论文标题
了解功能空间的变异推断
Understanding Variational Inference in Function-Space
论文作者
论文摘要
最近的工作试图直接近似贝叶斯模型的“功能空间”或预测后验分布，而没有近似于参数的后验分布。这在例如贝叶斯神经网络，我们只需要前者，而后者很难代表。在这项工作中，我们重点介绍了在这种情况下采用Kullback-Leibler差异的一些优势和局限性。例如，我们表明，将一类参数分布与（非分级）高斯过程诱导的后验之间的KL差异最小化导致了不确定的目标函数。然后，我们提出（特征）贝叶斯线性回归作为直接测量近似质量的“功能空间”推理方法的基准。我们将这种方法应用于评估Sun，Zhang，Shi和Grosse（2018）中考虑的目标函数和推理方案的各个方面，强调了贝叶斯推论的近似值而不是预测性能。
Recent work has attempted to directly approximate the `function-space' or predictive posterior distribution of Bayesian models, without approximating the posterior distribution over the parameters. This is appealing in e.g. Bayesian neural networks, where we only need the former, and the latter is hard to represent. In this work, we highlight some advantages and limitations of employing the Kullback-Leibler divergence in this setting. For example, we show that minimizing the KL divergence between a wide class of parametric distributions and the posterior induced by a (non-degenerate) Gaussian process prior leads to an ill-defined objective function. Then, we propose (featurized) Bayesian linear regression as a benchmark for `function-space' inference methods that directly measures approximation quality. We apply this methodology to assess aspects of the objective function and inference scheme considered in Sun, Zhang, Shi, and Grosse (2018), emphasizing the quality of approximation to Bayesian inference as opposed to predictive performance.
