# 6.3 Training GNN for Link Prediction with Neighborhood Sampling¶

## Define a neighborhood sampler and data loader with negative sampling¶

You can still use the same neighborhood sampler as the one in node/edge classification.

```
sampler = dgl.dataloading.MultiLayerFullNeighborSampler(2)
```

`EdgeDataLoader`

in DGL also
supports generating negative samples for link prediction. To do so, you
need to provide the negative sampling function.
`Uniform`

is a
function that does uniform sampling. For each source node of an edge, it
samples `k`

negative destination nodes.

The following data loader will pick 5 negative destination nodes uniformly for each source node of an edge.

```
dataloader = dgl.dataloading.EdgeDataLoader(
g, train_seeds, sampler,
negative_sampler=dgl.dataloading.negative_sampler.Uniform(5),
batch_size=args.batch_size,
shuffle=True,
drop_last=False,
pin_memory=True,
num_workers=args.num_workers)
```

For the builtin negative samplers please see Negative Samplers for Link Prediction.

You can also give your own negative sampler function, as long as it
takes in the original graph `g`

and the minibatch edge ID array
`eid`

, and returns a pair of source ID arrays and destination ID
arrays.

The following gives an example of custom negative sampler that samples negative destination nodes according to a probability distribution proportional to a power of degrees.

```
class NegativeSampler(object):
def __init__(self, g, k):
# caches the probability distribution
self.weights = g.in_degrees().float() ** 0.75
self.k = k
def __call__(self, g, eids):
src, _ = g.find_edges(eids)
src = src.repeat_interleave(self.k)
dst = self.weights.multinomial(len(src), replacement=True)
return src, dst
dataloader = dgl.dataloading.EdgeDataLoader(
g, train_seeds, sampler,
negative_sampler=NegativeSampler(g, 5),
batch_size=args.batch_size,
shuffle=True,
drop_last=False,
pin_memory=True,
num_workers=args.num_workers)
```

## Adapt your model for minibatch training¶

As explained in 5.3 Link Prediction, link prediction is trained via comparing the score of an edge (positive example) against a non-existent edge (negative example). To compute the scores of edges you can reuse the node representation computation model you have seen in edge classification/regression.

```
class StochasticTwoLayerGCN(nn.Module):
def __init__(self, in_features, hidden_features, out_features):
super().__init__()
self.conv1 = dgl.nn.GraphConv(in_features, hidden_features)
self.conv2 = dgl.nn.GraphConv(hidden_features, out_features)
def forward(self, blocks, x):
x = F.relu(self.conv1(blocks[0], x))
x = F.relu(self.conv2(blocks[1], x))
return x
```

For score prediction, since you only need to predict a scalar score for each edge instead of a probability distribution, this example shows how to compute a score with a dot product of incident node representations.

```
class ScorePredictor(nn.Module):
def forward(self, edge_subgraph, x):
with edge_subgraph.local_scope():
edge_subgraph.ndata['x'] = x
edge_subgraph.apply_edges(dgl.function.u_dot_v('x', 'x', 'score'))
return edge_subgraph.edata['score']
```

When a negative sampler is provided, DGL’s data loader will generate three items per minibatch:

A positive graph containing all the edges sampled in the minibatch.

A negative graph containing all the non-existent edges generated by the negative sampler.

A list of

*message flow graphs*(MFGs) generated by the neighborhood sampler.

So one can define the link prediction model as follows that takes in the three items as well as the input features.

```
class Model(nn.Module):
def __init__(self, in_features, hidden_features, out_features):
super().__init__()
self.gcn = StochasticTwoLayerGCN(
in_features, hidden_features, out_features)
def forward(self, positive_graph, negative_graph, blocks, x):
x = self.gcn(blocks, x)
pos_score = self.predictor(positive_graph, x)
neg_score = self.predictor(negative_graph, x)
return pos_score, neg_score
```

## Training loop¶

The training loop simply involves iterating over the data loader and feeding in the graphs as well as the input features to the model defined above.

```
def compute_loss(pos_score, neg_score):
# an example hinge loss
n = pos_score.shape[0]
return (neg_score.view(n, -1) - pos_score.view(n, -1) + 1).clamp(min=0).mean()
model = Model(in_features, hidden_features, out_features)
model = model.cuda()
opt = torch.optim.Adam(model.parameters())
for input_nodes, positive_graph, negative_graph, blocks in dataloader:
blocks = [b.to(torch.device('cuda')) for b in blocks]
positive_graph = positive_graph.to(torch.device('cuda'))
negative_graph = negative_graph.to(torch.device('cuda'))
input_features = blocks[0].srcdata['features']
pos_score, neg_score = model(positive_graph, negative_graph, blocks, input_features)
loss = compute_loss(pos_score, neg_score)
opt.zero_grad()
loss.backward()
opt.step()
```

DGL provides the unsupervised learning GraphSAGE that shows an example of link prediction on homogeneous graphs.

