6.4 Customizing Neighborhood Sampler

Although DGL provides some neighborhood sampling strategies, sometimes users would want to write their own sampling strategy. This section explains how to write your own strategy and plug it into your stochastic GNN training framework.

Recall that in How Powerful are Graph Neural Networks, the definition of message passing is:

\[\begin{split}\begin{gathered} \boldsymbol{a}_v^{(l)} = \rho^{(l)} \left( \left\lbrace \boldsymbol{h}_u^{(l-1)} : u \in \mathcal{N} \left( v \right) \right\rbrace \right) \\ \boldsymbol{h}_v^{(l)} = \phi^{(l)} \left( \boldsymbol{h}_v^{(l-1)}, \boldsymbol{a}_v^{(l)} \right) \end{gathered}\end{split}\]

where \(\rho^{(l)}\) and \(\phi^{(l)}\) are parameterized functions, and \(\mathcal{N}(v)\) is defined as the set of predecessors (or neighbors if the graph is undirected) of \(v\) on graph \(\mathcal{G}\).

For instance, to perform a message passing for updating the red node in the following graph:

Imgur

One needs to aggregate the node features of its neighbors, shown as green nodes:

Imgur

Neighborhood sampling with pencil and paper

We then consider how multi-layer message passing works for computing the output of a single node. In the following text we refer to the nodes whose GNN outputs are to be computed as seed nodes.

import torch
import dgl

src = torch.LongTensor(
    [0, 0, 0, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10,
     1, 2, 3, 3, 3, 4, 5, 5, 6, 5, 8, 6, 8, 9, 8, 11, 11, 10, 11])
dst = torch.LongTensor(
    [1, 2, 3, 3, 3, 4, 5, 5, 6, 5, 8, 6, 8, 9, 8, 11, 11, 10, 11,
     0, 0, 0, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10])
g = dgl.graph((src, dst))
g.ndata['x'] = torch.randn(12, 5)
g.ndata['y'] = torch.randn(12, 1)

Finding the message passing dependency

Consider computing with a 2-layer GNN the output of the seed node 8, colored red, in the following graph:

Imgur

By the formulation:

\[\begin{split}\begin{gathered} \boldsymbol{a}_8^{(2)} = \rho^{(2)} \left( \left\lbrace \boldsymbol{h}_u^{(1)} : u \in \mathcal{N} \left( 8 \right) \right\rbrace \right) = \rho^{(2)} \left( \left\lbrace \boldsymbol{h}_4^{(1)}, \boldsymbol{h}_5^{(1)}, \boldsymbol{h}_7^{(1)}, \boldsymbol{h}_{11}^{(1)} \right\rbrace \right) \\ \boldsymbol{h}_8^{(2)} = \phi^{(2)} \left( \boldsymbol{h}_8^{(1)}, \boldsymbol{a}_8^{(2)} \right) \end{gathered}\end{split}\]

We can tell from the formulation that to compute \(\boldsymbol{h}_8^{(2)}\) we need messages from node 4, 5, 7 and 11 (colored green) along the edges visualized below.

Imgur

This graph contains all the nodes in the original graph but only the edges necessary for message passing to the given output nodes. We call that the frontier of the second GNN layer for the red node 8.

Several functions can be used for generating frontiers. For instance, dgl.in_subgraph() is a function that induces a subgraph by including all the nodes in the original graph, but only all the incoming edges of the given nodes. You can use that as a frontier for message passing along all the incoming edges.

frontier = dgl.in_subgraph(g, [8])
print(frontier.all_edges())

For a concrete list, please refer to Subgraph Extraction Ops and dgl.sampling.

Technically, any graph that has the same set of nodes as the original graph can serve as a frontier. This serves as the basis for Implementing a Custom Neighbor Sampler.

The Bipartite Structure for Multi-layer Minibatch Message Passing

However, to compute \(\boldsymbol{h}_8^{(2)}\) from \(\boldsymbol{h}_\cdot^{(1)}\), we cannot simply perform message passing on the frontier directly, because it still contains all the nodes from the original graph. Namely, we only need nodes 4, 5, 7, 8, and 11 (green and red nodes) as input, as well as node 8 (red node) as output. Since the number of nodes for input and output is different, we need to perform message passing on a small, bipartite-structured graph instead. We call such a bipartite-structured graph that only contains the necessary input nodes and output nodes a block. The following figure shows the block of the second GNN layer for node 8.

