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Generating Fine-Grained Causality in Climate Time Series Data for Forecasting and Anomaly Detection

Dongqi Fu, Yada Zhu, Hanghang Tong, Kommy Weldemariam, Onkar Bhardwaj, Jingrui He

TL;DR

The paper addresses the challenge of uncovering fine-grained causal interactions in complex climate time series, including instantaneous effects, by introducing Time-Respecting Bayesian Network augmented Neural Granger Causality (TBN Granger Causality) and an end-to-end generative framework called TacSas. TacSas uses a bi-level optimization to first infer time-specific instantaneous causal graphs via a DAG-constrained variational encoder–decoder, then integrate these graphs with neural Granger causality to forecast and detect anomalies on tensor time series $\mathcal{X} \in \mathbb{R}^{N \times D \times T}$. The method is evaluated on synthetic Lorenz-96 as ground-truth causality and climate benchmarks ERA5 and NOAA, where TacSas demonstrates improved forecasting accuracy (MAE) and anomaly-detection performance (AUC-ROC) over strong baselines, while revealing interpretable time-respecting causal structures. This work offers a principled approach to structure learning in high-dimensional spatiotemporal data and has practical implications for climate forecasting and extreme-weather alerts.

Abstract

Understanding the causal interaction of time series variables can contribute to time series data analysis for many real-world applications, such as climate forecasting and extreme weather alerts. However, causal relationships are difficult to be fully observed in real-world complex settings, such as spatial-temporal data from deployed sensor networks. Therefore, to capture fine-grained causal relations among spatial-temporal variables for further a more accurate and reliable time series analysis, we first design a conceptual fine-grained causal model named TBN Granger Causality, which adds time-respecting Bayesian Networks to the previous time-lagged Neural Granger Causality to offset the instantaneous effects. Second, we propose an end-to-end deep generative model called TacSas, which discovers TBN Granger Causality in a generative manner to help forecast time series data and detect possible anomalies during the forecast. For evaluations, besides the causality discovery benchmark Lorenz-96, we also test TacSas on climate benchmark ERA5 for climate forecasting and the extreme weather benchmark of NOAA for extreme weather alerts.

Generating Fine-Grained Causality in Climate Time Series Data for Forecasting and Anomaly Detection

TL;DR

The paper addresses the challenge of uncovering fine-grained causal interactions in complex climate time series, including instantaneous effects, by introducing Time-Respecting Bayesian Network augmented Neural Granger Causality (TBN Granger Causality) and an end-to-end generative framework called TacSas. TacSas uses a bi-level optimization to first infer time-specific instantaneous causal graphs via a DAG-constrained variational encoder–decoder, then integrate these graphs with neural Granger causality to forecast and detect anomalies on tensor time series . The method is evaluated on synthetic Lorenz-96 as ground-truth causality and climate benchmarks ERA5 and NOAA, where TacSas demonstrates improved forecasting accuracy (MAE) and anomaly-detection performance (AUC-ROC) over strong baselines, while revealing interpretable time-respecting causal structures. This work offers a principled approach to structure learning in high-dimensional spatiotemporal data and has practical implications for climate forecasting and extreme-weather alerts.

Abstract

Understanding the causal interaction of time series variables can contribute to time series data analysis for many real-world applications, such as climate forecasting and extreme weather alerts. However, causal relationships are difficult to be fully observed in real-world complex settings, such as spatial-temporal data from deployed sensor networks. Therefore, to capture fine-grained causal relations among spatial-temporal variables for further a more accurate and reliable time series analysis, we first design a conceptual fine-grained causal model named TBN Granger Causality, which adds time-respecting Bayesian Networks to the previous time-lagged Neural Granger Causality to offset the instantaneous effects. Second, we propose an end-to-end deep generative model called TacSas, which discovers TBN Granger Causality in a generative manner to help forecast time series data and detect possible anomalies during the forecast. For evaluations, besides the causality discovery benchmark Lorenz-96, we also test TacSas on climate benchmark ERA5 for climate forecasting and the extreme weather benchmark of NOAA for extreme weather alerts.
Paper Structure (25 sections, 2 theorems, 20 equations, 7 figures, 3 tables)

This paper contains 25 sections, 2 theorems, 20 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminary
  3. TacSas: Discovering TBN Granger Causality via Generative Learning
  4. Inner Optimization of TacSas for Identifying Instantaneous Causal Relations in Time Series
  5. Outer Optimization of TacSas for Integrating Instantaneous Causality with Neural Granger
  6. Deployment of TacSas for Time Series Forecasting and Anomaly Detection
  7. Experiments
  8. Experiment Setup
  9. Forecasting Performance
  10. Anomaly Detection
  11. Related Work
  12. Conclusion
  13. Theoretical Analysis
  14. Proof of Lemma \ref{['eq:acyclicity']}
  15. Sketch Proof of Theorem \ref{['eq: discovery']}
  16. ...and 10 more sections

Key Result

Lemma 3.1

Let $\bm{A}^{(t)}$ be a weighted adjacency matrix (negative weights allowed). $\bm{A}^{(t)}$ has no $N$-length loops, if $\text{Tr}[(\bm{I} + \bm{A}^{(t)} \circ \bm{A}^{(t)})^{N}] - N =0$.

Figures (7)

  • Figure 1: (a) Tensor Time-Series Data: The Red Cell Means the Possible Anomaly. (b) Visualization of (Neural) Granger Causality's Time-Lagged Property without Instantaneous Effects.
  • Figure 2: Working Flow of TacSas: Discovering and Utilizing the TBN Granger Causality through a Bi-Level Optimization for Tensor Time Series Forecasting and Anomaly Detection.
  • Figure 3: Time-Respecting Bayesian Networks of at the Same Hour of Two Consecutive Days.
  • Figure 4: Accuracy of Causality Discovery in Lorenz-96 with Varying Number of Variables ($P$) and Timestamps ($T$).
  • Figure 5: Ablation of TacSas on Cross-Validation Group #2 (i.e., 2018 as testing)
  • ...and 2 more figures

Theorems & Definitions (3)

  • Lemma 3.1
  • Theorem 3.2
  • Remark 3.3