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Explaining Bayesian Networks in Natural Language using Factor Arguments. Evaluation in the medical domain

Jaime Sevilla, Nikolay Babakov, Ehud Reiter, Alberto Bugarin

TL;DR

This paper introduces the notion of factor argument independence to address the outstanding question of defining when arguments should be presented jointly or separately and presents an algorithm that produces a list of all independent factor arguments ordered by their strength.

Abstract

In this paper, we propose a model for building natural language explanations for Bayesian Network Reasoning in terms of factor arguments, which are argumentation graphs of flowing evidence, relating the observed evidence to a target variable we want to learn about. We introduce the notion of factor argument independence to address the outstanding question of defining when arguments should be presented jointly or separately and present an algorithm that, starting from the evidence nodes and a target node, produces a list of all independent factor arguments ordered by their strength. Finally, we implemented a scheme to build natural language explanations of Bayesian Reasoning using this approach. Our proposal has been validated in the medical domain through a human-driven evaluation study where we compare the Bayesian Network Reasoning explanations obtained using factor arguments with an alternative explanation method. Evaluation results indicate that our proposed explanation approach is deemed by users as significantly more useful for understanding Bayesian Network Reasoning than another existing explanation method it is compared to.

Explaining Bayesian Networks in Natural Language using Factor Arguments. Evaluation in the medical domain

TL;DR

This paper introduces the notion of factor argument independence to address the outstanding question of defining when arguments should be presented jointly or separately and presents an algorithm that produces a list of all independent factor arguments ordered by their strength.

Abstract

In this paper, we propose a model for building natural language explanations for Bayesian Network Reasoning in terms of factor arguments, which are argumentation graphs of flowing evidence, relating the observed evidence to a target variable we want to learn about. We introduce the notion of factor argument independence to address the outstanding question of defining when arguments should be presented jointly or separately and present an algorithm that, starting from the evidence nodes and a target node, produces a list of all independent factor arguments ordered by their strength. Finally, we implemented a scheme to build natural language explanations of Bayesian Reasoning using this approach. Our proposal has been validated in the medical domain through a human-driven evaluation study where we compare the Bayesian Network Reasoning explanations obtained using factor arguments with an alternative explanation method. Evaluation results indicate that our proposed explanation approach is deemed by users as significantly more useful for understanding Bayesian Network Reasoning than another existing explanation method it is compared to.

Paper Structure

This paper contains 21 sections, 12 equations, 15 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. A proposal for explaining Bayesian Networks
  4. Preliminaries
  5. Factor arguments
  6. Step effect and factor argument effect
  7. Factor argument strength
  8. Splitting factor arguments
  9. Core algorithm overview
  10. Ways to overcome algorithm limitations
  11. Textual explanation with extracted factor arguments
  12. Explanation of Factor Argument steps
  13. Explanation of the whole Factor Argument
  14. Experimental results
  15. Human-driven evaluation of the explanation method in the medical domain
  16. ...and 6 more sections

Figures (15)

  • Figure 1: (a) An example of a Bayesian Network is the ASIA Network 10.2307/2345762. (b) Visualization of an undirected subgraph of the ASIA BN factor graph, determining the nodes to be used for the reasoning explanation given two evidence nodes (XRay Result = abnormal and Tuberculosis = absent) and a target node Lung cancer. (c) Visualization of Factor Argument: directed acyclic subgraph of a factor graph BN. (d) Possible textual explanation of reasoning.
  • Figure 2: Visualization of Step Effect calculation. The numerator is calculated by multiplying the initial factor by incoming evidence factors, then normalizing, and marginalizing by the direct predecessor nodes. The denominator is calculated by marginalizing by the direct predecessor nodes and normalizing. After division, the resulting factor is normalized. Note that for compactness of visualization, we replaced explicit names of node states with "yes" and "no" notation. "ToC", "Bronc", and "Dysp" are the abbreviations of the corresponding nodes.
  • Figure 3: Visualization of Factor Argument Effect calculation. Step Effect is recursively calculated from evidence nodes to target node consequently updating the beliefs of all variable nodes within the Factor Argument. Note that for compactness of visualization, we replaced explicit names of node states with "yes" and "no" notation."ToC", "Tub", and "Lung" are the abbreviations of the corresponding nodes.
  • Figure 4: The complex factor argument (FA) can be decomposed into two simpler FAs. This decomposition is a good approximation if the factor argument effect (FAE) of the complex argument is approximately similar to the product of the FAEs of the simpler arguments. Arguments of SE (ToC, L, S, etc) are the abbreviations of the corresponding nodes.
  • Figure 5: Mean absolute probability error of our approximation vs message passing, Spearman rho correlation coefficient, and calculation time from 200 runs of our algorithm with random target and evidence nodes with different BNs from bnlearn website (cancer, earthquake, survey, asia, sachs, child, alarm). We express the relations both in terms of the total BN node number and the treewidth. The calculations are performed with MC = 2.
  • ...and 10 more figures

Theorems & Definitions (9)

  • Definition 1: Factor Argument (FA)
  • Definition 2: Direct Predecessors in Factor Argument ($Pred_{FA}$)
  • Definition 3: Step Effect (SE)
  • Definition 4: Factor Argument Effect (FAE)
  • Definition 5: Factor Argument Strength (FAS)
  • Definition 6: Independent Factor Arguments
  • Definition 7: Approximate Independence of Factor Arguments
  • Definition 8: Factor Argument Distance (FAD)
  • Definition 9: Approximately Proper Factor Argument