arXiv：cs.LG· A. Emilie J. Wedenborg, Jesper L{\o}ve Hinrich, Morten M{\o}rup·· 4 小时前
面向离散数据的高效可泛化原型分析框架
Efficient and Generalizable Archetypal Analysis for Discrete Data
AI 导读
研究者提出一种基于似然的原型分析（AA）框架，支持 Bernoulli、Poisson 和多项式观测模型，通过负对数似然的局部二次近似与序列最小优化（SMO）及活跃集方法实现约束更新。该方法引入交叉验证预测似然准则来选择原型数量，在单细胞 RNA 测序、微生物组组成和体细胞突变数据上捕获了可解释的领域结构，并取得有竞争力的似然拟合与稳定解。
正文
Abstract:Archetypal Analysis (AA) represents observations as convex combinations of extremal data-driven profiles, yielding interpretable low-dimensional descriptions of complex datasets. Classical AA relies on a least-squares objective, which is poorly suited to discrete observations such as binary, count, and categorical data. We introduce an efficient likelihood-based framework for AA supporting Bernoulli, Poisson, and multinomial observation models. Our optimization scheme employs local quadratic approximations of the negative log-likelihood, enabling constrained updates through sequential minimal optimization (SMO) and an active-set method. Scalability is improved by bounding the active set while preserving simplex feasibility. We further introduce a cross-validated predictive likelihood criterion for selecting the number of archetypes, providing a principled alternative to reconstruction-error heuristics and stability-based diagnostics. Synthetic experiments demonstrate computational efficiency and accurate recovery of model complexity. Applications to single-cell RNA sequencing, microbiome composition, and somatic mutation data show that the learned archetypes capture interpretable domain-specific structures while achieving competitive likelihood fits and stable solutions. Overall, the proposed framework enables efficient likelihood-based archetypal analysis of discrete data, complemented by predictive likelihood-based model selection.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.12035 [stat.ML] |
| (or arXiv:2610.12035v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.12035 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Anna Emilie Jennow Wedenborg [view email]
[v1]
Thu, 8 Oct 2026 14:27:02 UTC (7,257 KB)
来源：arXiv：cs.LG · arxiv.org