Systems with Switching Causal Relations: A Meta-Causal Perspective

TL;DR

The paper introduces meta-causal models (MCM) to capture switching causal relations by clustering SCMs into meta-causal states defined via type-based edges in meta-causal frames. It formalizes meta-causal frames and states, and treats meta-causal models as finite-state machines that transition with environmental changes, enabling qualitative changes in causal graphs to be analyzed beyond classical SCMs. Key contributions include a formal typing scheme for causal edges, a method to discover meta-causal states in the bivariate case, and a stress-fatigue example showing richer dynamics than standard causality. The work enables more nuanced attribution and discovery of mechanistic changes in dynamic environments, with potential applications in health, economics, and AI systems that must reason about evolving causal structures.

Abstract

Most work on causality in machine learning assumes that causal relationships are driven by a constant underlying process. However, the flexibility of agents' actions or tipping points in the environmental process can change the qualitative dynamics of the system. As a result, new causal relationships may emerge, while existing ones change or disappear, resulting in an altered causal graph. To analyze these qualitative changes on the causal graph, we propose the concept of meta-causal states, which groups classical causal models into clusters based on equivalent qualitative behavior and consolidates specific mechanism parameterizations. We demonstrate how meta-causal states can be inferred from observed agent behavior, and discuss potential methods for disentangling these states from unlabeled data. Finally, we direct our analysis towards the application of a dynamical system, showing that meta-causal states can also emerge from inherent system dynamics, and thus constitute more than a context-dependent framework in which mechanisms emerge only as a result of external factors.

Figures (3)

• Figure 1: Meta-Causality Identifies the Policy as a Meta Root Cause. Agent $A$ intends to maintain its distance from agent $B$ by conditioning its position $A_X$ on the position $B_X$, which establishes a control mechanism, $A_X := f(B_X)$. In standard causal inference, we would infer $B_X\rightarrow A_X$ and, therefore, $B$ to be the root cause. Taking a meta-causal perspective reveals however, that $A_{\mathop{\mathrm{\bm{\pi}}}\nolimits}$ establishes the edge $B_X\rightarrow A_X$ in the first place ($\text{$A_{\mathop{\mathrm{\bm{\pi}}}\nolimits}$}\rightarrow\text{($B_X\rightarrow A_X$)}$) such that $A_{\mathop{\mathrm{\bm{\pi}}}\nolimits}$ is considered the root cause on the meta-level. (Best Viewed in Color)
• Figure 2: Mechanistic Decomposition as Meta-Causal States. (left) The effect of the stress level on itself (orange) plotted against the identity (blue; corresponding to a non-self-reinforcing effect). Once a certain threshold is reached, the function switches its behavior from self-suppressing to a self-reinforcing effect. (center) Contribution of the stress level mechanism for varying external stressors. Red arrows indicate a self-reinforcing effect, while green arrows indicate a suppressive effect. The gray area highlights the system configuration without external stressors. Although all states are governed by the same structural equations, our meta-causal analysis identifies the mechanistic difference and decomposes the corresponding initial conditions into different meta-causal states. (right) The standard SCM gets decomposed into different meta-causal states. While the graph adjacency remains the same, the different starting conditions identify different behavioral types of the causal mechanism. (Best viewed in color.)
• Figure 3: Sampled Mechanisms. The figure shows a selection of different randomly sampled mechanism distributions, ranging from one to up to four simultaneously present mechanisms. The gray dotted lines represent the generating ground truth mechanisms. (Best Viewed In Color)

Theorems & Definitions (6)

• Definition 1: Meta-Causal Frame
• Definition 2: Meta-Causal State
• Definition 3: Meta-Causal Model
• Definition 4: MCM Reducability
• Theorem D.1: Specific Criterion for Meta-Causal Reducability
• proof