Imgur

Note that the output nodes also appear in the input nodes. The reason is that representations of output nodes from the previous layer are needed for feature combination after message passing (i.e. \(\phi^{(2)}\)).

DGL provides dgl.to_block() to convert any frontier to a block where the first argument specifies the frontier and the second argument specifies the output nodes. For instance, the frontier above can be converted to a block with output node 8 with the code as follows.

output_nodes = torch.LongTensor([8])
block = dgl.to_block(frontier, output_nodes)

To find the number of input nodes and output nodes of a given node type, one can use dgl.DGLHeteroGraph.number_of_src_nodes() and dgl.DGLHeteroGraph.number_of_dst_nodes() methods.

num_input_nodes, num_output_nodes = block.number_of_src_nodes(), block.number_of_dst_nodes()
print(num_input_nodes, num_output_nodes)

The block’s input node features can be accessed via member dgl.DGLHeteroGraph.srcdata and dgl.DGLHeteroGraph.srcnodes, and its output node features can be accessed via member dgl.DGLHeteroGraph.dstdata and dgl.DGLHeteroGraph.dstnodes. The syntax of srcdata/dstdata and srcnodes/dstnodes are identical to dgl.DGLHeteroGraph.ndata and dgl.DGLHeteroGraph.nodes in normal graphs.

block.srcdata['h'] = torch.randn(num_input_nodes, 5)
block.dstdata['h'] = torch.randn(num_output_nodes, 5)

If a block is converted from a frontier, which is in turn converted from a graph, one can directly read the feature of the block’s input and output nodes via

print(block.srcdata['x'])
print(block.dstdata['y'])
<b>ID Mappings</b>

The original node IDs of the input nodes and output nodes in the block can be found as the feature dgl.NID, and the mapping from the block’s edge IDs to the input frontier’s edge IDs can be found as the feature dgl.EID.

Output Nodes

DGL ensures that the output nodes of a block will always appear in the input nodes. The output nodes will always index firstly in the input nodes.

input_nodes = block.srcdata[dgl.NID]
output_nodes = block.dstdata[dgl.NID]
assert torch.equal(input_nodes[:len(output_nodes)], output_nodes)

As a result, the output nodes must cover all nodes that are the destination of an edge in the frontier.

For example, consider the following frontier

Imgur

where the red and green nodes (i.e. node 4, 5, 7, 8, and 11) are all nodes that is a destination of an edge. Then the following code will raise an error because the output nodes did not cover all those nodes.

dgl.to_block(frontier2, torch.LongTensor([4, 5]))   # ERROR

However, the output nodes can have more nodes than above. In this case, we will have isolated nodes that do not have any edge connecting to it. The isolated nodes will be included in both input nodes and output nodes.

# Node 3 is an isolated node that do not have any edge pointing to it.
block3 = dgl.to_block(frontier2, torch.LongTensor([4, 5, 7, 8, 11, 3]))
print(block3.srcdata[dgl.NID])
print(block3.dstdata[dgl.NID])

Heterogeneous Graphs

Blocks also work on heterogeneous graphs. Let’s say that we have the following frontier:

hetero_frontier = dgl.heterograph({
    ('user', 'follow', 'user'): ([1, 3, 7], [3, 6, 8]),
    ('user', 'play', 'game'): ([5, 5, 4], [6, 6, 2]),
    ('game', 'played-by', 'user'): ([2], [6])
}, num_nodes_dict={'user': 10, 'game': 10})

One can also create a block with output nodes User #3, #6, and #8, as well as Game #2 and #6.

hetero_block = dgl.to_block(hetero_frontier, {'user': [3, 6, 8], 'block': [2, 6]})

One can also get the input nodes and output nodes by type:

# input users and games
print(hetero_block.srcnodes['user'].data[dgl.NID], hetero_block.srcnodes['game'].data[dgl.NID])
# output users and games
print(hetero_block.dstnodes['user'].data[dgl.NID], hetero_block.dstnodes['game'].data[dgl.NID])

Implementing a Custom Neighbor Sampler

Recall that the following code performs neighbor sampling for node classification.

sampler = dgl.dataloading.MultiLayerFullNeighborSampler(2)

To implement your own neighborhood sampling strategy, you basically replace the sampler object with your own. To do that, let’s first see what BlockSampler, the parent class of MultiLayerFullNeighborSampler, is.

BlockSampler is responsible for generating the list of blocks starting from the last layer, with method sample_blocks(). The default implementation of sample_blocks is to iterate backwards, generating the frontiers and converting them to blocks.

