Ensembles of deep neural networks have achieved great success recently, but they do not offer a proper Bayesian justification. Moreover, while they allow for averaging of predictions over several hypotheses, they do not provide any guarantees for their diversity, leading to redundant solutions in function space. In contrast, particle-based inference methods, such as Stein variational gradient descent (SVGD), offer a Bayesian framework, but rely on the choice of a kernel to measure the similarity between ensemble members. In this work, we study different SVGD methods operating in the weight space, function space, and in a hybrid setting. % Defining the kernel directly on the neural network functions seems promising to overcome the limitations of deep ensembles. % However, ensuring diversity in function space while maintaining SVGD's theoretical guarantees is not trivial. % In this work, we provide an overview over different ensembling and SVGD methods in weight space and function space and propose new and assess their theoretical and empirical properties on synthetic and real-world tasks. We compare the SVGD approaches to other ensembling-based methods in terms of their theoretical properties and assess their empirical performance on synthetic and real-world tasks. We find that SVGD using functional and hybrid kernels can overcome the limitations of deep ensembles. It improves on functional diversity and uncertainty estimation and approaches the true Bayesian posterior more closely. Moreover, we show that using stochastic SVGD updates, as opposed to the standard deterministic ones, can further improve the performance.

本研究研究了使用不同的Stein变分梯度下降方法来解决深度神经网络的Bayesian框架的问题，通过改善功能多样性和不确定性估计，逼近真实的Bayesian后验，并展示使用随机SVGD更新可以进一步改善性能。

关于斯坦变分神经网络集成