GNNExplainer代码解读及其PyG实现

使用GNNExplainer
GNNExplainer源码速读
- 前向传播
- 损失函数
基于GNNExplainer图分类解释的PyG代码示例
参考资料

接上一篇博客图神经网络的可解释性方法及GNNexplainer代码示例，我们这里简单分析GNNExplainer源码，并用PyTorch Geometric手动实现。
GNNExplainer的源码地址：https://github.com/RexYing/gnn-model-explainer

使用GNNExplainer

（1）安装：

git clone https://github.com/RexYing/gnn-model-explainer

推荐使用python3.7以及创建虚拟环境：

virtualenv venv -p /usr/local/bin/python3
source venv/bin/activate

（2）训练一个GCN模型

python train.py --dataset=EXPERIMENT_NAME

其中EXPERIMENT_NAME表示想要复现的实验名称。

训练GCN模型的完整选项列表：

python train.py --help

（3）解释一个GCN模型
要运行解释器，请运行以下内容：

python explainer_main.py --dataset=EXPERIMENT_NAME

（4）可视化解释
使用Tensorboard：优化的结果可以通过Tensorboard可视化。

tensorboard --logdir log

GNNExplainer源码速读

GNNExplainer会从2个角度解释图：

边（edge）：会生成一个edge mask，表示每条边在图中出现的概率，值为0-1之间的浮点数。edge mask也可以当作一个权重，可以取topk的edge连成的子图来解释。
结点特征（node feature）：node feature（NF）即结点向量，比如一个结点128维表示128个特征，那么它同时会生成一个NF mask来表示每个特征的权重，这个可以不要。

代码目录

explainer目录下的ExplainModel类定义了GNNExplainer网络的模块结构，继承torch.nn.Module:
- 在初始化init的时候，用construct_edge_mask和construct_feat_mask函数初始化要学习的两个mask（分别对应于两个nn.Parameter类型的变量：维的mask，d维全0的feat_mask）；diag_mask即主对角线上是0，其余元素均为1的矩阵，用于_masked_adj函数。
- _masked_adj函数将mask用sigmod或ReLU激活后，加上自身转置再除以2，以转为对称矩阵，然后乘上diag_mask，最终将原邻接矩阵adj变换为masked_adj。
Explainer类实现了解释的逻辑，主函数是其中的explain，用于解释原模型在单节点的预测结果，主要步骤：
1. 取子图的adj, x, label。图解释：取graph_idx对应的整个计算图；节点解释：调用extract_neighborhood函数取该节点num_gc_layers阶数的邻居。
2. 将传入的模型预测输出pred转为pred_label。
3. 构建ExplainModule，进行num_epochs轮训练（前向+反向传播）

adj   = torch.tensor(sub_adj, dtype=torch.float)
x     = torch.tensor(sub_feat, requires_grad=True, dtype=torch.float)
label = torch.tensor(sub_label, dtype=torch.long)

if self.graph_mode:
	pred_label = np.argmax(self.pred[0][graph_idx], axis=0)
	print("Graph predicted label: ", pred_label)
else:
	pred_label = np.argmax(self.pred[graph_idx][neighbors], axis=1)
	print("Node predicted label: ", pred_label[node_idx_new])

explainer = ExplainModule(
	adj=adj,
	x=x,
	model=self.model,
	label=label,
	args=self.args,
	writer=self.writer,
	graph_idx=self.graph_idx,
	graph_mode=self.graph_mode,
)
if self.args.gpu:
	explainer = explainer.cuda()

...

# NODE EXPLAINER
def explain_nodes(self, node_indices, args, graph_idx=0):
...

def explain_nodes_gnn_stats(self, node_indices, args, graph_idx=0, model="exp"):
...

