CorrectAndSmooth

gtrick.dgl.CorrectAndSmooth(num_correction_layers, correction_alpha, num_smoothing_layers, smoothing_alpha, autoscale=True, scale=1.0)

Bases: nn.Module

The correct and smooth (C&S) post-processing model from the "Combining Label Propagation And Simple Models Out-performs Graph Neural Networks paper, where soft predictions \(\mathbf{Z}\) (obtained from a simple base predictor) are first corrected based on ground-truth training label information \(\mathbf{Y}\) and residual propagation

\[ \mathbf{e}^{(0)}_i = \begin{cases} \mathbf{y}_i - \mathbf{z}_i, \text{if }i \text{ is training node,}\\ \mathbf{0}, \text{else} \end{cases} \]

\[ \mathbf{E}^{(\ell)} = \alpha_1 \mathbf{D}^{-1/2}\mathbf{A} \mathbf{D}^{-1/2} \mathbf{E}^{(\ell - 1)} + (1 - \alpha_1) \mathbf{E}^{(\ell - 1)} \]

\[ \mathbf{\hat{Z}} = \mathbf{Z} + \gamma \cdot \mathbf{E}^{(L_1)} \]

where \(\gamma\) denotes the scaling factor (either fixed or automatically determined), and then smoothed over the graph via label propagation

\[ \mathbf{\hat{z}}^{(0)}_i = \begin{cases} \mathbf{y}_i, \text{if }i\text{ is training node,}\\ \mathbf{\hat{z}}_i, \text{else} \end{cases} \]

\[ \mathbf{\hat{Z}}^{(\ell)} = \alpha_2 \mathbf{D}^{-1/2}\mathbf{A} \mathbf{D}^{-1/2} \mathbf{\hat{Z}}^{(\ell - 1)} + (1 - \alpha_1) \mathbf{\hat{Z}}^{(\ell - 1)} \]

to obtain the final prediction \(\mathbf{\hat{Z}}^{(L_2)}\).

This trick is helpful for Node Level Task.

Note

To use this trick, call correct at first, then call smooth.

Examples: CorrectAndSmooth (DGL)

Parameters:

Name	Type	Description	Default
num_correction_layers	int	The number of propagations \(L_1\).	required
correction_alpha	float	The \(\alpha_1\) coefficient.	required
num_smoothing_layers	int	The number of propagations \(L_2\).	required
smoothing_alpha	float	The \(\alpha_2\) coefficient.	required
autoscale	bool	If set to True, will automatically determine the scaling factor \(\gamma\).	True
scale	float	The scaling factor \(\gamma\), in case autoscale = False.	1.0

correct(graph, y_soft, y_true, mask, edge_weight=None)

Parameters:

Name	Type	Description	Default
graph	dgl.DGLGraph	The graph.	required
y_soft	Tensor	The soft predictions \(\mathbf{Z}\) obtained from a simple base predictor.	required
y_true	Tensor	The ground-truth label information \(\mathbf{Y}\) of training nodes.	required
mask	LongTensor or BoolTensor	A mask or index tensor denoting which nodes were used for training.	required
edge_weight	Tensor	The edge weights.	None

Returns:

Type	Description
torch.Tensor	The corrected prediction.

smooth(graph, y_soft, y_true, mask, edge_weight=None)

Parameters:

Name	Type	Description	Default
graph	dgl.DGLGraph	The graph.	required
y_soft	Tensor	The soft predictions \(\mathbf{Z}\) obtained from a simple base predictor.	required
y_true	Tensor	The ground-truth label information \(\mathbf{Y}\) of training nodes.	required
mask	LongTensor or BoolTensor	A mask or index tensor denoting which nodes were used for training.	required
edge_weight	Tensor	The edge weights.	None

Returns:

Type	Description
torch.Tensor	The final prediction.