用混合高斯过程提升复杂分布预测能力
GGMPs: Generalized Gaussian Mixture Processes
- 基于局部混合高斯拟合与组件对齐，构建可解析的混合密度预测
- 在多模态非高斯数据上显著优于传统GP，保持不确定性校准
- 适合需要精确分布建模的复杂场景，如科学计算与医疗分析
条件密度估计因多模态性、异方差性和强非高斯性而复杂。高斯过程（GPs）提供了一个具有校准不确定性的非参数框架，但标准GP回归受限于单一高斯预测形式。我们提出广义高斯混合过程（GGMP），一种基于GP的多模态条件密度估计方法，适用于每个输入对应复杂输出分布而非单一标量响应的情形。GGMP结合局部高斯混合拟合、跨输入组件对齐和分组件异方差GP训练，生成闭式高斯混合预测密度。该方法可计算、兼容标准GP求解器与可扩展方法，避免了朴素多模态GP中指数级增长的隐变量结构。实验表明，GGMP在具有显著非高斯性和多模态性的合成与真实数据集上均提升了分布近似效果。
原文摘要 · Abstract (English)
Conditional density estimation is complicated by multimodality, heteroscedasticity, and strong non-Gaussianity. Gaussian processes (GPs) provide a principled nonparametric framework with calibrated uncertainty, but standard GP regression is limited by its unimodal Gaussian predictive form. We introduce the Generalized Gaussian Mixture Process (GGMP), a GP-based method for multimodal conditional density estimation in settings where each input may be associated with a complex output distribution rather than a single scalar response. GGMP combines local Gaussian mixture fitting, cross-input component alignment and per-component heteroscedastic GP training to produce a closed-form Gaussian mixture predictive density. The method is tractable, compatible with standard GP solvers and scalable methods, and avoids the exponentially large latent-assignment structure of naive multimodal GP formulations. Empirically, GGMPs improve distributional approximation on synthetic and real-world datasets with pronounced non-Gaussianity and multimodality.
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