# GRAPH EXPLAINER
def explain_graphs(self, graph_indices):
...

explain_nodes、explain_nodes_gnn_stats、explain_graphs这三个函数都是在它的基础上实现的。

下面分析其中的forward和loss函数。

前向传播

首先把待学习的参数mask和feat_mask分别乘上原邻接矩阵和特征向量，得到变换后的masked_adj和x。前者通过调用_masked_adj函数完成，后者的实现如下：

feat_mask = (
	torch.sigmoid(self.feat_mask)
	if self.use_sigmoid
	else self.feat_mask
)
if marginalize:
	std_tensor = torch.ones_like(x, dtype=torch.float) / 2
	mean_tensor = torch.zeros_like(x, dtype=torch.float) - x
	z = torch.normal(mean=mean_tensor, std=std_tensor)
	x = x + z * (1 - feat_mask)
else:
	x = x * feat_mask

完整代码如下：
forward

如果同mask一样学习feature_mask，在某些情况下回导致重要特征也被忽略（学到的特征遮罩也是接近于0的值），因此，依据的经验边缘分布使用Monte Carlo方法来抽样得到.
为了解决随机变量的反向传播的问题，引入了”重参数化”的技巧，即将其表示为一个无参的随机变量的确定性变换：
其中，是依据经验分布采样得到的维随机变量，是表示保留的最大特征数的参数（utils/io_utils.py中的denoise_graph函数）。

接着将masked_adj和x输入原始模型得到ExplainModule结果pred。

损失函数

loss = pred_loss + size_loss + lap_loss + mask_ent_loss + feat_size_loss

可知，总的loss包含五项，除了对应于论文中损失函数公式的pred_loss，其余各项损失的作用参考论文Integrating additional constraints into explanations，它们的权重定义在coeffs中：

self.coeffs = {
	"size": 0.005,
	"feat_size": 1.0,
	"ent": 1.0,
	"feat_ent": 0.1,
	"grad": 0,
	"lap": 1.0,
}

Integrating additional constraints into explanations

pred_loss

mi_obj = False
if mi_obj:
	pred_loss = -torch.sum(pred * torch.log(pred))
else:
	pred_label_node = pred_label if self.graph_mode else pred_label[node_idx]
	gt_label_node = self.label if self.graph_mode else self.label[0][node_idx]
	logit = pred[gt_label_node]
	pred_loss = -torch.log(logit)

其中pred是当前的预测结果，pred_label是原始特征上的预测结果。

mask_ent_loss

# entropy
mask_ent = -mask * torch.log(mask) - (1 - mask) * torch.log(1 - mask)
mask_ent_loss = self.coeffs["ent"] * torch.mean(mask_ent)

size_loss

# size
mask = self.mask
if self.mask_act == "sigmoid":
	mask = torch.sigmoid(self.mask)
elif self.mask_act == "ReLU":
	mask = nn.ReLU()(self.mask)
size_loss = self.coeffs["size"] * torch.sum(mask)

feat_size_loss

# pre_mask_sum = torch.sum(self.feat_mask)
feat_mask = (
	torch.sigmoid(self.feat_mask) if self.use_sigmoid else self.feat_mask
)
feat_size_loss = self.coeffs["feat_size"] * torch.mean(feat_mask)

lap_loss

# laplacian
D = torch.diag(torch.sum(self.masked_adj[0], 0))
m_adj = self.masked_adj if self.graph_mode else self.masked_adj[self.graph_idx]
L = D - m_adj
pred_label_t = torch.tensor(pred_label, dtype=torch.float)
if self.args.gpu:
	pred_label_t = pred_label_t.cuda()
	L = L.cuda()
if self.graph_mode:
	lap_loss = 0
else:
	lap_loss = (self.coeffs["lap"] * (pred_label_t @ L @ pred_label_t) / self.adj.numel())

基于GNNExplainer图分类解释的PyG代码示例

对于图分类问题的解释，关键点有两个：

要学习的Mask作用在整个图上，不用取子图
标签预测和损失函数的对象是单个graph

实现代码如下：

#!/usr/bin/env python
# encoding: utf-8
# Created by BIT09 at 2023/4/28
import torch
import networkx as nx
import numpy as np
import matplotlib.pyplot as plt
from math import sqrt
from tqdm import tqdm
from torch_geometric.nn import MessagePassing
from torch_geometric.data import Data
from torch_geometric.utils import k_hop_subgraph, to_networkx

