用神经网络替代高斯过程采样，提速并保持精度。
DeepRV: Accelerating Spatiotemporal Inference with Pre-trained Neural Priors
- 用神经网络做高斯过程先验的代理模型，实现快速采样。
- 在4994个地点的数据上，推理速度显著提升，精度接近完整高斯过程。
- 可直接替换现有概率编程工具中的高斯过程，适合实际应用者。
高斯过程（GPs）为时空建模提供了灵活且统计严谨的基础，但其计算复杂度为$O(N^3)$，难以处理大规模数据。近似方法如变分推断、诱导点稀疏GP、低秩核近似（如Nystrom方法和随机傅里叶特征）及INLA等虽提升了可扩展性，但通常以牺牲准确性、校准性或建模灵活性为代价。本文提出DeepRV，一种神经网络代理模型，用于替代GP先验采样，在推理阶段（包括超参数估计）仍能保持与全量GP相当的精度，同时将复杂度降至$O(N^2)$，显著提升可扩展性和推理速度。DeepRV可作为现成的替代方案集成于基于MCMC的概率编程流程中，保留完整模型灵活性。在模拟基准测试、非分离时空GP及伦敦教育剥夺真实数据（n=4,994个位置）的应用中，DeepRV在逼近精确GP方面表现最优，且大幅加速推理。代码已开源至dl4bi Python包，所有实验均在单张消费级GPU上完成，确保实践者的可访问性。
原文摘要 · Abstract (English)
Gaussian Processes (GPs) provide a flexible and statistically principled foundation for modelling spatiotemporal phenomena, but their $O(N^3)$ scaling makes them intractable for large datasets. Approximate methods such as variational inference (VI), inducing-point (sparse) GPs, low-rank kernel approximations (e.g., Nystrom methods and random Fourier features), and approximations such as INLA improve scalability but typically trade off accuracy, calibration, or modelling flexibility. We introduce DeepRV, a neural-network surrogate that replaces GP prior sampling, while closely matching full GP accuracy at inference including hyperparameter estimates, and reducing computational complexity to $O(N^2)$, increasing scalability and inference speed. DeepRV serves as a drop-in replacement for GP prior realisations in e.g. MCMC-based probabilistic programming pipelines, preserving full model flexibility. Across simulated benchmarks, non-separable spatiotemporal GPs, and a real-world application to education deprivation in London (n = 4,994 locations), DeepRV achieves the highest fidelity to exact GPs while substantially accelerating inference. Code is provided in the dl4bi Python package, with all experiments run on a single consumer-grade GPU to ensure accessibility for practitioners.
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