# Radflow: A Recurrent, Aggregated, and Decomposable Model for Networks of Time Series

arXiv: https://arxiv.org/abs/2102.07289 · HTML: https://mlsanity.com/paper/2102.07289/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 48 references that are in the map.
- First posted on arXiv 15 Feb 2021.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [T-GCN: A Temporal Graph ConvolutionalNetwork for Traffic Prediction](https://mlsanity.com/paper/1811.05320/) (2018)
- [Know-Evolve: Deep Temporal Reasoning for Dynamic Knowledge Graphs](https://mlsanity.com/paper/1705.05742/) (2017)
- [Deep Transformer Models for Time Series Forecasting: The Influenza Prevalence Case](https://mlsanity.com/paper/2001.08317/) (2020)
- [Dynamic Graph Convolutional Networks](https://mlsanity.com/paper/1704.06199/) (2017)
- [Graph Transformer for Graph-to-Sequence Learning](https://mlsanity.com/paper/1911.07470/) (2019)
- [Deep and Confident Prediction for Time Series at Uber](https://mlsanity.com/paper/1709.01907/) (2017)
- [Graph2Seq: Graph to Sequence Learning with Attention-based Neural Networks](https://mlsanity.com/paper/1804.00823/) (2018)
- [Feature Driven and Point Process Approaches for Popularity Prediction](https://mlsanity.com/paper/1608.04862/) (2016)
- [Estimating Attention Flow in Online Video Networks](https://mlsanity.com/paper/1908.07123/) (2019)
- [WikiLinkGraphs: A Complete, Longitudinal and Multi-Language Dataset of the Wikipedia Link Networks](https://mlsanity.com/paper/1902.04298/) (2019)
- [AttentionFlow: Visualising Influence in Networks of Time Series](https://mlsanity.com/paper/2102.01974/) (2021)

## Built on by (most cited first, 3 of 3)

- [FormerTime: Hierarchical Multi-Scale Representations for Multivariate Time Series Classification](https://mlsanity.com/paper/2302.09818/) (2023)
- [MixSeq: Connecting Macroscopic Time Series Forecasting with Microscopic Time Series Data](https://mlsanity.com/paper/2110.14354/) (2021)
- [Contextually Enhanced ES-dRNN with Dynamic Attention for Short-Term Load Forecasting](https://mlsanity.com/paper/2212.09030/) (2022)

## Abstract (arXiv)

We propose a new model for networks of time series that influence each other. Graph structures among time series are found in diverse domains, such as web traffic influenced by hyperlinks, product sales influenced by recommendation, or urban transport volume influenced by road networks and weather. There has been recent progress in graph modeling and in time series forecasting, respectively, but an expressive and scalable approach for a network of series does not yet exist. We introduce Radflow, a novel model that embodies three key ideas: a recurrent neural network to obtain node embeddings that depend on time, the aggregation of the flow of influence from neighboring nodes with multi-head attention, and the multi-layer decomposition of time series. Radflow naturally takes into account dynamic networks where nodes and edges change over time, and it can be used for prediction and data imputation tasks. On real-world datasets ranging from a few hundred to a few hundred thousand nodes, we observe that Radflow variants are the best performing model across a wide range of settings. The recurrent component in Radflow also outperforms N-BEATS, the state-of-the-art time series model. We show that Radflow can learn different trends and seasonal patterns, that it is robust to missing nodes and edges, and that correlated temporal patterns among network neighbors reflect influence strength. We curate WikiTraffic, the largest dynamic network of time series with 366K nodes and 22M time-dependent links spanning five years. This dataset provides an open benchmark for developing models in this area, with applications that include optimizing resources for the web. More broadly, Radflow has the potential to improve forecasts in correlated time series networks such as the stock market, and impute missing measurements in geographically dispersed networks of natural phenomena.