over existing worst-case bounds.

Maedeh Zarvandi, Michael Timothy, Theresa Wasserer et al.

Kernel methods provide a theoretically grounded framework for non-linear and non-parametric learning, with strong analytic foundations and statistical guarantees. Yet, their scalability has long been limited by prohibitive time and memory costs. While progress has been made in scaling kernel regression, no framework exists for scalable kernel-based representation learning, restricting their use in the era of foundation models where representations are learned from massive unlabeled data. We introduce KREPES -- a unified, scalable framework for kernel-based representation learning via Nyström approximation. KREPES accommodates a wide range of unsupervised and self-supervised losses, and experiments on large image and tabular datasets demonstrate its efficiency. Crucially, KREPES enables principled interpretability of the learned representations, an immediate benefit over deep models, which we substantiate through dedicated analysis.