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Causal Influence in Federated Edge Inference

Mert Kayaalp, Yunus Inan, Visa Koivunen, Ali H. Sayed

TL;DR

This work analyzes causal influence in federated edge inference where $K$ heterogeneous agents observe unlabeled streaming data to infer a true state $\theta^{\circ}$ via a fusion center. It extends the synchronous collaboration model with two asynchronous participation patterns and uses interventions $\text{do}(\cdot)$ to quantify each agent's impact on the joint decision, deriving closed-form expressions for the asymptotic log-belief ratio $\widetilde{\lambda}_{\infty}(\theta)$ and the causal impact $C_m$. Pre-intervention beliefs converge to the true hypothesis, while interventions yield measurable shifts captured by $C_m = 1 - \widetilde{\mu}_{\infty}(\theta^{\circ})$, with $\widetilde{\mu}_{\infty}$ expressed via $\widetilde{\lambda}_{\infty}(\theta)$. Theoretical results are validated on synthetic data and a real-world multi-camera crowd counting task (WILDTRACK), revealing how participation patterns and FC policies shape robustness to adversarial or faulty data and highlighting a trade-off between resilience and fair attribution in decision making.

Abstract

In this paper, we consider a setting where heterogeneous agents with connectivity are performing inference using unlabeled streaming data. Observed data are only partially informative about the target variable of interest. In order to overcome the uncertainty, agents cooperate with each other by exchanging their local inferences with and through a fusion center. To evaluate how each agent influences the overall decision, we adopt a causal framework in order to distinguish the actual influence of agents from mere correlations within the decision-making process. Various scenarios reflecting different agent participation patterns and fusion center policies are investigated. We derive expressions to quantify the causal impact of each agent on the joint decision, which could be beneficial for anticipating and addressing atypical scenarios, such as adversarial attacks or system malfunctions. We validate our theoretical results with numerical simulations and a real-world application of multi-camera crowd counting.

Causal Influence in Federated Edge Inference

TL;DR

This work analyzes causal influence in federated edge inference where heterogeneous agents observe unlabeled streaming data to infer a true state via a fusion center. It extends the synchronous collaboration model with two asynchronous participation patterns and uses interventions to quantify each agent's impact on the joint decision, deriving closed-form expressions for the asymptotic log-belief ratio and the causal impact . Pre-intervention beliefs converge to the true hypothesis, while interventions yield measurable shifts captured by , with expressed via . Theoretical results are validated on synthetic data and a real-world multi-camera crowd counting task (WILDTRACK), revealing how participation patterns and FC policies shape robustness to adversarial or faulty data and highlighting a trade-off between resilience and fair attribution in decision making.

Abstract

In this paper, we consider a setting where heterogeneous agents with connectivity are performing inference using unlabeled streaming data. Observed data are only partially informative about the target variable of interest. In order to overcome the uncertainty, agents cooperate with each other by exchanging their local inferences with and through a fusion center. To evaluate how each agent influences the overall decision, we adopt a causal framework in order to distinguish the actual influence of agents from mere correlations within the decision-making process. Various scenarios reflecting different agent participation patterns and fusion center policies are investigated. We derive expressions to quantify the causal impact of each agent on the joint decision, which could be beneficial for anticipating and addressing atypical scenarios, such as adversarial attacks or system malfunctions. We validate our theoretical results with numerical simulations and a real-world application of multi-camera crowd counting.
Paper Structure (21 sections, 5 theorems, 73 equations, 10 figures, 3 algorithms)

This paper contains 21 sections, 5 theorems, 73 equations, 10 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Contributions
  3. Related Work
  4. Causal influence estimation
  5. Cooperative inference
  6. Federated Inference
  7. Synchronous Collaboration
  8. Two Asynchronous Scenarios
  9. Asymmetric communication
  10. Symmetric communication
  11. Causal Influence
  12. Theoretical Results
  13. Experimental Results
  14. Synthetic data
  15. Application: Multi-camera crowd counting
  16. ...and 6 more sections

Key Result

Theorem 1

For the synchronous as well as the symmetric and asymmetric asynchronous communication protocols discussed in Sec. sec:problem_formulation, the belief vector $\bm{\mu}_i$ converges to a steady-state probability mass function that places a value of $1$ on the true hypothesis $\theta^\circ$ almost sur

Figures (10)

  • Figure 1: Intelligent vehicles and infrastructure can collaborate to enhance awareness of road conditions. Real-time and spontaneous cooperation is crucial in this context, as it allows for immediate responses to dynamic conditions, and hence improving the safety and efficiency of transportation.
  • Figure 2: Visual representation of the federated inference framework. At each time instant $i$, $(a)$ each agent receives an external observation, $(b)$ processes it locally and transmits it to a fusion center (FC), and $(c)$ FC center broadcasts the combined soft-decision (belief) back to agents.
  • Figure 3: Visual representation of a hypothetical intervention $do(\bm{\psi}_{m,i} := \mu_m)$ on the graphical model in Fig. \ref{['fig:federated_intervention']}. Agent $m$ keeps sending information to the server with probability $p_m$, however, its belief is now fixed and is not dependent on any other variable.
  • Figure 4: Simulated log-belief ratios averaged over 1000 Monte Carlo (MC) simulations and theoretical expressions over time overlap with each other, verifying the derivations in Theorems \ref{['prop:sync_collab']}--\ref{['theorem:symmetric']}.
  • Figure 5: Causal impact of agent $m=1$ on the joint decision with changing participation probability $p_m$. Note that $p_m$ is constant for the synchronous case, and the corresponding constant line is also provided in the plot for comparison purposes.
  • ...and 5 more figures

Theorems & Definitions (9)

  • Theorem 1: Pre-intervention
  • proof
  • Theorem 2: Synchronous collaboration kayaalp2023causal
  • Theorem 3: Asymmetric communication
  • proof
  • Theorem 4: Symmetric communication
  • proof
  • Corollary 1: Comparison of asynchronous scenarios
  • proof