Causal Discovery from Time Series with Hybrids of Constraint-Based and Noise-Based Algorithms

TL;DR

This work tackles causal discovery from observational time series when individual method families struggle under unvalidated assumptions. It proposes two hybrid classes, NBCB (orient-then-prune) and CBNB (prune-then-orient), that integrate noise-based orientation with constraint-based pruning in two complementary orders to recover window or extended summary causal graphs. The framework provides theoretical guarantees under standard assumptions and analyzes failure modes under adjacency faithfulness and identifiable functional model constraints, demonstrating robustness across diverse datasets. Extensive simulations, Lotka-Volterra ecological data, and nine real IT datasets—including two novel IT monitoring datasets—show that NBCB/CBNB achieve competitive or superior performance to baselines, particularly when some assumptions are violated. The results offer a practical, scalable toolkit for time-series causal discovery with improved resistance to common methodological limitations and broad applicability to complex dynamical systems.

Abstract

Constraint-based methods and noise-based methods are two distinct families of methods proposed for uncovering causal graphs from observational data. However, both operate under strong assumptions that may be challenging to validate or could be violated in real-world scenarios. In response to these challenges, there is a growing interest in hybrid methods that amalgamate principles from both methods, showing robustness to assumption violations. This paper introduces a novel comprehensive framework for hybridizing constraint-based and noise-based methods designed to uncover causal graphs from observational time series. The framework is structured into two classes. The first class employs a noise-based strategy to identify a super graph, containing the true graph, followed by a constraint-based strategy to eliminate unnecessary edges. In the second class, a constraint-based strategy is applied to identify a skeleton, which is then oriented using a noise-based strategy. The paper provides theoretical guarantees for each class under the condition that all assumptions are satisfied, and it outlines some properties when assumptions are violated. To validate the efficacy of the framework, two algorithms from each class are experimentally tested on simulated data, realistic ecological data, and real datasets sourced from diverse applications. Notably, two novel datasets related to Information Technology monitoring are introduced within the set of considered real datasets. The experimental results underscore the robustness and effectiveness of the hybrid approaches across a broad spectrum of datasets.

Figures (9)

• Figure 1: Running example. Left: Dynamic structural causal model (dynamic SCM). Right: Associated full-time causal graph $\mathcal{G}^{\mathrm{f}}$ (FTCG).
• Figure 2: Illustration of the violation of the faithfulness and the adjacency faithfulness assumption. (a) violates the faithfulness assumption but satisfies the adjacency faithfulness assumption and (b) violates the adjacency faithfulness which implies that it violates the faithfulness assumption.
• Figure 3: Different causal graphs to represent the dynamic SCM in Equation (\ref{['eq:SCM']}): (a) window causal graph (WCG) with a maximal temporal lag equal to $2$, (b) extended summary causal graph (ECG), and (c) summary causal graph (SCG).
• Figure 4: Illustration of the NBCB algorithm for the running example. (a) Output of the NB1 step (b) Output of the CB1$^\prime$.
• Figure 5: Illustration of items (2) and (3) in Proposition \ref{['propNBCB']}.

Theorems & Definitions (20)

• Definition 1: Window Causal Graph, WCG
• Definition 2: Extended Summary Causal Graph, ECG
• Definition 3: Summary Causal Graph, SCG
• Definition 4: Causal Order of Instantaneous Nodes
• Theorem 1
• Proposition 1: Violation of Assumption \ref{['assum:adj_faithfulness']}
• Definition 5: Undirected Cycle Walk
• Definition 6: Undirected Cycle Group
• Theorem 2
• Proposition 2: Violation of Assumption \ref{['assum:semi_parametric']}