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, ARIMA and the 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)
Changes Since Last Submission: (this revision)
- Defined neighbours $\mathcal{U}_v$
- footnote for $q=12$
- footnote for $M=20$
- Provided clarification for Problem 2.1
- footnote contrasting single-step and multi-step forecasting results of mspace
- Added a paragraph on dataset diversity in Discusssion
- Mentioned that mspace-SN is essentially a Markov chain with Gaussian transition function
These changes are all marked in `magenta` in the revised version.
(previous revision)
- The notations paragraph is updated
- Added a paragraph on paper organization towards the end of Introduction.
- Sec. 2 (Methodology) has been rewritten to improve clarity.
- Added a figure (Fig 1) to aid the explanation of the Markov chain approximation
- Problem 2.1 has been rewritten in terms of the state and sampling functions
- Assumption 2.2 is modified in light of the reviewers' comments
- The references are updated to replace the arXiv versions with the conference/journal versions
- Some typos are fixed
Assigned Action Editor: ~Olgica_Milenkovic1
Submission Number: 3397
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