用几何映射实现多分类高斯过程的精确校准与高效推理
Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process Classification
- 将类别概率映射到欧氏空间，简化多分类为低维回归
- 无需近似分布，预测概率准确且与真实标签匹配度高
- 兼容稀疏高斯过程，适合大规模数据集，适合追求精度的从业者
我们提出一种共轭且可校准的高斯过程模型用于多分类任务，利用概率单纯形的几何结构。通过Aitchison几何将单纯形上的类别概率映射至无约束的欧氏空间，将分类问题转化为低维高斯过程回归，其隐变量维度少于传统多分类高斯过程方法。该方法实现共轭推断，无需在模型构建中依赖分布近似，从而获得可靠的预测概率。模型兼容标准稀疏高斯过程技术，支持大规模数据集的高效推理。实验结果表明，在合成与真实数据集上均表现出良好校准性和竞争力。
原文摘要 · Abstract (English)
We propose a conjugate and calibrated Gaussian process (GP) model for multi-class classification by exploiting the geometry of the probability simplex. Our approach uses Aitchison geometry to map simplex-valued class probabilities to an unconstrained Euclidean representation, turning classification into a GP regression problem with fewer latent dimensions than standard multi-class GP classifiers. This yields conjugate inference and reliable predictive probabilities without relying on distributional approximations in the model construction. The method is compatible with standard sparse GP regression techniques, enabling scalable inference on larger datasets. Empirical results show well-calibrated and competitive performance across synthetic and real-world datasets.
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