EPS = 1e-15


class GNNExplainer(torch.nn.Module):
    r"""
    Args:
        model (torch.nn.Module): The GNN module to explain.
        epochs (int, optional): The number of epochs to train.
            (default: :obj:`100`)
        lr (float, optional): The learning rate to apply.
            (default: :obj:`0.01`)
        log (bool, optional): If set to :obj:`False`, will not log any learning
            progress. (default: :obj:`True`)
    """

    coeffs = {
        'edge_size': 0.001,
        'node_feat_size': 1.0,
        'edge_ent': 1.0,
        'node_feat_ent': 0.1,
    }

    def __init__(self, model, epochs=100, lr=0.01, log=True, node=False):  # disable node_feat_mask by default
        super(GNNExplainer, self).__init__()
        self.model = model
        self.epochs = epochs
        self.lr = lr
        self.log = log
        self.node = node

    def __set_masks__(self, x, edge_index, init="normal"):
        (N, F), E = x.size(), edge_index.size(1)

        std = 0.1
        if self.node:
            self.node_feat_mask = torch.nn.Parameter(torch.randn(F) * 0.1)

        std = torch.nn.init.calculate_gain('relu') * sqrt(2.0 / (2 * N))
        self.edge_mask = torch.nn.Parameter(torch.randn(E) * std)
        self.edge_mask = torch.nn.Parameter(torch.zeros(E) * 50)

        for module in self.model.modules():
            if isinstance(module, MessagePassing):
                module.__explain__ = True
                module.__edge_mask__ = self.edge_mask

    def __clear_masks__(self):
        for module in self.model.modules():
            if isinstance(module, MessagePassing):
                module.__explain__ = False
                module.__edge_mask__ = None
        if self.node:
            self.node_feat_masks = None
        self.edge_mask = None

    def __num_hops__(self):
        num_hops = 0
        for module in self.model.modules():
            if isinstance(module, MessagePassing):
                num_hops += 1
        return num_hops

    def __flow__(self):
        for module in self.model.modules():
            if isinstance(module, MessagePassing):
                return module.flow
        return 'source_to_target'

    def __subgraph__(self, node_idx, x, edge_index, **kwargs):
        num_nodes, num_edges = x.size(0), edge_index.size(1)

        if node_idx is not None:
            subset, edge_index, mapping, edge_mask = k_hop_subgraph(
                node_idx, self.__num_hops__(), edge_index, relabel_nodes=True,
                num_nodes=num_nodes, flow=self.__flow__())
            x = x[subset]
        else:
            x = x
            edge_index = edge_index
            row, col = edge_index
            edge_mask = row.new_empty(row.size(0), dtype=torch.bool)
            edge_mask[:] = True
            mapping = None

        for key, item in kwargs:
            if torch.is_tensor(item) and item.size(0) == num_nodes:
                item = item[subset]
            elif torch.is_tensor(item) and item.size(0) == num_edges:
                item = item[edge_mask]
            kwargs[key] = item

        return x, edge_index, mapping, edge_mask, kwargs

    def __graph_loss__(self, log_logits, pred_label):
        loss = -torch.log(log_logits[0, pred_label])
        m = self.edge_mask.sigmoid()
        loss = loss + self.coeffs['edge_size'] * m.sum()
        ent = -m * torch.log(m + EPS) - (1 - m) * torch.log(1 - m + EPS)
        loss = loss + self.coeffs['edge_ent'] * ent.mean()

        return loss

    def visualize_subgraph(self, node_idx, edge_index, edge_mask, y=None,
                           threshold=None, **kwargs):
        r"""Visualizes the subgraph around :attr:`node_idx` given an edge mask
        :attr:`edge_mask`.

        Args:
            node_idx (int): The node id to explain.
            edge_index (LongTensor): The edge indices.
            edge_mask (Tensor): The edge mask.
            y (Tensor, optional): The ground-truth node-prediction labels used
                as node colorings. (default: :obj:`None`)
            threshold (float, optional): Sets a threshold for visualizing
                important edges. If set to :obj:`None`, will visualize all
                edges with transparancy indicating the importance of edges.
                (default: :obj:`None`)
            **kwargs (optional): Additional arguments passed to
                :func:`nx.draw`.

