$k$-Variance: A Clustered Notion of Variance

2020-12-13 · Justin Solomon, Kristjan Greenewald, Haikady N. Nagaraja

We introduce $k$-variance, a generalization of variance built on the machinery of random bipartite matchings. $K$-variance measures the expected cost of matching two sets of $k$ samples from a distribution to each other, capturing local rather than global information about a measure as $k$ increases; it is easily approximated stochastically using sampling and linear programming. In addition to defining $k$-variance and proving its basic properties, we provide in-depth analysis of this quantity in several key cases, including one-dimensional measures, clustered measures, and measures concentrated on low-dimensional subsets of $\mathbb R^n$. We conclude with experiments and open problems motivated by this new way to summarize distributional shape.

📄 PDF Abstract BibTeX arXiv:2012.06958

Code (0)

등록된 구현이 없습니다.

Design-Based Multi-Way Clustering

2023-09-04 · Luther Yap

This paper extends the design-based framework to settings with multi-way cluster dependence, and shows how multi-way clustering can be justified when clustered assignment and clustered sampling occurs on different dimens…

Clustering valid

Joint Estimation of Clustered User Activity and Correlated Channels with Unknown Covariance in mMTC

2022-11-30 · Hamza Djelouat, Markus Leinonen, Markku Juntti

This paper considers joint user identification and channel estimation (JUICE) in grant-free access with a \emph{clustered} user activity pattern. In particular, we address the JUICE in massive machine-type communications…

Action Detection Activity Detection User Identification

Gradient Boosted Mixed Models: Flexible Estimation of Mean and Variance Components for Clustered Data

2025-10-31 · Mitchell L. Prevett, Francis K. C. Hui, Zhi Yang Tho, A. H. Welsh 외 arxiv

We introduce Gradient Boosted Mixed Models (GBMixed), a framework which extends boosting to clustered data by jointly modeling the mean and variance components in a linear mixed model via likelihood-based gradients. GBMi…

Less is More: Clustered Cross-Covariance Control for Offline RL

2026-01-28 · Nan Qiao, Sheng Yue, Shuning Wang, Yongheng Deng 외 arxiv

A fundamental challenge in offline reinforcement learning is distributional shift. Scarce data or datasets dominated by out-of-distribution (OOD) areas exacerbate this issue. Our theoretical analysis and experiments show…

Reinforcement Learning Offline RL

Clustered Sampling: Low-Variance and Improved Representativity for Clients Selection in Federated Learning

2021-05-12 · Yann Fraboni, Richard Vidal, Laetitia Kameni, Marco Lorenzi

This work addresses the problem of optimizing communications between server and clients in federated learning (FL). Current sampling approaches in FL are either biased, or non optimal in terms of server-clients communica…

Clustering Federated Learning Model Compression