Cause-effect inference through spectral independence in linear dynamical\n systems: theoretical foundations

2021/10/29 by Michel Besserve, Naji Shajarisales, Besserve, Michel +5
Chemistry · Computer Science · Neuroscience · #Bayesian Modeling and Causal Inference #Electrochemical Analysis and Applications #FOS: Computer and information sciences #Functional Brain Connectivity Studies #Machine Learning (stat.ML) #Methodology (stat.ME) #Molecular spectroscopy and chirality

paper · pdf · doi:10.48550/arxiv.2110.15595

openalex publication_date 2021/10/29 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

Distinguishing between cause and effect using time series observational data\nis a major challenge in many scientific fields. A new perspective has been\nprovided based on the principle of Independence of Causal Mechanisms (ICM),\nleading to the Spectral Independence Criterion (SIC), postulating that the\npower spectral density (PSD) of the cause time series is uncorrelated with the\nsquared modulus of the frequency response of the filter generating the effect.\nSince SIC rests on methods and assumptions in stark contrast with most causal\ndiscovery methods for time series, it raises questions regarding what\ntheoretical grounds justify its use. In this paper, we provide answers covering\nseveral key aspects. After providing an information theoretic interpretation of\nSIC, we present an identifiability result that sheds light on the context for\nwhich this approach is expected to perform well. We further demonstrate the\nrobustness of SIC to downsampling - an obstacle that can spoil Granger-based\ninference. Finally, an invariance perspective allows to explore the limitations\nof the spectral independence assumption and how to generalize it. Overall,\nthese results support the postulate of Spectral Independence is a well grounded\nleading principle for causal inference based on empirical time series.\n

Citations

• Telling cause from effect in deterministic linear dynamical systems
• Telling cause from effect based on high-dimensional observations
• Towards a Learning Theory of Cause-Effect Inference
• Measurement of Linear Dependence and Feedback between Multiple Time Series
• Investigating Causal Relations by Econometric Models and Cross-spectral Methods
• A theory of independent mechanisms for extrapolation in generative\n models

Related

• Telling cause from effect in deterministic linear dynamical systems
• Causal inference for temporal patterns
• Stationary Processes, Wiener-Granger Causality, and Matrix Spectral Factorization
• Quantitative causality analysis with coarsely sampled time series
• Causal Inference on Process Graphs, Part II: Causal Structure and Effect Identification