论文标题
使用Gibbs先验发现归纳偏见：近似贝叶斯推断的诊断工具
Discovering Inductive Bias with Gibbs Priors: A Diagnostic Tool for Approximate Bayesian Inference
论文作者
论文摘要
完整的贝叶斯后期很少在分析上是可拖延的，这就是为什么现实世界中的贝叶斯推论在很大程度上依赖于近似技术的原因。近似值通常与真实的后部有所不同，需要诊断工具来评估是否仍然可以信任推论。我们研究了一种诊断近似推断的新方法：通过将近似值视为精确和反向工程相应的先验，近似不匹配归因于电感偏差的变化。我们表明，问题比乍一看更为复杂，因为解决方案通常取决于观察结果。通过根据不兼容的条件分布来重新构架问题，我们得出了一种自然解决方案：gibbs先验。由此产生的诊断基于伪GIBBS抽样，该采样广泛适用且易于实现。我们说明了如何使用Gibbs先验来发现在受控的高斯环境中以及各种贝叶斯模型和近似值中的电感偏差。
Full Bayesian posteriors are rarely analytically tractable, which is why real-world Bayesian inference heavily relies on approximate techniques. Approximations generally differ from the true posterior and require diagnostic tools to assess whether the inference can still be trusted. We investigate a new approach to diagnosing approximate inference: the approximation mismatch is attributed to a change in the inductive bias by treating the approximations as exact and reverse-engineering the corresponding prior. We show that the problem is more complicated than it appears to be at first glance, because the solution generally depends on the observation. By reframing the problem in terms of incompatible conditional distributions we arrive at a natural solution: the Gibbs prior. The resulting diagnostic is based on pseudo-Gibbs sampling, which is widely applicable and easy to implement. We illustrate how the Gibbs prior can be used to discover the inductive bias in a controlled Gaussian setting and for a variety of Bayesian models and approximations.
