Profit-Based Counterfactual Explanations for Product Improvement - A Case Study of Manga Sales in Japan

Aug 20, 2026

Uploaded by Mia

Counterfactual explanation (CE) supports interpretability and decision-making from machine learning predictions, but standard CE relies on an exogenously chosen target value and an externally defined distance metric, whose validity and economic meaning remain unclear. This work formulates counterfactual explanation as profit maximization to overcome those gaps in regression-style settings. The proposed profit-based counterfactual explanation (PBCE) removes target specification by maximizing profit directly, while redefining the distance term as the cost of modifying product attributes.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages8

Reading Time20 min

AccessFree to download

Introduction

Interpretability and the role of counterfactual explanations

Limitations of target specification

Limitations of distance-function interpretation

From prediction changes to decision-objective optimization

Profit-Based Counterfactual Explanations for Product Improvement: A Case Study of Manga Sales in Japan* Keita Kinjo 1 and Takeshi Ebina2 arXiv :2607 .0 16 10v 1 [ cs .AI] 2 Jul 2026 Abstract—Counterfactual explanation (CE) is widely used to enhance the interpretability of machine learning models and support data-driven decision-making based on model predictions. However, existing CE methods typically require two exogenously specified inputs: a desired output value (target) and a distance function that quantifies changes in explanatory variables. In regression settings, neither the validity of target specification nor the practical interpretation of the distance metric has been sufficiently addressed. Furthermore, most existing CE methods focus on altering predictions rather than optimizing a decision objective, even though real-world decision-making often requires explicit objective maximization. To address these limitations, we formulate CE as a profit maximization problem in management and marketing contextsand propose a framework termed profit-based counterfactual explanation (PBCE). PBCE eliminates the need for exogenous target specification by directly maximizing profit as the primary optimization objective. Concurrently, the distance term is reinterpreted as the cost of modifying product attributes, providing a clear and economically grounded interpretation. I. INTRODUCTION Applications of artificial intelligence (AI) and machine learning have been rapidly expanding across a wide range of fields. In particular, machine-learning-based prediction and control methods are increasingly utilized in domains such as economics, healthcare, and marketing. Despite their strong predictive performance, many machine learning models possess highly complex internal structures and are often regarded as black-box models, in which the reasoning behind the predictions is not explicitly interpretable. Consequently, understanding why a particular prediction was made, or how decision-makers should respond to it, is often difficult. Therefore, considerable research has been focused on improving the interpretability and explainability of machine learning models [1] . Many approaches have been proposed for extracting human-interpretable information from blackbox models. Counterfactual explanations (CE) have emerged as a prominent framework for explaining individual predictions [2]–[4] . The basic concept of CE is as follows: Given a trained machine learning model and the predicted value for a specific instance, the CE identifies how explanatory variables should be modified to move the predicted outcome toward a * Research supported by JSPS KAKENHI Grant-in-Aid for Scientific Research. 1 K. Kinjo is with the Faculty of Business Studies, Kyoritsu Women’s University, 2-2-1, Hitotsubashi, Chiyoda-ku, Tokyo, 101-8437, Japan (corresponding author; phone: +81-3-3237-2159; [kkinjo@kyoritsu-wu.ac.jp](kkinjo@kyoritsu-wu.ac.jp)) 2T. Ebina is with the School of Commerce, Meiji University, 1-1, Kanda-surugadai, Chiyoda-ku, Tokyo, 101-8301, Japan [ebina@meiji.ac.jp](ebina@meiji.ac.jp) desired target value. Simultaneously, a constraint is typically imposed to ensure that the modified explanatory variables do not deviate excessively from their original input values. This is usually implemented by minimizing the distance between the original and counterfactual inputs. In other words, the CE problem is formulated as finding counterfactual instances that jointly minimize prediction loss with respect to the target value and distance from the original input. By presenting counterfactual examples, CE enables users to identify explanatory variables that play an important role in generating predictions. The concept of CE is also closely related to algorithmic recourse and has theoretical connections with research on adversarial example generation [4] . A wide range of CE methods have been proposed, differing in model type (e.g., differentiable vs. no

FAQs

What key limitations of existing counterfactual explanation methods does this paper address?

It addresses two main limitations: exogenous target specification and unclear interpretability of the distance metric, plus the broader issue that many methods change predictions rather than optimizing an explicit decision objective.

How does PBCE remove the need for an exogenous target value?

PBCE reformulates CE as a profit maximization problem, directly maximizing profit as the optimization objective rather than requiring a pre-specified desired target output value.

What does the distance term represent in the proposed framework?

The distance term is reinterpreted as the cost of modifying product attributes, giving an economically grounded meaning to the modification magnitude.

Aug 20, 2026

Uploaded by Mia

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