86 lines
3.5 KiB
Markdown
86 lines
3.5 KiB
Markdown
---
|
||
title: "CuBAS: Information Geometric Curvature-Based Adaptive Sampling for Supervised Classification"
|
||
created: 2026-07-10
|
||
updated: 2026-07-10
|
||
type: paper
|
||
tags: ["adaptive-sampling", "information-geometry", "supervised-classification", "fisher-information", "potts-mrf"]
|
||
arxiv: "2607.03145"
|
||
authors: ["Alexandre L. M. Levada"]
|
||
venue: "arXiv preprint"
|
||
year: 2026
|
||
sources: ["https://arxiv.org/abs/2607.03145"]
|
||
---
|
||
|
||
# CuBAS: Curvature-Based Adaptive Sampling (2026)
|
||
|
||
**CuBAS**（Curvature-Based Adaptive Sampling）是一个**信息几何驱动的自适应数据选择框架**，将监督分类中的训练集筛选转化为[[statistical-manifold|统计流形]]的局部曲率分析问题。
|
||
|
||
## 核心问题
|
||
|
||
> 如何在带标签数据集中识别**最具信息量**的样本？
|
||
|
||
传统方法依赖随机采样或基于分类器不确定性的试探，CuBAS 则从**数据分布的内在几何**出发——将带标签 k-NN 图视为由 [[potts-markov-random-field|Potts MRF]] 诱导的统计流形，曲率直接编码信息密度。
|
||
|
||
## 方法论架构
|
||
|
||
```
|
||
Labeled Dataset D
|
||
│
|
||
▼
|
||
k-NN Graph G ──→ Potts MRF (β by MPL)
|
||
│
|
||
▼
|
||
Node-wise Curvature Scores S_i(β) = -Ψ_i/(Φ_i+λ)
|
||
│ ↑
|
||
│ Φ_i: 1st-order Fisher (metric)
|
||
│ Ψ_i: 2nd-order Fisher (curvature)
|
||
▼
|
||
Adaptive Threshold ──→ L (low-curvature) + H (high-curvature)
|
||
│
|
||
▼
|
||
Curvature-Aware Subsampling → Compact & Informative Training Set
|
||
```
|
||
|
||
## 关键贡献
|
||
|
||
1. **统计流形曲率作为信息量度量**：通过 [[observed-fisher-information|一阶/二阶观测 Fisher 信息]] 比值定义每个节点的标量曲率
|
||
2. **CuBAS 算法**：模型无关、仅需图拓扑 + Potts 充分统计量，无需预训练分类器
|
||
3. **自适应阈值级联**：[[adaptive-threshold-estimation|Otsu → Ashman's D → Tukey-fence]]，每数据集自动调优
|
||
4. **大规模验证**：60+ 数据集（表格/图像/基因组），15 种训练比例 × 100 次重复，全胜 Random 和 Entropy
|
||
|
||
## 关键结果
|
||
|
||
| 场景 | CuBAS | Entropy | Random |
|
||
|------|-------|---------|--------|
|
||
| 全部 60+ 数据集均值 | **0.8455** | 0.7623 | 0.7273 |
|
||
| 10% 训练预算（42 数据集） | **0.8691** | 0.7345 | — |
|
||
| breast_cancer | **0.9996** | 0.9752 | 0.9469 |
|
||
| wine-quality-red | **0.5214** | 0.2731 | 0.2703 |
|
||
|
||
Wilcoxon 检验 p < 10⁻¹⁰，证实 CuBAS 优势系统性而非偶然。
|
||
|
||
## 数据效率特性
|
||
|
||
CuBAS 在小训练比例下即可达到 Random 采样在大训练比例下的精度——这一**数据效率**特性在医学影像、基因组分析等标注成本高的领域有直接应用价值。
|
||
|
||
## 限制
|
||
|
||
- 超小样本高维场景（n ≪ p）：k-NN 图稀疏，曲率信号噪声大
|
||
- 文本稀疏 bag-of-words 特征：k-NN 图几何结构弱
|
||
- 当前仅被动采样，未扩展至主动学习
|
||
|
||
## 相关概念
|
||
|
||
- [[curvature-based-adaptive-sampling|CuBAS]]
|
||
- [[potts-markov-random-field|Potts MRF]]
|
||
- [[shape-operator|Shape Operator]]
|
||
- [[maximum-pseudo-likelihood|MPL Estimation]]
|
||
- [[observed-fisher-information|Observed Fisher Information]]
|
||
- [[adaptive-threshold-estimation|Adaptive Threshold]]
|
||
- [[low-curvature-high-curvature-decomposition|L/H Decomposition]]
|
||
- [[statistical-manifold|Statistical Manifold]]
|
||
- [[information-geometry|Information Geometry]]
|
||
- [[fisher-information-metric|Fisher Information Metric]]
|
||
|
||
来源: [原始存档](raw/papers/Levada-CuBAS-curvature-adaptive-sampling-2026.md) | [arXiv](https://arxiv.org/abs/2607.03145) | [Code](https://github.com/alexandrelevada/CuBAS)
|