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

Harshavardhan Kamarthi, Lingkai Kong, Alexander Rodriguez, Chao Zhang, B Aditya Prakash

TL;DR

This paper tackles probabilistic forecasting for multivariate time-series by jointly learning a stochastic graph structure and forecast distributions. It introduces STOIC, a neural-process-inspired framework that encodes individual series with uncertainty, generates a stochastic relation graph, refines representations through a recurrent graph encoder, leverages past-pattern references via a Reference Correlation Network, and decodes forecasts using an adaptive combination of graph-aware embeddings. The model achieves state-of-the-art accuracy and calibration across diverse datasets, and demonstrates robustness to noise through explicit uncertainty modeling. Beyond forecasting, STOIC uncovers meaningful relational patterns (e.g., sector correlations, sensor proximity, geographical mobility) that align with domain knowledge, highlighting its practical utility for interpretable, calibrated multivariate forecasting.

Abstract

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.

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

TL;DR

This paper tackles probabilistic forecasting for multivariate time-series by jointly learning a stochastic graph structure and forecast distributions. It introduces STOIC, a neural-process-inspired framework that encodes individual series with uncertainty, generates a stochastic relation graph, refines representations through a recurrent graph encoder, leverages past-pattern references via a Reference Correlation Network, and decodes forecasts using an adaptive combination of graph-aware embeddings. The model achieves state-of-the-art accuracy and calibration across diverse datasets, and demonstrates robustness to noise through explicit uncertainty modeling. Beyond forecasting, STOIC uncovers meaningful relational patterns (e.g., sector correlations, sensor proximity, geographical mobility) that align with domain knowledge, highlighting its practical utility for interpretable, calibrated multivariate forecasting.

Abstract

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.
Paper Structure (30 sections, 13 equations, 4 figures, 4 tables)

This paper contains 30 sections, 13 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Problem Formulation
  4. Overview
  5. Probabilistic Time-series Encoder
  6. Probabilistic Graph Generation Module
  7. Recurrent Graph Neural Encoder
  8. Reference Correlation Network
  9. Adaptive Distribution Decoder
  10. Training and Inference
  11. Experiment Setup
  12. Baselines
  13. Datasets
  14. Evaluation Metrics
  15. Forecast Accuracy and Calibration
  16. ...and 15 more sections

Figures (4)

  • Figure 1: Overview of StoIC's pipeline. Probabilistic Time-series encoder encodes the input time-series into stochastic latent embeddings which are used to learn the relational graph. The relational graph is leveraged by Recurrent Graph Neural Encoder to model both temporal and structural patterns of multivariate time-series represented by Graph-refined embeddings. Reference Correlation Network extracts similar patterns from past data in form of RCN embeddings. Finally, the decoder uses Graph-refined embeddings and RCN embeddings to derive the parameters of the forecast distribution.
  • Figure 2: % increase in CRPS with an increase in gaussian Noise ($\rho$) added to the input sequence. Performance decrease of StoIC is significantly lower than most of the baselines.
  • Figure 3: StoIC is better adapted to noise than other ablation variants. % increase in CRPS of StoIC and ablation variants with an increase in gaussian Noise ($\rho$) added to the input sequence.
  • Figure 4: Most confident edges ($\theta > 0.8$) of state relation graph generated by StoIC for Epidemic Forecasting tasks. Note that most edges connect US states which have geographical proximity.