Causal Identification in Time Series Models

2025-04-28

AI Summary

This paper addresses the identifiability of causal effects across arbitrary time lags in causal time-series graphs with latent variables. Due to infinite temporal unfolding of the graph structure, conventional approaches require unbounded historical windows, rendering identifiability checking computationally infeasible. We propose a novel method integrating do-calculus, temporal graph unfolding analysis, and structural causal model theory. Our key contribution is the first derivation of a **tight, finite time-window bound**, dependent solely on the number of variables per time step and the maximum lag. We prove that identifiability over infinite time horizons can be decided by analyzing only this constant-sized temporal segment. This reduces the infinite-graph identifiability problem to a constant-scale subgraph analysis, dramatically improving computational tractability. Moreover, our result provides the first theoretically rigorous finiteness guarantee for causal effect identification in time-series settings with latent confounding.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

In this paper, we analyze the applicability of the Causal Identification algorithm to causal time series graphs with latent confounders. Since these graphs extend over infinitely many time steps, deciding whether causal effects across arbitrary time intervals are identifiable appears to require computation on graph segments of unbounded size. Even for deciding the identifiability of intervention effects on variables that are close in time, no bound is known on how many time steps in the past need to be considered. We give a first bound of this kind that only depends on the number of variables per time step and the maximum time lag of any direct or latent causal effect. More generally, we show that applying the Causal Identification algorithm to a constant-size segment of the time series graph is sufficient to decide identifiability of causal effects, even across unbounded time intervals.

Problem

• Determining causal effects in time series with latent confounders
• Bounding time steps needed for causal identifiability analysis
• Applying Causal Identification algorithm to finite graph segments

Innovation

• Bounds causal effect identifiability in time series
• Uses constant-size graph segments for analysis
• Considers variable count and maximum time lag