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Natural Counterfactuals With Necessary Backtracking

Guang-Yuan Hao, Jiji Zhang, Biwei Huang, Hao Wang, Kun Zhang

TL;DR

A novel optimization framework that permits but also controls the extent of backtracking with a naturalness criterion and a method for generating counterfactuals that are more feasible with respect to the actual data distribution is proposed.

Abstract

Counterfactual reasoning is pivotal in human cognition and especially important for providing explanations and making decisions. While Judea Pearl's influential approach is theoretically elegant, its generation of a counterfactual scenario often requires too much deviation from the observed scenarios to be feasible, as we show using simple examples. To mitigate this difficulty, we propose a framework of \emph{natural counterfactuals} and a method for generating counterfactuals that are more feasible with respect to the actual data distribution. Our methodology incorporates a certain amount of backtracking when needed, allowing changes in causally preceding variables to minimize deviations from realistic scenarios. Specifically, we introduce a novel optimization framework that permits but also controls the extent of backtracking with a naturalness criterion. Empirical experiments demonstrate the effectiveness of our method. The code is available at https://github.com/GuangyuanHao/natural_counterfactuals.

Natural Counterfactuals With Necessary Backtracking

TL;DR

A novel optimization framework that permits but also controls the extent of backtracking with a naturalness criterion and a method for generating counterfactuals that are more feasible with respect to the actual data distribution is proposed.

Abstract

Counterfactual reasoning is pivotal in human cognition and especially important for providing explanations and making decisions. While Judea Pearl's influential approach is theoretically elegant, its generation of a counterfactual scenario often requires too much deviation from the observed scenarios to be feasible, as we show using simple examples. To mitigate this difficulty, we propose a framework of \emph{natural counterfactuals} and a method for generating counterfactuals that are more feasible with respect to the actual data distribution. Our methodology incorporates a certain amount of backtracking when needed, allowing changes in causally preceding variables to minimize deviations from realistic scenarios. Specifically, we introduce a novel optimization framework that permits but also controls the extent of backtracking with a naturalness criterion. Empirical experiments demonstrate the effectiveness of our method. The code is available at https://github.com/GuangyuanHao/natural_counterfactuals.
Paper Structure (7 sections, 1 theorem, 2 equations, 2 figures)

This paper contains 7 sections, 1 theorem, 2 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Distance-based Theory
  3. Prior-based Theory
  4. Others
  5. Natural Generation
  6. New
  7. Experiments

Key Result

Theorem 3.1

With the model $<{\mathcal{M}}, p({\mathbf{U}})>$, the probability $p({\mathbf{B}}_{\mathbf{A}}|{\mathbf{e}})$ of a counterfactual condition "Given the evidence ${\mathbf{e}}$, if it were ${\mathbf{A}}$ then ${\mathbf{B}}$", can be predicted by the next two steps. ${\mathbf{C}}^*$ is the set of caus

Figures (2)

  • Figure 1: Causal relationship among exercise, BMI, and cardiometabolic risk.
  • Figure 2: Causal relationship among exercise, BMI, and cardiometabolic risk.

Theorems & Definitions (1)

  • Theorem 3.1: Partial Backtracking Counterfactuals