# Learning Graph Structures and Uncertainty for Accurate and Calibrated Time-series Forecasting

arXiv: https://arxiv.org/abs/2407.02641 · HTML: https://mlsanity.com/paper/2407.02641/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 34 references that are in the map.
- First posted on arXiv 2 Jul 2024.

## Builds on (most cited first, 19 of 19)

- [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)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Graph Neural Network-Based Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2106.06947/) (2021)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Learning Discrete Structures for Graph Neural Networks](https://mlsanity.com/paper/1903.11960/) (2019)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Discrete Graph Structure Learning for Forecasting Multiple Time Series](https://mlsanity.com/paper/2101.06861/) (2021)
- [Coupled Layer-wise Graph Convolution for Transportation Demand Prediction](https://mlsanity.com/paper/2012.08080/) (2020)
- [The Functional Neural Process](https://mlsanity.com/paper/1906.08324/) (2019)
- [When in Doubt: Neural Non-Parametric Uncertainty Quantification for Epidemic Forecasting](https://mlsanity.com/paper/2106.03904/) (2021)

## Abstract (arXiv)

Multi-variate time series forecasting is an important problem with a wide range of applications. Recent works model the relations between time-series as graphs and have shown that propagating information over the relation graph can improve time series forecasting. However, in many cases, relational information is not available or is noisy and reliable. Moreover, most works ignore the underlying uncertainty of time-series both for structure learning and deriving the forecasts resulting in the structure not capturing the uncertainty resulting in forecast distributions with poor uncertainty estimates. We tackle this challenge and introduce STOIC, that leverages stochastic correlations between time-series to learn underlying structure between time-series and to provide well-calibrated and accurate forecasts. Over a wide-range of benchmark datasets STOIC provides around 16% more accurate and 14% better-calibrated forecasts. STOIC also shows better adaptation to noise in data during inference and captures important and useful relational information in various benchmarks.