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。
-
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： n × n n×n n×n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。
- 在初始化
-
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：- 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。 - 将传入的模型预测输出
pred转为pred_label。 - 构建
ExplainModule，进行num_epochs轮训练（前向+反向传播）
- 取子图的
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：
这里需要说明的是marginalize为True的情况，参考论文中的Learning binary feature selector F:
- 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 X S X_S XS的经验边缘分布使用Monte Carlo方法来抽样得到 X = X S F X=X_S^F X=XSF. - 为了解决随机变量
X
X
X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
Z
Z
Z的确定性变换：
X
=
Z
+
(
X
S
−
Z
)
⊙
F
X=Z+(X_S-Z)\odot F
X=Z+(XS−Z)⊙F
s
.
t
.
∑
j
F
j
≤
K
F
s.t. \sum_{j}F_j\le K_F
s.t.j∑Fj≤KF
其中， Z Z Z是依据经验分布采样得到的 d d d维随机变量， K F K_F KF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,
}
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：文章来源：https://www.toymoban.com/news/detail-528314.html
- 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：文章来源地址https://www.toymoban.com/news/detail-528314.html
#!/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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