HGCN(O): A Self-Tuning GCN HyperModel Toolkit for Outcome Prediction in Event-Sequence Data

Fang Wang; Paolo Ceravolo; Ernesto Damiani

cs.LGJul 30, 2025

HGCN(O): A Self-Tuning GCN HyperModel Toolkit for Outcome Prediction in Event-Sequence Data

Authors: Fang Wang, Paolo Ceravolo, Ernesto Damiani

Organizations: College of Computing and Mathematical Sciences, Khalifa University, P.O. Box 127788, Abu Dhabi, United Arab Emirates · Department of Computer Science, University of Milan, Via Festa del Perdono 7, 20122, Milano, MI, Italy

Abstract

Outcome prediction from event sequence data requires effective use of information at two distinct semantic levels: attributes of individual events and attributes of the complete sequence. Although graph models can explicitly represent temporal relations between events, existing approaches commonly rely on predefined representations and manually configured architectures, with limited consideration of how event and sequence information should be incorporated at their corresponding GNN levels or how GNN models should be fitted to different datasets without manual tuning. We propose HGCN(O), an end to end self tuning graph toolkit for hierarchical information representation and automated model configuration. Its core T-GCN architecture processes event information at the node level and sequence information at the graph level, while O-GCN provides a one level reference for early integration of sequence attributes. TP-GCN and TE-GCN extend T-GCN with a pseudo informative duration embedding and a learned activity embedding, respectively. HGCN(O) integrates these architecture specific designs with hypermodel optimization to jointly determine model structure and training configuration. The core T-GCN achieves F1 scores of 1.0000 on two balanced benchmarks and a weighted F1 of 0.8639 on a highly imbalanced dataset, compared with 0.8318 for GAT and 0.8453 for TransformerConv. Prefix and ablation analyses further demonstrate its effectiveness for outcome prediction from incomplete sequences and quantify the contributions of temporal edge weights and graph level sequence attributes.

Figures & tables

Model	Role	Event Level Input	Sequence Level Input	Sequence Attribute Integration	Auxiliary Representation	Key Formulation
O-GCN	Reference	Event attributes	Sequence attributes replicated across nodes	Node level, before graph convolution	None	$\mathbb{V}_{G_{j}}^{O}=\left[\mathbb{V}_{G_{j}},\mathbf{1}_{n_{j}}\mathbf{v}_{G_{j}}^{\intercal}\right]$
T-GCN	Core model	Event attributes	Sequence attributes	Graph level, after pooling	None	$\mathcal{Z}_{G_{j}}=\left[\mathbf{z}_{G_{j}},\mathbf{v}_{G_{j}}^{(d)}\right]$
TP-GCN	Extension	Event attributes	Sequence attributes	Graph level, after pooling	Pseudo informative duration embedding	$\mathbb{H}_{G_{j}}^{TP}=\left[\mathbb{H}_{G_{j}}^{N},\mathbb{H}_{G_{j}}^{P}\right]$
TE-GCN	Extension	Event attributes	Sequence attributes	Graph level, after pooling	Learned activity embedding; optional pseudo embedding	$\mathbb{H}_{G_{j}}^{TE}=\left[\mathbb{H}_{G_{j}}^{N},\mathbb{H}_{G_{j}}^{E}\right]$ or $\left[\mathbb{H}_{G_{j}}^{N},\mathbb{H}_{G_{j}}^{P},\mathbb{H}_{G_{j}}^{E}\right]$

Table 1: Comparative Summary of HGCN(O) Model Variants

Component	Hyperparameter	Search Space
Architecture	Graph convolution layers	1-5 per applicable branch
	Graph convolution hidden units	32-256 per layer
	Fully connected layers	1-3 per applicable branch
	Fully connected hidden units	32-256 per layer
	TE embedding dimension	10-50
	Graph pooling	mean, max, add

Table 2: HGCN(O) Hyperparameter Search Space

Dataset	#Seq	#Act	#Cls	IR	Med( $l$ )	Range( $l$ )	Med( $T$ )	Graph attr	Node attr
BPI12-A	6,672	9	3	$\sim$ 1:1	6	3-7	14,579	1 numerical	universal: 2 categorical
BPI12-O	2,406	7	3	$\sim$ 1:1	5	4-30	20,542	1 numerical	universal: 2 categorical
Patients	2,140	10	6	36:1	7	4-9	8,505	3 numerical	specific: 3 numerical; 1 categorical
Patients	2,140	10	6	36:1	7	4-9	8,505	1 categorical	universal: 1 categorical