        :rtype: :class:`matplotlib.axes.Axes`, :class:`networkx.DiGraph`
        """

        assert edge_mask.size(0) == edge_index.size(1)

        if node_idx is not None:
            # Only operate on a k-hop subgraph around `node_idx`.
            subset, edge_index, _, hard_edge_mask = k_hop_subgraph(
                node_idx, self.__num_hops__(), edge_index, relabel_nodes=True,
                num_nodes=None, flow=self.__flow__())

            edge_mask = edge_mask[hard_edge_mask]
            subset = subset.tolist()
            if y is None:
                y = torch.zeros(edge_index.max().item() + 1,
                                device=edge_index.device)
            else:
                y = y[subset].to(torch.float) / y.max().item()
                y = y.tolist()
        else:
            subset = []
            for index, mask in enumerate(edge_mask):
                node_a = edge_index[0, index]
                node_b = edge_index[1, index]
                if node_a not in subset:
                    subset.append(node_a.item())
                if node_b not in subset:
                    subset.append(node_b.item())
            y = [y for i in range(len(subset))]

        if threshold is not None:
            edge_mask = (edge_mask >= threshold).to(torch.float)

        data = Data(edge_index=edge_index, att=edge_mask, y=y,
                    num_nodes=len(y)).to('cpu')
        G = to_networkx(data, edge_attrs=['att'])  # , node_attrs=['y']
        mapping = {k: i for k, i in enumerate(subset)}
        G = nx.relabel_nodes(G, mapping)

        kwargs['with_labels'] = kwargs.get('with_labels') or True
        kwargs['font_size'] = kwargs.get('font_size') or 10
        kwargs['node_size'] = kwargs.get('node_size') or 800
        kwargs['cmap'] = kwargs.get('cmap') or 'cool'

        pos = nx.spring_layout(G)
        ax = plt.gca()
        for source, target, data in G.edges(data=True):
            ax.annotate(
                '', xy=pos[target], xycoords='data', xytext=pos[source],
                textcoords='data', arrowprops=dict(
                    arrowstyle="->",
                    alpha=max(data['att'], 0.1),
                    shrinkA=sqrt(kwargs['node_size']) / 2.0,
                    shrinkB=sqrt(kwargs['node_size']) / 2.0,
                    connectionstyle="arc3,rad=0.1",
                ))
        nx.draw_networkx_nodes(G, pos, node_color=y, **kwargs)
        nx.draw_networkx_labels(G, pos, **kwargs)

        return ax, G

    def explain_graph(self, data, **kwargs):
        self.model.eval()
        self.__clear_masks__()
        x, edge_index, batch = data.x, data.edge_index, data.batch

        num_edges = edge_index.size(1)

        # Only operate on a k-hop subgraph around `node_idx`.
        x, edge_index, _, hard_edge_mask, kwargs = self.__subgraph__(node_idx=None, x=x, edge_index=edge_index,
                                                                     **kwargs)
        # Get the initial prediction.
        with torch.no_grad():
            log_logits = self.model(data, **kwargs)
            probs_Y = torch.softmax(log_logits, 1)
            pred_label = probs_Y.argmax(dim=-1)

        self.__set_masks__(x, edge_index)
        self.to(x.device)

        if self.node:
            optimizer = torch.optim.Adam([self.node_feat_mask, self.edge_mask],
                                         lr=self.lr)
        else:
            optimizer = torch.optim.Adam([self.edge_mask], lr=self.lr)

        epoch_losses = []
        for epoch in range(1, self.epochs + 1):
            epoch_loss = 0
            optimizer.zero_grad()
            if self.node:
                h = x * self.node_feat_mask.view(1, -1).sigmoid()

            log_logits = self.model(data, **kwargs)
            pred = torch.softmax(log_logits, 1)
            loss = self.__graph_loss__(pred, pred_label)
            loss.backward()

            optimizer.step()
            epoch_loss += loss.detach().item()
            epoch_losses.append(epoch_loss)

        edge_mask = self.edge_mask.detach().sigmoid()
        print(edge_mask)

        self.__clear_masks__()

        return edge_mask, epoch_losses

    def __repr__(self):
        return f'{self.__class__.__name__}()'

参考资料

gnn-explainer
图神经网络的可解释性方法及GNNexplainer代码示例
Pytorch实现GNNExplainer
How to Explain Graph Neural Network — GNNExplainer
https://gist.github.com/hongxuenong/9f7d4ce96352d4313358bc8368801707

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【图神经网络】GNNExplainer代码解读及其PyG实现