Therefore, for neighborhood sampling, you only need to implement thesample_frontier()method. Given which layer the sampler is generating frontier for, as well as the original graph and the nodes to compute representations, this method is responsible for generating a frontier for them.

Meanwhile, you also need to pass how many GNN layers you have to the parent class.

For example, the implementation of MultiLayerFullNeighborSampler can go as follows.

class MultiLayerFullNeighborSampler(dgl.dataloading.BlockSampler):
    def __init__(self, n_layers):
        super().__init__(n_layers)

    def sample_frontier(self, block_id, g, seed_nodes):
        frontier = dgl.in_subgraph(g, seed_nodes)
        return frontier

dgl.dataloading.neighbor.MultiLayerNeighborSampler, a more complicated neighbor sampler class that allows you to sample a small number of neighbors to gather message for each node, goes as follows.

class MultiLayerNeighborSampler(dgl.dataloading.BlockSampler):
    def __init__(self, fanouts):
        super().__init__(len(fanouts))

        self.fanouts = fanouts

    def sample_frontier(self, block_id, g, seed_nodes):
        fanout = self.fanouts[block_id]
        if fanout is None:
            frontier = dgl.in_subgraph(g, seed_nodes)
        else:
            frontier = dgl.sampling.sample_neighbors(g, seed_nodes, fanout)
        return frontier

Although the functions above can generate a frontier, any graph that has the same nodes as the original graph can serve as a frontier.

For example, if one want to randomly drop inbound edges to the seed nodes with a probability, one can simply define the sampler as follows:

class MultiLayerDropoutSampler(dgl.dataloading.BlockSampler):
    def __init__(self, p, n_layers):
        super().__init__()

        self.n_layers = n_layers
        self.p = p

    def sample_frontier(self, block_id, g, seed_nodes, *args, **kwargs):
        # Get all inbound edges to `seed_nodes`
        src, dst = dgl.in_subgraph(g, seed_nodes).all_edges()
        # Randomly select edges with a probability of p
        mask = torch.zeros_like(src).bernoulli_(self.p)
        src = src[mask]
        dst = dst[mask]
        # Return a new graph with the same nodes as the original graph as a
        # frontier
        frontier = dgl.graph((src, dst), num_nodes=g.number_of_nodes())
        return frontier

    def __len__(self):
        return self.n_layers

After implementing your sampler, you can create a data loader that takes in your sampler and it will keep generating lists of blocks while iterating over the seed nodes as usual.

sampler = MultiLayerDropoutSampler(0.5, 2)
dataloader = dgl.dataloading.NodeDataLoader(
    g, train_nids, sampler,
    batch_size=1024,
    shuffle=True,
    drop_last=False,
    num_workers=4)

model = StochasticTwoLayerRGCN(in_features, hidden_features, out_features)
model = model.cuda()
opt = torch.optim.Adam(model.parameters())

for input_nodes, blocks in dataloader:
    blocks = [b.to(torch.device('cuda')) for b in blocks]
    input_features = blocks[0].srcdata     # returns a dict
    output_labels = blocks[-1].dstdata     # returns a dict
    output_predictions = model(blocks, input_features)
    loss = compute_loss(output_labels, output_predictions)
    opt.zero_grad()
    loss.backward()
    opt.step()

Heterogeneous Graphs

Generating a frontier for a heterogeneous graph is nothing different than that for a homogeneous graph. Just make the returned graph have the same nodes as the original graph, and it should work fine. For example, we can rewrite the MultiLayerDropoutSampler above to iterate over all edge types, so that it can work on heterogeneous graphs as well.

class MultiLayerDropoutSampler(dgl.dataloading.BlockSampler):
    def __init__(self, p, n_layers):
        super().__init__()

        self.n_layers = n_layers
        self.p = p

    def sample_frontier(self, block_id, g, seed_nodes, *args, **kwargs):
        # Get all inbound edges to `seed_nodes`
        sg = dgl.in_subgraph(g, seed_nodes)

        new_edges_masks = {}
        # Iterate over all edge types
        for etype in sg.canonical_etypes:
            edge_mask = torch.zeros(sg.number_of_edges(etype))
            edge_mask.bernoulli_(self.p)
            new_edges_masks[etype] = edge_mask.bool()

        # Return a new graph with the same nodes as the original graph as a
        # frontier
        frontier = dgl.edge_subgraph(new_edge_masks, preserve_nodes=True)
        return frontier

    def __len__(self):
        return self.n_layers