Current approaches in approximate inference for Bayesian neural networks minimise the Kullback-Leibler divergence to approximate the true posterior over the weights. However, this approximation is without knowledge of the final application, and therefore cannot guarantee optimal predictions for a given task. To make more suitable task-specific approximations, we introduce a new loss-calibrated evidence lower bound for Bayesian neural networks in the context of supervised learning, informed by Bayesian decision theory. By introducing a lower bound that depends on a utility function, we ensure that our approximation achieves higher utility than traditional methods for applications that have asymmetric utility functions. Furthermore, in using dropout inference, we highlight that our new objective is identical to that of standard dropout neural networks, with an additional utility-dependent penalty term. We demonstrate our new loss-calibrated model with an illustrative medical example and a restricted model capacity experiment, and highlight failure modes of the comparable weighted cross entropy approach. Lastly, we demonstrate the scalability of our method to real world applications with per-pixel semantic segmentation on an autonomous driving data set.

本文提出了一种基于Bayesian决策理论的新的、具有损失校准的证据下界来近似贝叶斯神经网络的真实后验分布，该下界依赖于一种效用函数，以确保我们的逼近方法对于具有非对称效用函数的应用程序具有更高的效用。此外，该方法具有与标准dropout神经网络相同的目标，但具有额外的依赖于效用函数的惩罚项。

贝叶斯神经网络中基于损失校准的近似推断