发表机构
Aalborg University（奥尔堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出广义Matheron变分隐式过程（GMVIP），一种路径式变分族，用于隐式先验的后验推断，通过锚定校正保留先验结构，并在回归、分类和预测任务中与现有方法竞争。
AI 中文摘要
隐式过程先验通过样本前向机制（如贝叶斯神经网络和随机模拟器）指定函数上的分布，但其函数空间密度通常不可用。我们引入了广义Matheron变分隐式过程（GMVIP），一种用于此类先验的后验推断的路径式变分族。对于高斯过程先验，GMVIP恢复了标准的诱导变量变分高斯过程构造；对于一般隐式先验，其经验协方差构造在总体极限下保留了先验均值和协方差。GMVIP通过从先验中抽取一个函数并应用以一组诱导输入为锚点的校正来构造后验样本。该校正远离诱导输入的效果直接由先验样本决定，使得后验能够保留原始隐式过程的结构和变异性。（代理）先验和变分后验使用相同的路径式构造，仅在白化诱导系数的分布上有所不同，从而产生可处理的系数空间Kullback-Leibler散度。在回归、分类和预测任务上，使用模拟器定义和检索条件的经验轨迹先验进行的实验表明，GMVIP与现有方法总体上具有竞争力。
英文摘要
Implicit-process priors specify distributions over functions through sample-forward mechanisms such as Bayesian neural networks and stochastic simulators, but their function-space densities are typically unavailable. We introduce Generalized Matheron Variational Implicit Processes (GMVIP), a pathwise variational family for posterior inference with such priors. For Gaussian-process priors, GMVIP recovers the standard inducing-variable variational GP construction; for general implicit priors, its empirical covariance construction preserves the prior mean and covariance in the population limit. GMVIP constructs posterior samples by drawing a function from the prior and applying a correction anchored at a set of inducing inputs. The effect of this correction away from the inducing inputs is determined directly from prior samples, allowing the posterior to retain the structure and variability of the original implicit process. The (surrogate) prior and variational posterior use the same pathwise construction and differ only in the distribution of whitened inducing coefficients, yielding a tractable coefficient-space Kullback-Leibler divergence. Experiments on regression, classification, and forecasting with simulator-defined and retrieval-conditioned empirical trajectory priors show that GMVIP is broadly competitive with existing methods.
Comments36 pages, 10 figures, 19 tables. Submitted for review