## For heterogeneous graphs¶

The models computing the node representations on heterogeneous graphs can also be used for computing incident node representations for edge classification/regression.

```
class StochasticTwoLayerRGCN(nn.Module):
def __init__(self, in_feat, hidden_feat, out_feat, rel_names):
super().__init__()
self.conv1 = dglnn.HeteroGraphConv({
rel : dglnn.GraphConv(in_feat, hidden_feat, norm='right')
for rel in rel_names
})
self.conv2 = dglnn.HeteroGraphConv({
rel : dglnn.GraphConv(hidden_feat, out_feat, norm='right')
for rel in rel_names
})
def forward(self, blocks, x):
x = self.conv1(blocks[0], x)
x = self.conv2(blocks[1], x)
return x
```

For score prediction, the only implementation difference between the
homogeneous graph and the heterogeneous graph is that we are looping
over the edge types for `dgl.DGLHeteroGraph.apply_edges()`

.

```
class ScorePredictor(nn.Module):
def forward(self, edge_subgraph, x):
with edge_subgraph.local_scope():
edge_subgraph.ndata['x'] = x
for etype in edge_subgraph.canonical_etypes:
edge_subgraph.apply_edges(
dgl.function.u_dot_v('x', 'x', 'score'), etype=etype)
return edge_subgraph.edata['score']
class Model(nn.Module):
def __init__(self, in_features, hidden_features, out_features, num_classes,
etypes):
super().__init__()
self.rgcn = StochasticTwoLayerRGCN(
in_features, hidden_features, out_features, etypes)
self.pred = ScorePredictor()
def forward(self, positive_graph, negative_graph, blocks, x):
x = self.rgcn(blocks, x)
pos_score = self.pred(positive_graph, x)
neg_score = self.pred(negative_graph, x)
return pos_score, neg_score
```

Data loader definition is also very similar to that of edge classification/regression. The only difference is that you need to give the negative sampler and you will be supplying a dictionary of edge types and edge ID tensors instead of a dictionary of node types and node ID tensors.

```
sampler = dgl.dataloading.MultiLayerFullNeighborSampler(2)
dataloader = dgl.dataloading.EdgeDataLoader(
g, train_eid_dict, sampler,
negative_sampler=dgl.dataloading.negative_sampler.Uniform(5),
batch_size=1024,
shuffle=True,
drop_last=False,
num_workers=4)
```

If you want to give your own negative sampling function, the function should take in the original graph and the dictionary of edge types and edge ID tensors. It should return a dictionary of edge types and source-destination array pairs. An example is given as follows:

```
class NegativeSampler(object):
def __init__(self, g, k):
# caches the probability distribution
self.weights = {
etype: g.in_degrees(etype=etype).float() ** 0.75
for _, etype, _ in g.canonical_etypes
}
self.k = k
def __call__(self, g, eids_dict):
result_dict = {}
for etype, eids in eids_dict.items():
src, _ = g.find_edges(eids, etype=etype)
src = src.repeat_interleave(self.k)
dst = self.weights[etype].multinomial(len(src), replacement=True)
result_dict[etype] = (src, dst)
return result_dict
```

Then you can give the dataloader a dictionary of edge types and edge IDs as well as the negative sampler. For instance, the following iterates over all edges of the heterogeneous graph.

```
train_eid_dict = {
g.edges(etype=etype, form='eid')
for etype in g.etypes}
dataloader = dgl.dataloading.EdgeDataLoader(
g, train_eid_dict, sampler,
negative_sampler=NegativeSampler(g, 5),
batch_size=1024,
shuffle=True,
drop_last=False,
num_workers=4)
```

The training loop is again almost the same as that on homogeneous graph,
except for the implementation of `compute_loss`

that will take in two
dictionaries of node types and predictions here.

```
model = Model(in_features, hidden_features, out_features, num_classes, etypes)
model = model.cuda()
opt = torch.optim.Adam(model.parameters())
for input_nodes, positive_graph, negative_graph, blocks in dataloader:
blocks = [b.to(torch.device('cuda')) for b in blocks]
positive_graph = positive_graph.to(torch.device('cuda'))
negative_graph = negative_graph.to(torch.device('cuda'))
input_features = blocks[0].srcdata['features']
pos_score, neg_score = model(positive_graph, negative_graph, blocks, input_features)
loss = compute_loss(pos_score, neg_score)
opt.zero_grad()
loss.backward()
opt.step()
```