We introduce a novel framework for uncertainty quantification in clustering. By combining the martingale posterior paradigm with density-based clustering, uncertainty in the estimated density is naturally propagated to the clustering structure. The approach scales effectively to high-dimensional and irregularly shaped data by leveraging modern neural density estimators and GPU-friendly parallel computation. We establish frequen-tist consistency guarantees and validate the methodology on synthetic and real data.

We study the fundamental problem of clustering $n$ points into $K$ groups drawn from a mixture of isotropic Gaussians in $\mathbb{R}^d$. Specifically, we investigate the requisite minimal distance $Δ$ between mean vectors to partially recover the underlying partition. While the minimax-optimal threshold for $Δ$ is well-established, a significant gap exists between this information-theoretic limit and the performance of known polynomial-time procedures. Although this gap was recently characterized in the high-dimensional regime ($n \leq dK$), it remains largely unexplored in the moderate-dimensional regime ($n \geq dK$). In this manuscript, we address this regime by establishing a new low-degree polynomial lower bound for the moderate-dimensional case when $d \geq K$. We show that while the difficulty of clustering for $n \leq dK$ is primarily driven by dimension reduction and spectral methods, the moderate-dimensional regime involves more delicate phenomena leading to a "non-parametric rate". We provide a novel non-spectral algorithm matching this rate, shedding new light on the computational limits of the clustering problem in moderate dimension.

We introduce a framework to transfer knowledge acquired from a repository of (heterogeneous) supervised datasets to new unsupervised datasets. Our perspective avoids the subjectivity inherent in unsupervised learning by reducing it to supervised learning, and provides a principled way to evaluate unsupervised algorithms. We demonstrate the versatility of our framework via rigorous agnostic bounds on a variety of unsupervised problems. In the context of clustering, our approach helps choose the number of clusters and the clustering algorithm, remove the outliers, and provably circumvent Kleinberg's impossibility result. Experiments across hundreds of problems demonstrate improvements in performance on unsupervised data with simple algorithms despite the fact our problems come from heterogeneous domains. Additionally, our framework lets us leverage deep networks to learn common features across many small datasets, and perform zero shot learning.

Neural Information Processing Systems http://nips.cc/

Large language models (LLMs) are increasingly used as agents to solve complex tasks such as question answering (QA), scientific debate, and software development. A standard evaluation procedure aggregates multiple responses from LLM agents into a single final answer, often via majority voting, and compares it against reference answers. However, this process can obscure the quality and distributional characteristics of the original responses. In this paper, we propose a novel evaluation framework based on the empirical cumulative distribution function (ECDF) of cosine similarities between generated responses and reference answers. This enables a more nuanced assessment of response quality beyond exact match metrics. To analyze the response distributions across different agent configurations, we further introduce a clustering method for ECDFs using their distances and the $k$-medoids algorithm. Our experiments on a QA dataset demonstrate that ECDFs can distinguish between agent settings with similar final accuracies but different quality distributions. The clustering analysis also reveals interpretable group structures in the responses, offering insights into the impact of temperature, persona, and question topics.

Ingraph based co-clustering methods, abipartite graph isconstructed todepict the relation between features and samples.