[Model] Implemented SubgraphX Explainer for Homogeneous graph (dmlc#5315

)

* subgraphx commit

* nits

* newline eof added

* lint fix

* test script updated to use default values

* lint fix

* graphs that are used for test cases are updated to a small graph

* lint formatted

* test paramter adj to complete the test under 20s

* lint fixes

---------

Co-authored-by: kxm180046 <[email protected]>

docs/source/api/python/nn-pytorch.rst

@@ -124,6 +124,7 @@ Utility Modules
     ~dgl.nn.pytorch.sparse_emb.NodeEmbedding
     ~dgl.nn.pytorch.explain.GNNExplainer
     ~dgl.nn.pytorch.explain.HeteroGNNExplainer
+    ~dgl.nn.pytorch.explain.SubgraphX
     ~dgl.nn.pytorch.utils.LabelPropagation
     ~dgl.nn.pytorch.graph_transformer.DegreeEncoder
     ~dgl.nn.pytorch.utils.LaplacianPosEnc

python/dgl/nn/pytorch/explain/__init__.py

@@ -1,4 +1,5 @@
 """Torch modules for explanation models."""
 # pylint: disable= no-member, arguments-differ, invalid-name
 
-from .gnnexplainer import GNNExplainer, HeteroGNNExplainer
+from .gnnexplainer import *
+from .subgraphx import *

