流变换隐式过程用于函数空间变分推断
Flow-Transformed Implicit Processes for Function-Space Variational Inference
AI总结：
提出流变换隐式过程（FTIP），通过归一化流增强组合权重的变分分布，从而在函数空间中捕获非对称、重尾和多模态后验结构，并使用黑盒α目标进行优化。
摘要：
隐式过程先验通过灵活的生成机制定义函数上的分布，使其对贝叶斯函数空间建模具有吸引力。然而，使用此类先验进行后验推断具有挑战性，因为其诱导的函数空间分布通常没有闭式解。一种实用策略是使用有限个采样函数的集合来近似先验，然后将后验函数表示为这些样本的学习组合。现有方法通常对组合权重施加高斯变分分布。虽然易于处理，但这种选择限制了可表示的后验不确定性形状，特别是当真实后验是非对称、重尾或多模态时。我们提出流变换隐式过程（FTIP），一种变分推断方法，使这种有限维函数空间近似更具表达力。FTIP不使用高斯分布，而是使用归一化流来定义更丰富的变分分布，从而在保持可处理优化的同时诱导灵活的后验函数分布。我们使用黑盒α目标训练模型，从而能够比较质量覆盖和模式寻找的变分行为。实验表明，FTIP捕获了函数空间中的非对称和多模态后验结构，而高斯系数近似往往会平滑或崩溃这些结构。
英文摘要：
Implicit-process priors define distributions over functions through flexible generative mechanisms, making them attractive for Bayesian function-space modelling. However, performing posterior inference with such priors is challenging because their induced function-space distributions are typically not available in closed form. One practical strategy is to approximate the prior using a finite collection of sampled functions, and then represent posterior functions as learned combinations of these samples. Existing approaches commonly place a Gaussian variational distribution over the combination weights. While tractable, this choice limits the shapes of posterior uncertainty that can be represented, especially when the true posterior is asymmetric, heavy-tailed, or multimodal. We propose Flow-Transformed Implicit Processes (FTIP), a variational inference method that makes this finite-dimensional function-space approximation more expressive. Instead of using a Gaussian distribution over the combination weights, FTIP uses a normalizing flow to define a richer variational distribution. This induces a flexible posterior distribution over functions while preserving tractable optimization. We train the model using a Black-Box α objective, allowing us to compare mass-covering and mode-seeking variational behaviour. Experiments show that FTIP captures asymmetric and multimodal posterior structure in function space that Gaussian coefficient approximations tend to smooth or collapse.
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