提出一种能控制多样性的统一预测框架，提升不确定性建模能力。
Structured Basis Function Networks: Loss-Centric Multi-Hypothesis Ensembles with Controllable Diversity
- 用Bregman散度诱导中心聚合，统一多假设与集成学习
- 可调多样性机制实现偏差-方差-多样性平衡，提升泛化性能
- 适用于回归与分类，适合深度学习中复杂任务的不确定性分析
现有预测不确定性方法要么依赖多假设预测（促进多样性但缺乏合理聚合），要么依赖集成学习（提高精度但难以捕捉结构化模糊性）。这本质上意味着缺乏与损失几何一致的统一框架。本文提出的结构基函数网络通过Bregman散度诱导的中心聚合，将多假设预测与集成学习相连接。该方法在回归与分类任务中均适用，其预测与损失几何对齐，并支持闭式最小二乘估计和通用目标的梯度优化过程。可调多样性机制实现对偏差-方差-多样性权衡的参数化控制，将多假设泛化与损失感知集成聚合联系起来。实验验证了这一关系，并利用该机制在逐渐困难的数据集上研究深度学习预测器的复杂度-容量-多样性权衡。
原文摘要 · Abstract (English)
Existing approaches to predictive uncertainty rely either on multi-hypothesis prediction, which promotes diversity but lacks principled aggregation, or on ensemble learning, which improves accuracy but rarely captures the structured ambiguity. This implicitly means that a unified framework consistent with the loss geometry remains absent. The Structured Basis Function Network addresses this gap by linking multi-hypothesis prediction and ensembling through centroidal aggregation induced by Bregman divergences. The formulation applies across regression and classification by aligning predictions with the geometry of the loss, and supports both a closed-form least-squares estimator and a gradient-based procedure for general objectives. A tunable diversity mechanism provides parametric control of the bias-variance-diversity trade-off, connecting multi-hypothesis generalisation with loss-aware ensemble aggregation. Experiments validate this relation and use the mechanism to study the complexity-capacity-diversity trade-off across datasets of increasing difficulty with deep-learning predictors.
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