用于可扩展贝叶斯矩条件推断的子采样伪后验
Subsampled Pseudo-posteriors for Scalable Bayesian Moment-condition Inference
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中文总结 AI 辅助
针对矩条件下贝叶斯伪推断的两大障碍，本文提出子采样伪后验方法，通过小批量伪后验聚合结合矩函数控制变量，近似全数据伪后验并降低计算成本。
中文摘要 AI 辅助
基于矩条件的贝叶斯伪后验，例如贝叶斯经验似然（EL）和贝叶斯指数倾斜经验似然（ETEL），当模型仅通过矩约束指定时，为贝叶斯推断提供了一种鲁棒的途径，但它们的计算通常代价高昂。在这项工作中，我们解决了矩约束下贝叶斯伪推断的两个障碍：第一，对于海量数据，可扩展采样具有挑战性，因为伪似然无法在观测间对数可加，因此标准的似然子采样方法不适用；第二，在基于模拟和潜变量的问题中，矩函数本身可能通过难以处理的期望定义，使得全数据伪后验推断不可行。我们开发了一种新的子采样伪后验族，用小批量伪后验的聚合替代全数据伪后验。我们发现，朴素的小批量处理会引发移位混合失真，产生的聚合虽中心正确但过于分散。为消除这种失真，我们引入矩函数层面的控制变量，使小批量矩方程围绕参考估计量对齐，恢复全数据后验形状。对于贝叶斯ETEL，我们建立了与全数据伪后验的有限样本总变差界，允许不连续且难以处理的矩函数。数值实验表明，该方法广泛适用于基于矩条件的贝叶斯伪推断，能紧密近似全数据伪后验，且大幅降低计算成本。
英文摘要
Bayesian pseudo-posteriors based on moment conditions, such as Bayesian empirical likelihood (EL) and Bayesian exponentially tilted empirical likelihood (ETEL), provide a robust route to Bayesian inference when the model is specified only through moment restrictions, but their computation is often prohibitive. In this work, we address two barriers to Bayesian pseudo-inference under moment restrictions. First, scalable sampling is challenging for tall data because the pseudo-likelihoods are not log-additive across observations, so standard likelihood-subsampling methods do not apply. Second, in simulation-based and latent-variable problems, the moment function itself may be defined through an intractable expectation, making full-data pseudo-posterior inference infeasible. We develop a new family of subsampled pseudo-posteriors that replaces the full-data pseudo-posterior with an aggregate of mini-batch pseudo-posteriors. We show that naive mini-batching induces a shifted-mixture distortion, yielding aggregates that are correctly centered but overly diffuse. To remove this distortion, we introduce moment-function-level control variates that align mini-batch moment equations around a reference estimator and recover the full-data posterior shape. For Bayesian ETEL, we establish finite-sample total variation bounds to the full-data pseudo-posterior, allowing discontinuous and intractable moment functions. Numerical experiments show that the method applies broadly across moment-condition-based Bayesian pseudo-inference, closely approximates full-data pseudo-posteriors, and substantially reduces computational cost.
发表机构
- Hong Kong University of Science and Technology（香港科技大学）
机构由 AI 辅助整理，请以论文原文为准。
