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

arXiv: https://arxiv.org/abs/2607.01610 · HTML: https://mlsanity.com/paper/2607.01610/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 19 references that are in the map.
- First posted on arXiv 2 Jul 2026.

## Builds on (most cited first, 8 of 8)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [Decisions, Counterfactual Explanations and Strategic Behavior](https://mlsanity.com/paper/2002.04333/) (2020)
- [Constrained Monotonic Neural Networks](https://mlsanity.com/paper/2205.11775/) (2022)
- [Robust Counterfactual Explanations in Machine Learning: A Survey](https://mlsanity.com/paper/2402.01928/) (2024)
- [Learning Recourse Costs from Pairwise Feature Comparisons](https://mlsanity.com/paper/2409.13940/) (2024)

## Abstract (arXiv)

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 contexts and 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.