用自适应混合流提升变分推断的鲁棒性
Adaptive Heterogeneous Mixtures of Normalising Flows for Robust Variational Inference
- 组合MAF、RealNVP、RBIG三种流，分两阶段训练
- 在六类后验分布上负对数似然更低，运输距离更优
- 无需样本门控，适合各类复杂后验结构
归一化流变分推断（VI）能逼近复杂后验，但单一流模型在不同分布上表现不一致。我们提出自适应混合流变分推断（AMF-VI），采用互补流（MAF、RealNVP、RBIG）的异质混合，分两阶段训练：(i) 逐个训练各专家流，(ii) 通过似然驱动更新全局权重，无需每样本门控或结构改动。在香蕉形、X形、双月形、环形、双峰和五模态混合共六类典型后验分布上，AMF-VI始终优于单一流基线，负对数似然更低，且在Wasserstein-2和最大均值差异（MDD）上保持稳定提升，表明其在形状与模态上的鲁棒性增强。该方法高效且架构无关，相比标准流训练仅增加极少开销，证明异质流的自适应混合是跨多种后验族实现可靠变分推断的有效路径，同时保留各专家的归纳偏置。
原文摘要 · Abstract (English)
Normalising-flow variational inference (VI) can approximate complex posteriors, yet single-flow models often behave inconsistently across qualitatively different distributions. We propose Adaptive Mixture Flow Variational Inference (AMF-VI), a heterogeneous mixture of complementary flows (MAF, RealNVP, RBIG) trained in two stages: (i) sequential expert training of individual flows, and (ii) adaptive global weight estimation via likelihood-driven updates, without per-sample gating or architectural changes. Evaluated on six canonical posterior families of banana, X-shape, two-moons, rings, a bimodal, and a five-mode mixture, AMF-VI achieves consistently lower negative log-likelihood than each single-flow baseline and delivers stable gains in transport metrics (Wasserstein-2) and maximum mean discrepancy (MDD), indicating improved robustness across shapes and modalities. The procedure is efficient and architecture-agnostic, incurring minimal overhead relative to standard flow training, and demonstrates that adaptive mixtures of diverse flows provide a reliable route to robust VI across diverse posterior families whilst preserving each expert's inductive bias.
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