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Advancing Explainable AI with Causal Analysis in Large-Scale Fuzzy Cognitive Maps

Marios Tyrovolas, Nikolaos D. Kallimanis, Chrysostomos Stylios

TL;DR

This work tackles the bottleneck of computing total causal effects in large-scale Fuzzy Cognitive Maps (FCMs), where exhaustive causal-path enumeration is intractable. It introduces the Total Causal Effect Calculation for FCMs (TCEC-FCM) algorithm, which sorts nonzero weights and uses a binary-search over weights combined with BFS reachability checks to identify the first weight that establishes a causal path, achieving $O(n \cdot e \log e)$ time and $O(n^2)$ space. The approach provides a scalable, intrinsic XAI tool for causal analysis in FCMs and is validated on synthetic large-scale FCMs, showing substantial speedups over exhaustive methods and robust performance across densities. The findings broaden the practical applicability of FCMs in complex domains, and the authors outline future directions toward parallel implementations to push scalability to very large systems.

Abstract

In the quest for accurate and interpretable AI models, eXplainable AI (XAI) has become crucial. Fuzzy Cognitive Maps (FCMs) stand out as an advanced XAI method because of their ability to synergistically combine and exploit both expert knowledge and data-driven insights, providing transparency and intrinsic interpretability. This letter introduces and investigates the "Total Causal Effect Calculation for FCMs" (TCEC-FCM) algorithm, an innovative approach that, for the first time, enables the efficient calculation of total causal effects among concepts in large-scale FCMs by leveraging binary search and graph traversal techniques, thereby overcoming the challenge of exhaustive causal path exploration that hinder existing methods. We evaluate the proposed method across various synthetic FCMs that demonstrate TCEC-FCM's superior performance over exhaustive methods, marking a significant advancement in causal effect analysis within FCMs, thus broadening their usability for modern complex XAI applications.

Advancing Explainable AI with Causal Analysis in Large-Scale Fuzzy Cognitive Maps

TL;DR

This work tackles the bottleneck of computing total causal effects in large-scale Fuzzy Cognitive Maps (FCMs), where exhaustive causal-path enumeration is intractable. It introduces the Total Causal Effect Calculation for FCMs (TCEC-FCM) algorithm, which sorts nonzero weights and uses a binary-search over weights combined with BFS reachability checks to identify the first weight that establishes a causal path, achieving time and space. The approach provides a scalable, intrinsic XAI tool for causal analysis in FCMs and is validated on synthetic large-scale FCMs, showing substantial speedups over exhaustive methods and robust performance across densities. The findings broaden the practical applicability of FCMs in complex domains, and the authors outline future directions toward parallel implementations to push scalability to very large systems.

Abstract

In the quest for accurate and interpretable AI models, eXplainable AI (XAI) has become crucial. Fuzzy Cognitive Maps (FCMs) stand out as an advanced XAI method because of their ability to synergistically combine and exploit both expert knowledge and data-driven insights, providing transparency and intrinsic interpretability. This letter introduces and investigates the "Total Causal Effect Calculation for FCMs" (TCEC-FCM) algorithm, an innovative approach that, for the first time, enables the efficient calculation of total causal effects among concepts in large-scale FCMs by leveraging binary search and graph traversal techniques, thereby overcoming the challenge of exhaustive causal path exploration that hinder existing methods. We evaluate the proposed method across various synthetic FCMs that demonstrate TCEC-FCM's superior performance over exhaustive methods, marking a significant advancement in causal effect analysis within FCMs, thus broadening their usability for modern complex XAI applications.
Paper Structure (12 sections, 1 theorem, 5 equations, 6 figures, 2 tables, 1 algorithm)

This paper contains 12 sections, 1 theorem, 5 equations, 6 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Fuzzy Cognitive Maps
  4. Indirect and Total Causal Effect Analysis
  5. Total Causal Effect Calculation for FCMs (Tcec-Fcm)
  6. Conceptual Framework and Strategy
  7. Practical Implementation and Algorithmic Workflow
  8. Time and Space Complexity Analysis
  9. Experimental Results
  10. Execution Time Analysis in WCS
  11. Execution Time Analysis Across Various FCM Densities
  12. Conclusions

Key Result

Proposition 2.1

Consider $m$ causal paths from concept $C_{i}$ to $C_{j}$, each denoted as ($C_i \rightarrow C_{k_{1}^{l}} \rightarrow \ldots \rightarrow C_{k_{n}^{l}} \rightarrow C_j$), where $1 \leq l \leq m$ and $C_{k_{x}^{l}}$ are intermediate concepts within the $l^{th}$ causal path. The indirect effect of $C_ where $w(C_p, C_{p+1})$ indicates the causal weight between each pair of consecutive concepts $C_p$

Figures (6)

  • Figure 1: Example FCM with four concepts.
  • Figure 2: Step-by-step illustration of TCEC-FCM for the example of Fig.\ref{['fig:fcm_example']}.
  • Figure 3: Execution times of TCEC-FCM across fully interconnected FCM trials with 1000 concepts.
  • Figure 4: TCEC-FCM-LS
  • Figure 5: TCEC-FCM
  • ...and 1 more figures

Theorems & Definitions (1)

  • Proposition 2.1: Kosko1986-zl