We propose an approach to do learning in Gaussian factor graphs. We treat all relevant quantities (inputs, outputs, parameters, latents) as random variables in a graphical model, and view both training and prediction as inference problems with different observed nodes. Our experiments show that these problems can be efficiently solved with belief propagation (BP), whose updates are inherently local, presenting exciting opportunities for distributed and asynchronous training. Our approach can be scaled to deep networks and provides a natural means to do continual learning: use the BP-estimated parameter marginals of the current task as parameter priors for the next. On a video denoising task we demonstrate the benefit of learnable parameters over a classical factor graph approach and we show encouraging performance of deep factor graphs for continual image classification on MNIST.

我们提出了一种在高斯因子图中进行学习的方法，将所有相关的量（输入、输出、参数、潜变量）都视为随机变量，并将训练和预测视为具有不同观察节点的推理问题。我们的实验结果表明，这些问题可以通过信念传播（BP）进行高效求解，其更新在本质上是局部的，为分布式和异步训练提供了令人兴奋的机会。我们的方法可以扩展到深度网络，并提供了一种自然的方法进行连续学习：使用当前任务的BP估计参数边缘作为下一个任务的参数先验。在视频去噪任务中，我们展示了可学习参数相对于经典因子图方法的优势，并展示了深度因子图在MNIST连续图像分类上令人鼓舞的性能。

用高斯置信传播在深度因子图中学习