PREF-VG: Topology-Conditioned Residual Adaptation for Probabilistic Multi-Horizon Student Engagement Forecasting

Forecasting student engagement can inform timely support in online education. However, the incremental predictive value of evolving behavioural topology beyond numerical temporal representations remains unclear. Here, behavioural engagement is operationalised through recorded activity in the virtual learning environment (VLE). We propose Prefix-based Residual Engagement Forecasting with Visibility Graphs (PREF-VG) for probabilistic multi-horizon forecasting. Within each observed window, natural visibility graphs yield ordered insertion-time descriptors of connection spans and local connectivity. A recurrent encoder summarises this sequence, and a gated residual adapter refines selected logit and log-mean parameters of a pretrained causal temporal convolutional network forecaster (Raw-TCN). The model estimates a hurdle negative-binomial click-count distribution and a binomial active-day marginal across four consecutive weeks from 56-day histories. Experiments on the Open University Learning Analytics Dataset used chronologically held-out course presentations and student-disjoint partitions. In the primary evaluation, under shared validation-based post-processing, results averaged across four horizons and five seeds showed that PREF-VG reduced click-count and active-day mean absolute errors by 3.24% and 4.19% relative to Raw-TCN, while increasing the area under the precision–recall curve for future inactivity from 0.7518 to 0.7686. On the primary test set, PREF-VG improved all five metrics over a parameter-matched raw-sequence adapter. In the alternative evaluation, gains over this control were supported for activity probabilities, inactivity ranking and active-day forecasts, with less certain click-count improvements. These comparisons support the incremental predictive value of insertion-time topology within the evaluated residual adaptation framework.