python/dgl/nn/pytorch/explain/subgraphx.py

@@ -0,0 +1,366 @@
+"""Torch Module for SubgraphX"""
+import math
+
+import networkx as nx
+import numpy as np
+import torch
+import torch.nn as nn
+
+from ....base import NID
+from ....convert import to_networkx
+from ....subgraph import node_subgraph
+from ....transforms.functional import remove_nodes
+
+__all__ = ["SubgraphX"]
+
+
+class MCTSNode:
+    r"""Monte Carlo Tree Search Node
+
+    Parameters
+    ----------
+    nodes : Tensor
+        The node IDs of the graph that are associated with this tree node
+    """
+
+    def __init__(self, nodes):
+        self.nodes = nodes
+        self.num_visit = 0
+        self.total_reward = 0.0
+        self.immediate_reward = 0.0
+        self.children = []
+
+    def __repr__(self):
+        r"""Get the string representation of the node.
+
+        Returns
+        -------
+        str
+            The string representation of the node
+        """
+        return str(self.nodes)
+
+
+class SubgraphX(nn.Module):
+    r"""SubgraphX from `On Explainability of Graph Neural Networks via Subgraph
+    Explorations <https://arxiv.org/abs/2102.05152>`
+
+    It identifies the most important subgraph from the original graph that
+    plays a critical role in GNN-based graph classification.
+
+    It employs Monte Carlo tree search (MCTS) in efficiently exploring
+    different subgraphs for explanation and uses Shapley values as the measure
+    of subgraph importance.
+
+    Parameters
+    ----------
+    model : nn.Module
+        The GNN model to explain that tackles multiclass graph classification
+
+        * Its forward function must have the form
+          :attr:`forward(self, graph, nfeat)`.
+        * The output of its forward function is the logits.
+    num_hops : int
+        Number of message passing layers in the model
+    coef : float, optional
+        This hyperparameter controls the trade-off between exploration and
+        exploitation. A higher value encourages the algorithm to explore
+        relatively unvisited nodes. Default: 10.0
+    high2low : bool, optional
+        If True, it will use the "High2low" strategy for pruning actions,
+        expanding children nodes from high degree to low degree when extending
+        the children nodes in the search tree. Otherwise, it will use the
+        "Low2high" strategy. Default: True
+    num_child : int, optional
+        This is the number of children nodes to expand when extending the
+        children nodes in the search tree. Default: 12
+    num_rollouts : int, optional
+        This is the number of rollouts for MCTS. Default: 20
+    node_min : int, optional
+        This is the threshold to define a leaf node based on the number of
+        nodes in a subgraph. Default: 3
+    shapley_steps : int, optional
+        This is the number of steps for Monte Carlo sampling in estimating
+        Shapley values. Default: 100
+    log : bool, optional
+        If True, it will log the progress. Default: False
+    """
+
+    def __init__(
+        self,
+        model,
+        num_hops,
+        coef=10.0,
+        high2low=True,
+        num_child=12,
+        num_rollouts=20,
+        node_min=3,
+        shapley_steps=100,
+        log=False,
+    ):
+        super().__init__()
+        self.num_hops = num_hops
+        self.coef = coef
+        self.high2low = high2low
+        self.num_child = num_child
+        self.num_rollouts = num_rollouts
+        self.node_min = node_min
+        self.shapley_steps = shapley_steps
+        self.log = log
+
+        self.model = model
+
+    def shapley(self, subgraph_nodes):
+        r"""Compute Shapley value with Monte Carlo approximation.
+
+        Parameters
+        ----------
+        subgraph_nodes : tensor
+            The tensor node ids of the subgraph that are associated with this
+            tree node
+
+        Returns
+        -------
+        float
+            Shapley value
+        """
+        num_nodes = self.graph.num_nodes()
+        subgraph_nodes = subgraph_nodes.tolist()
+
+        # Obtain neighboring nodes of the subgraph g_i, P'.
+        local_region = subgraph_nodes
+        for _ in range(self.num_hops - 1):
+            in_neighbors, _ = self.graph.in_edges(local_region)
+            _, out_neighbors = self.graph.out_edges(local_region)
+            neighbors = torch.cat([in_neighbors, out_neighbors]).tolist()
+            local_region = list(set(local_region + neighbors))
+
+        split_point = num_nodes
+        coalition_space = list(set(local_region) - set(subgraph_nodes)) + [
+            split_point
+        ]
+
+        marginal_contributions = []
+        device = self.feat.device
+        for _ in range(self.shapley_steps):
+            permuted_space = np.random.permutation(coalition_space)
+            split_idx = int(np.where(permuted_space == split_point)[0])
+
+            selected_nodes = permuted_space[:split_idx]
+
+            # Mask for coalition set S_i
+            exclude_mask = torch.ones(num_nodes)
+            exclude_mask[local_region] = 0.0
+            exclude_mask[selected_nodes] = 1.0
+
+            # Mask for set S_i and g_i
+            include_mask = exclude_mask.clone()
+            include_mask[subgraph_nodes] = 1.0
+
+            exclude_feat = self.feat * exclude_mask.unsqueeze(1).to(device)
+            include_feat = self.feat * include_mask.unsqueeze(1).to(device)
+
+            with torch.no_grad():
+                exclude_probs = self.model(
+                    self.graph, exclude_feat, **self.kwargs
+                ).softmax(dim=-1)
+                exclude_value = exclude_probs[:, self.target_class]
+                include_probs = self.model(
+                    self.graph, include_feat, **self.kwargs
+                ).softmax(dim=-1)
+                include_value = include_probs[:, self.target_class]
+            marginal_contributions.append(include_value - exclude_value)
+
+        return torch.cat(marginal_contributions).mean().item()
+
+    def get_mcts_children(self, mcts_node):
+        r"""Get the children of the MCTS node for the search.
+
+        Parameters
+        ----------
+        mcts_node : MCTSNode
+            Node in MCTS
+
+        Returns
+        -------
+        list
+            Children nodes after pruning
+        """
+        if len(mcts_node.children) > 0:
+            return mcts_node.children
+
+        subg = node_subgraph(self.graph, mcts_node.nodes)