Table 3: Characteristics of the Evaluation Datasets

Dataset	Model	Accuracy	Macro Average			Weighted Average
Dataset	Model	Accuracy	Precision	Recall	F1	Precision	Recall	F1
BPI12-A	T-GCNConv	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000
	T-GraphConv	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000
	GAT	0.9610	0.9649	0.9612	0.9609	0.9651	0.9610	0.9609
	TransformerConv	0.9235	0.9338	0.9239	0.9228	0.9341	0.9235	0.9228
BPI12-O	T-GCNConv	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000

Table 4: Performance Comparison with GNN Baselines

	O-GCNConv			O-GraphConv			T-GCNConv			T-GraphConv
Class	Precision	Recall	F1	Precision	Recall	F1	Precision	Recall	F1	Precision	Recall	F1	Support
0	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	92
1	0.7838	1.0000	0.8788	0.7953	0.9828	0.8792	0.7838	1.0000	0.8788	0.7838	1.0000	0.8788	174
2	1.0000	1.0000	1.0000	0.625	1.0000	0.7692	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	5
3	0.9545	1.0000	0.9767	1.0000	0.9048	0.95	1.0000	0.9048	0.95	0.9524	0.9524	0.9524	21
4	0.8649	1.0000	0.9275	0.8611	0.9688	0.9118	0.9143	1.0000	0.9552	0.8889	1.0000	0.9412	32

Table 5: Class Specific Performance and Training Stability of HGCN(O) Models on the Imbalanced Patients Dataset

Figure 1: Training and test learning curves for the eight HGCN(O) configurations on the imbalanced Patients dataset over 300 epochs. The upper row shows O-GCNConv, T-GCNConv, TP-GCNConv, and TE-GCNConv, while the lower row shows the corresponding GraphConv configurations. For each model, the left panel reports the F1 score and the right panel reports the loss for the training and test sets.

Figure 2: Training and test learning curves for the selected HGCN(O) configurations on the balanced BPI12-A and BPI12-O datasets over 300 epochs. Rows correspond to the O-GCN, T-GCN, and TE-GCN architectures, while columns compare their GCNConv and GraphConv implementations. For each configuration, the left panel reports accuracy and the right panel reports loss on the training and test sets.

Dataset	Model	Prefix (%)	Accuracy	Macro Average			Weighted Average
Dataset	Model	Prefix (%)	Accuracy	Precision	Recall	F1	Precision	Recall	F1
BPI12-A	T-GCNConv	30	0.7114	0.7121	0.7110	0.7094	0.7122	0.7114	0.7096
		50	0.7286	0.7700	0.7279	0.7211	0.7704	0.7286	0.7217
		70	0.8396	0.8513	0.8390	0.8367	0.8511	0.8396	0.8369
		100	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000
		Cochran’s $Q=509.3361$ , $p=4.5221\times 10^{-110}$ ( $p<0.001$ )

Table 6: Predictive Performance of T-GCNConv and T-GraphConv Across Sequence Completion Levels on the BPI12-A/O Datasets

Dataset	Model	T-GCNConv							T-GraphConv
		Acc	Macro Average			Weighted Average			Acc	Macro Average			Weighted Average
		Acc	P	R	F1	P	R	F1	Acc	P	R	F1	P	R	F1
BPI12-A	Full	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000
	$-\mathbf{w}_{G_{j}}$	0.9625	0.9661	0.9627	0.9624	0.9663	0.9625	0.9624	0.9633	0.9654	0.9634	0.9632	0.9656	0.9633	0.9632
	$-\mathbf{v}_{G_{j}}$	0.9610	0.9649	0.9612	0.9609	0.9651	0.9610	0.9609	0.9610	0.9649	0.9612	0.9609	0.9651	0.9610	0.9609
BPI12-O	Full	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000

Table 7: Ablation Results of T-GCNConv and T-GraphConv on the Three Datasets

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Temporal Knowledge Graphs (TKGs) record how facts evolve over time, but forecasting future events on a TKG remains difficult for three reasons: (i) long-range temporal dependencies are hard to encode; (ii) events on different chains mutually excite or inhibit one another in ways that snapshot-level models cannot express; and (iii) inter-arrival times are heavy-tailed and statistically sparse, so deterministic time predictors are unreliable. We address these three issues with a single framework, the Group Attention Neural Hawkes Process (GAttNHP), built around three matched components. First, a self-attention encoder casts each subject--relation chain as a continuous-time point process and captures the lingering excitation of distant history. Second, a semantic soft-grouping module turns globally learnable Hawkes priors into an analytical cross-attention mask, so chains share excitation patterns through their latent group memberships rather than through exhaustive pairwise computation. Third, a Non-Crossing Quantile (NCQ) regression head replaces mean-based time prediction, providing calibrated, monotonically ordered quantile estimates that remain stable under heavy-tailed inter-arrival distributions. On six benchmark TKG datasets, GAttNHP improves over state-of-the-art baselines on both entity prediction and time prediction, and ablations confirm that its largest gains arise on the long-tail event chains where existing models fail most severely.

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