面向离散数据的高效且可泛化的原型分析

中文摘要 AI 辅助

原型分析（AA）将观测值表示为基于数据的极值轮廓的凸组合，从而为复杂数据集提供可解释的低维描述。经典AA依赖最小二乘目标函数，该函数不适用于二元、计数、分类等离散观测数据。我们引入了一种高效的基于似然的AA框架，支持伯努利、泊松和多项观测模型。我们的优化方案采用负对数似然的局部二次近似，通过序列最小优化（SMO）和有效集方法实现约束更新。通过在保持单纯形可行性的同时限制有效集，提升了可扩展性。我们还引入了交叉验证预测似然准则，用于选择原型数量，为基于重构误差的启发式方法和基于稳定性的诊断提供了原则性替代方案。合成实验证明了该框架的计算效率和对模型复杂度的准确恢复能力。将其应用于单细胞RNA测序、微生物组组成和体细胞突变数据，结果表明，学习到的原型能够捕获可解释的特定领域结构，同时实现具有竞争力的似然拟合和稳定的解。总体而言，所提出的框架支持对离散数据进行高效的基于似然的原型分析，并辅以基于预测似然的模型选择。

英文摘要

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.

发表机构

• Technical University of Denmark（丹麦技术大学）

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