+        node_degrees = subg.out_degrees() + subg.in_degrees()
+        k = min(subg.num_nodes(), self.num_child)
+        chosen_nodes = torch.topk(
+            node_degrees, k, largest=self.high2low
+        ).indices
+
+        mcts_children_maps = dict()
+
+        for node in chosen_nodes:
+            new_subg = remove_nodes(subg, node.to(subg.idtype), store_ids=True)
+            # Get the largest weakly connected component in the subgraph.
+            nx_graph = to_networkx(new_subg.cpu())
+            largest_cc_nids = list(
+                max(nx.weakly_connected_components(nx_graph), key=len)
+            )
+            # Map to the original node IDs.
+            largest_cc_nids = new_subg.ndata[NID][largest_cc_nids].long()
+            largest_cc_nids = subg.ndata[NID][largest_cc_nids].sort().values
+            if str(largest_cc_nids) not in self.mcts_node_maps:
+                child_mcts_node = MCTSNode(largest_cc_nids)
+                self.mcts_node_maps[str(child_mcts_node)] = child_mcts_node
+            else:
+                child_mcts_node = self.mcts_node_maps[str(largest_cc_nids)]
+
+            if str(child_mcts_node) not in mcts_children_maps:
+                mcts_children_maps[str(child_mcts_node)] = child_mcts_node
+
+        mcts_node.children = list(mcts_children_maps.values())
+        for child_mcts_node in mcts_node.children:
+            if child_mcts_node.immediate_reward == 0:
+                child_mcts_node.immediate_reward = self.shapley(
+                    child_mcts_node.nodes
+                )
+
+        return mcts_node.children
+
+    def mcts_rollout(self, mcts_node):
+        r"""Perform a MCTS rollout.
+
+        Parameters
+        ----------
+        mcts_node : MCTSNode
+            Starting node for MCTS
+
+        Returns
+        -------
+        float
+            Reward for visiting the node this time
+        """
+        if len(mcts_node.nodes) <= self.node_min:
+            return mcts_node.immediate_reward
+
+        children_nodes = self.get_mcts_children(mcts_node)
+        children_visit_sum = sum([child.num_visit for child in children_nodes])
+        children_visit_sum_sqrt = math.sqrt(children_visit_sum)
+        chosen_child = max(
+            children_nodes,
+            key=lambda c: c.total_reward / max(c.num_visit, 1)
+            + self.coef
+            * c.immediate_reward
+            * children_visit_sum_sqrt
+            / (1 + c.num_visit),
+        )
+        reward = self.mcts_rollout(chosen_child)
+        chosen_child.num_visit += 1
+        chosen_child.total_reward += reward
+
+        return reward
+
+    def explain_graph(self, graph, feat, target_class, **kwargs):
+        r"""Find the most important subgraph from the original graph for the
+        model to classify the graph into the target class.
+
+        Parameters
+        ----------
+        graph : DGLGraph
+            A homogeneous graph
+        feat : Tensor
+            The input node feature of shape :math:`(N, D)`, :math:`N` is the
+            number of nodes, and :math:`D` is the feature size
+        target_class : int
+            The target class to explain
+        kwargs : dict
+            Additional arguments passed to the GNN model
+
+        Returns
+        -------
+        Tensor
+            Nodes that represent the most important subgraph
+
+        Examples
+        --------
+
+        >>> import torch
+        >>> import torch.nn as nn
+        >>> import torch.nn.functional as F
+        >>> from dgl.data import GINDataset
+        >>> from dgl.dataloading import GraphDataLoader
+        >>> from dgl.nn import GraphConv, AvgPooling, SubgraphX
+
+        >>> # Define the model
+        >>> class Model(nn.Module):
+        ...     def __init__(self, in_dim, n_classes, hidden_dim=128):
+        ...         super().__init__()
+        ...         self.conv1 = GraphConv(in_dim, hidden_dim)
+        ...         self.conv2 = GraphConv(hidden_dim, n_classes)
+        ...         self.pool = AvgPooling()
+        ...
+        ...     def forward(self, g, h):
+        ...         h = F.relu(self.conv1(g, h))
+        ...         h = self.conv2(g, h)
+        ...         return self.pool(g, h)
+
+        >>> # Load dataset
+        >>> data = GINDataset('MUTAG', self_loop=True)
+        >>> dataloader = GraphDataLoader(data, batch_size=64, shuffle=True)
+
+        >>> # Train the model
+        >>> feat_size = data[0][0].ndata['attr'].shape[1]
+        >>> model = Model(feat_size, data.gclasses)
+        >>> criterion = nn.CrossEntropyLoss()
+        >>> optimizer = torch.optim.Adam(model.parameters(), lr=1e-2)
+        >>> for bg, labels in dataloader:
+        ...     logits = model(bg, bg.ndata['attr'])
+        ...     loss = criterion(logits, labels)
+        ...     optimizer.zero_grad()
+        ...     loss.backward()
+        ...     optimizer.step()
+
+        >>> # Initialize the explainer
+        >>> explainer = SubgraphX(model, num_hops=2)
+
+        >>> # Explain the prediction for graph 0
+        >>> graph, l = data[0]
+        >>> graph_feat = graph.ndata.pop("attr")
+        >>> g_nodes_explain = explainer.explain_graph(graph, graph_feat,
+        ...                                           target_class=l)
+        """
+        self.model.eval()
+        assert (
+            graph.num_nodes() > self.node_min
+        ), f"The number of nodes in the\
+            graph {graph.num_nodes()} should be bigger than {self.node_min}."
+
+        self.graph = graph
+        self.feat = feat
+        self.target_class = target_class
+        self.kwargs = kwargs
+
+        # book all nodes in MCTS
+        self.mcts_node_maps = dict()
+
+        root = MCTSNode(graph.nodes())
+        self.mcts_node_maps[str(root)] = root
+
+        for i in range(self.num_rollouts):
+            if self.log:
+                print(
+                    f"Rollout {i}/{self.num_rollouts}, \
+                    {len(self.mcts_node_maps)} subgraphs have been explored."
+                )
+            self.mcts_rollout(root)
+
+        best_leaf = None
+        best_immediate_reward = float("-inf")
+        for mcts_node in self.mcts_node_maps.values():
+            if len(mcts_node.nodes) > self.node_min:
+                continue
+
+            if mcts_node.immediate_reward > best_immediate_reward:
+                best_leaf = mcts_node
+                best_immediate_reward = best_leaf.immediate_reward
+
+        return best_leaf.nodes