Show HN: Graph Convolutional Networks – Intro to neural networks on graphs (opens in new tab)

Mini-batching is indeed tricky, as you need the information of the complete local neighborhood for all nodes in a mini-batch. Let's say you select N nodes for a mini-batch, then you would also have to provide all nodes of the k-th order neighborhood for a neural net with k layers (if you want an exact procedure). I'd recommend to do some subsampling in this case, although this is not trivial. We're currently looking into this. Otherwise full-batch gradient descent tends to work very well on most datasets. Datasets up to ~1 million nodes should fit into memory and the training updates should still be quite fast.

Both graph-level and node-level classification are possible. Graph-level classification requires some from of pooling operation (simplest case: mean-pooling over all nodes, but there are more elaborate things one can do)

In a graphical model, you'd explicitly model the probabilistic assumptions that you make with respect to the data. In this neural network-based approach the goal can be thought of more like learning a function that maps from some input to some desired output. But indeed the form of the propagation rule resembles mean field inference in graphical models.

I know little, but how about classification of neuro–developmental disorders from network graphs derived from resting state fMRI?