Node Feature Forecasting in Temporal Graphs: an Interpretable Online Algorithm
Abstract: In this paper, we propose an online algorithm **mspace** for forecasting node features in temporal graphs, which captures spatial cross-correlation among different nodes as well as the temporal auto-correlation within a node. The algorithm can be used for both probabilistic and deterministic multi-step forecasting, making it applicable for estimation and generation tasks. Comparative evaluations against various baselines, including temporal graph neural network (TGNN) models and classical Kalman filters, demonstrate that **mspace** performs at par with the state-of-the-art and even surpasses them on some datasets. Importantly, **mspace** demonstrates consistent performance across datasets with varying training sizes, a notable advantage over TGNN models that require abundant training samples to effectively learn the spatiotemporal trends in the data. Therefore, employing **mspace** is advantageous in scenarios where the training sample availability is limited.
Additionally, we establish theoretical bounds on multi-step forecasting error of **mspace** and show that it scales linearly with the number of forecast steps $q$ as $\mathcal{O}(q)$. For an asymptotically large number of nodes $n$, and timesteps $T$, the computational complexity of **mspace** grows linearly with both $n$, and $T$, i.e., $\mathcal{O}(nT)$, while its space complexity remains constant $\mathcal{O}(1)$.
We compare the performance of various **mspace** variants against ten recent TGNN baselines and two classical baselines, \texttt{ARIMA} and the \texttt{Kalman} filter across ten real-world datasets. Lastly, we have investigated the interpretability of different **mspace** variants by analyzing model parameters alongside dataset characteristics to jointly derive model-centric and data-centric insights.
Submission Length: Long submission (more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=LByC4hGIVQ
Changes Since Last Submission: 1. Added a line on Markov assumption limitation, p3 - line 106-107
2. Motivation, p1 - line 30-34
3. Comment on C and S, p3 - footnote 1
4. Brief summary of the state functions, p5 - line 155-158
5. Clarified that the shock is of arbitrary size, p3 - line 105
6. Clarify the meaning of interpretability, p1 - line 37-39
7. Update code link, p2 - line 75
8. Recursive forecasting using TGNN, p2 - line 49-50
9. Poor performance of Kalman filters when applied to shocks, p8 - line 260-263
10. Clarified the meaning of training size, p8 - footnote 4
11. Explaining why mspace-Tmu performs poorly on PEMSBAY and METRLA from data, p28 - line 671 - 674
12. Further explained Fig. 8, p11 - line 336-338
13. Add NVAR to Related Works, p7 - line 237-242
All the new additions are marked in magenta.
Assigned Action Editor: ~Olgica_Milenkovic1
Submission Number: 3903
Loading