The need for function estimation in label-limited settings is common in the natural sciences. At the same time, prior knowledge of function values is often available in these domains. For example, data-free biophysics-based models can be informative on protein properties, while quantum-based computations can be informative on small molecule properties. How can we coherently leverage such prior knowledge to help improve a neural network model that is quite accurate in some regions of input space -- typically near the training data -- but wildly wrong in other regions? Bayesian neural networks (BNN) enable the user to specify prior information only on the neural network weights, not directly on the function values. Moreover, there is in general no clear mapping between these. Herein, we tackle this problem by developing an approach to augment BNNs with prior information on the function values themselves. Our probabilistic approach yields predictions that rely more heavily on the prior information when the epistemic uncertainty is large, and more heavily on the neural network when the epistemic uncertainty is small.
翻译:在受标签限制的环境下进行功能估计的必要性在自然科学中很常见。 同时,先前对功能值的知识往往存在于这些领域。例如,基于无数据的生物物理模型可以提供关于蛋白质特性的信息,而基于量子的计算可以提供关于小分子特性的信息。我们如何一致地利用这种先前的知识来帮助改进在输入空间的某些地区非常精确的神经网络模型 -- -- 通常在培训数据附近,但在其他地区则大错特错?Bayesian神经网络(BNN)使用户能够事先只提供关于神经网络重量的信息,而不是直接关于功能值的信息。此外,这些模型之间一般没有清晰的绘图。在这里,我们通过开发一种方法,利用功能值本身的先前信息来增加BNN来解决这一问题。我们的危险性方法产生预测,在上位不确定性大时,更依赖先前的信息,而在上位不确定性小时,则更多地依靠神经网络。