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A Model of Causal Explanation on Neural Networks for Tabular Data

Takashi Isozaki, Masahiro Yamamoto, Atsushi Noda

TL;DR

This work introduces CENNET, a framework that provides causal explanations for neural networks on tabular data by identifying characteristic correlated variables (CCVs) via structural causal models embedded in a neural latent layer (NNLU). It defines entropy-based explanation powers and derives both global explanations (per-neuron CCVs) and local explanations (instance-level CCV contributions) with an EMC/EEP-TEP formalism, enabling non-additive, combinatorial reasoning. Through synthetic and quasi-real experiments, CENNET demonstrates improved identification of direct causal factors over LIME, SHAP, ACV, and related methods, while maintaining scalability through parallelizable causal discovery. The approach paves the way for more causally faithful explanations and actionable interventions in NN-based predictions on tabular data, supported by rigorous information-theoretic quantification.

Abstract

The problem of explaining the results produced by machine learning methods continues to attract attention. Neural network (NN) models, along with gradient boosting machines, are expected to be utilized even in tabular data with high prediction accuracy. This study addresses the related issues of pseudo-correlation, causality, and combinatorial reasons for tabular data in NN predictors. We propose a causal explanation method, CENNET, and a new explanation power index using entropy for the method. CENNET provides causal explanations for predictions by NNs and uses structural causal models (SCMs) effectively combined with the NNs although SCMs are usually not used as predictive models on their own in terms of predictive accuracy. We show that CEN-NET provides such explanations through comparative experiments with existing methods on both synthetic and quasi-real data in classification tasks.

A Model of Causal Explanation on Neural Networks for Tabular Data

TL;DR

This work introduces CENNET, a framework that provides causal explanations for neural networks on tabular data by identifying characteristic correlated variables (CCVs) via structural causal models embedded in a neural latent layer (NNLU). It defines entropy-based explanation powers and derives both global explanations (per-neuron CCVs) and local explanations (instance-level CCV contributions) with an EMC/EEP-TEP formalism, enabling non-additive, combinatorial reasoning. Through synthetic and quasi-real experiments, CENNET demonstrates improved identification of direct causal factors over LIME, SHAP, ACV, and related methods, while maintaining scalability through parallelizable causal discovery. The approach paves the way for more causally faithful explanations and actionable interventions in NN-based predictions on tabular data, supported by rigorous information-theoretic quantification.

Abstract

The problem of explaining the results produced by machine learning methods continues to attract attention. Neural network (NN) models, along with gradient boosting machines, are expected to be utilized even in tabular data with high prediction accuracy. This study addresses the related issues of pseudo-correlation, causality, and combinatorial reasons for tabular data in NN predictors. We propose a causal explanation method, CENNET, and a new explanation power index using entropy for the method. CENNET provides causal explanations for predictions by NNs and uses structural causal models (SCMs) effectively combined with the NNs although SCMs are usually not used as predictive models on their own in terms of predictive accuracy. We show that CEN-NET provides such explanations through comparative experiments with existing methods on both synthetic and quasi-real data in classification tasks.
Paper Structure (16 sections, 2 theorems, 6 equations, 4 figures, 2 tables, 1 algorithm)

This paper contains 16 sections, 2 theorems, 6 equations, 4 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Preliminaries
  5. The Architecture
  6. Global Explanation with Causal Analysis
  7. Local Explanation with NNLU Neurons and CCVs
  8. Experiments
  9. Discussion
  10. Conclusion
  11. Background of Probabilistic Structural Causal Models
  12. Proof of Theorem 1
  13. The Details of Experiments
  14. Common Experimental Settings
  15. Synthetic Datasets
  16. ...and 1 more sections

Key Result

Theorem 1

In a given dataset $\mathcal{D}$ with a discrete random variable set $\bm{V}$, if there is a causal DAG for the set $\bm{V}$, the entropy of $X \in \bm{V}$ subject to the variable set CCVs of $X$ (CCV ($X$)), $H(X\,|\,\text{CCV}(X))$, achieves the lower limit of the conditional entropy given any set

Figures (4)

  • Figure 1: The nearest neighbor latent unit (NNLU) to output variable $Y$ in a neural network with input variable set $\bm{X}$. The proposed method causally analyzes the neurons in the NNLU.
  • Figure 2: The overview of CENNET method. In an NN model, CENNET extracts $p$ NNLU neurons and infers $p$ causal models consisting of input variables $\bm{X}$ for each NNLU neuron.
  • Figure 3: (a) Box plots for three experiments. Left: Non-Linear Additive. Middle: Non-Linear Non-Additive. Right: Category. Orange lines and green triangles in each box denote the median and mean, respectively. Lower average ranks are better. (b) Bar plots for two experiments. Left: Non-Linear Non-Additive. Right: Category. Blue and orange bars denote the top-1 and top-5 ratios, respectively.
  • Figure 4: The Alarm-DAG model for an example used in the Quasi-real data experiments.

Theorems & Definitions (4)

  • Definition 1
  • Theorem 1
  • Theorem 1
  • proof : Proof