Riku Green

Alex O. Davies, Riku W. Green, Nirav S. Ajmeri et al.

The principal benefit of unsupervised representation learning is that a pre-trained model can be fine-tuned where data or labels are scarce. Existing approaches for graph representation learning are domain specific, maintaining consistent node and edge features across the pre-training and target datasets. This has precluded transfer to multiple domains. We present Topology Only Pre-Training (ToP), a graph pre-training method based on node and edge feature exclusion. We show positive transfer on evaluation datasets from multiple domains, including domains not present in pre-training data, running directly contrary to assumptions made in contemporary works. On 75% of experiments, ToP models perform significantly $p \leq 0.01$ better than a supervised baseline. Performance is significantly positive on 85.7% of tasks when node and edge features are used in fine-tuning. We further show that out-of-domain topologies can produce more useful pre-training than in-domain. Under ToP we show better transfer from non-molecule pre-training, compared to molecule pre-training, on 79% of molecular benchmarks. Against the limited set of other generalist graph models ToP performs strongly, including against models with many orders of magnitude larger. These findings show that ToP opens broad areas of research in both transfer learning on scarcely populated graph domains and in graph foundation models.

Riku Green, Grant Stevens, Zahraa Abdallah et al.

A key aspect of temporal domains is the ability to make predictions multiple time steps into the future, a process known as multi-step forecasting (MSF). At the core of this process is selecting a forecasting strategy, however, with no existing frameworks to map out the space of strategies, practitioners are left with ad-hoc methods for strategy selection. In this work, we propose Stratify, a parameterised framework that addresses multi-step forecasting, unifying existing strategies and introducing novel, improved strategies. We evaluate Stratify on 18 benchmark datasets, five function classes, and short to long forecast horizons (10, 20, 40, 80). In over 84% of 1080 experiments, novel strategies in Stratify improved performance compared to all existing ones. Importantly, we find that no single strategy consistently outperforms others in all task settings, highlighting the need for practitioners explore the Stratify space to carefully search and select forecasting strategies based on task-specific requirements. Our results are the most comprehensive benchmarking of known and novel forecasting strategies. We make code available to reproduce our results.

Riku Green, Huw Day, Zahraa S. Abdallah et al.

Multi-step forecasting is often described through a simple rule of thumb: recursive strategies are said to have high bias and low variance, while direct strategies are said to have low bias and high variance. We revisit this belief by decomposing the expected multi-step forecast error into three parts: irreducible noise, a structural approximation gap, and an estimation-variance term. For linear predictors we show that the structural gap is identically zero for any dataset. For nonlinear predictors, however, the repeated composition used in recursion can increase model expressivity, making the structural gap depend on both the model and the data. We further show that the estimation variance of the recursive strategy at any horizon can be written as the one-step variance multiplied by a Jacobian-based amplification factor that measures how sensitive the composed predictor is to parameter error. This perspective explains when recursive forecasting may simultaneously have lower bias and higher variance than direct forecasting. Experiments with multilayer perceptrons on the ETTm1 dataset confirm these findings. The results offer practical guidance for choosing between recursive and direct strategies based on model nonlinearity and noise characteristics, rather than relying on traditional bias-variance intuition.

Riku Green, Grant Stevens, Telmo de Menezes e Silva Filho et al.

Multi-step forecasting (MSF) in time-series, the ability to make predictions multiple time steps into the future, is fundamental to almost all temporal domains. To make such forecasts, one must assume the recursive complexity of the temporal dynamics. Such assumptions are referred to as the forecasting strategy used to train a predictive model. Previous work shows that it is not clear which forecasting strategy is optimal a priori to evaluating on unseen data. Furthermore, current approaches to MSF use a single (fixed) forecasting strategy. In this paper, we characterise the instance-level variance of optimal forecasting strategies and propose Dynamic Strategies (DyStrat) for MSF. We experiment using 10 datasets from different scales, domains, and lengths of multi-step horizons. When using a random-forest-based classifier, DyStrat outperforms the best fixed strategy, which is not knowable a priori, 94% of the time, with an average reduction in mean-squared error of 11%. Our approach typically triples the top-1 accuracy compared to current approaches. Notably, we show DyStrat generalises well for any MSF task.