# Counterfactual Explanation via Search in Gaussian Mixture Distributed Latent Space

arXiv: https://arxiv.org/abs/2307.13390 · HTML: https://mlsanity.com/paper/2307.13390/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 25 Jul 2023.

## Builds on (most cited first, 16 of 16)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Counterfactual Visual Explanations](https://mlsanity.com/paper/1904.07451/) (2019)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Learning Model-Agnostic Counterfactual Explanations for Tabular Data](https://mlsanity.com/paper/1910.09398/) (2019)
- [Explaining in Style: Training a GAN to explain a classifier in StyleSpace](https://mlsanity.com/paper/2104.13369/) (2021)
- [Inverse Classification for Comparison-based Interpretability in Machine Learning](https://mlsanity.com/paper/1712.08443/) (2017)
- [Rethinking Feature Distribution for Loss Functions in Image Classification](https://mlsanity.com/paper/1803.02988/) (2018)
- [Explaining Data-Driven Decisions made by AI Systems: The Counterfactual Approach](https://mlsanity.com/paper/2001.07417/) (2020)
- [Model-agnostic and Scalable Counterfactual Explanations via Reinforcement Learning](https://mlsanity.com/paper/2106.02597/) (2021)
- [A Two-Step Disentanglement Method](https://mlsanity.com/paper/1709.00199/) (2017)
- [Latent-CF: A Simple Baseline for Reverse Counterfactual Explanations](https://mlsanity.com/paper/2012.09301/) (2020)
- [A budget-constrained inverse classification framework for smooth classifiers](https://mlsanity.com/paper/1605.09068/) (2016)
- [Counterfactual Explanations via Latent Space Projection and Interpolation](https://mlsanity.com/paper/2112.00890/) (2021)

## Abstract (arXiv)

Counterfactual Explanations (CEs) are an important tool in Algorithmic Recourse for addressing two questions: 1. What are the crucial factors that led to an automated prediction/decision? 2. How can these factors be changed to achieve a more favorable outcome from a user's perspective? Thus, guiding the user's interaction with AI systems by proposing easy-to-understand explanations and easy-to-attain feasible changes is essential for the trustworthy adoption and long-term acceptance of AI systems. In the literature, various methods have been proposed to generate CEs, and different quality measures have been suggested to evaluate these methods. However, the generation of CEs is usually computationally expensive, and the resulting suggestions are unrealistic and thus non-actionable. In this paper, we introduce a new method to generate CEs for a pre-trained binary classifier by first shaping the latent space of an autoencoder to be a mixture of Gaussian distributions. CEs are then generated in latent space by linear interpolation between the query sample and the centroid of the target class. We show that our method maintains the characteristics of the input sample during the counterfactual search. In various experiments, we show that the proposed method is competitive based on different quality measures on image and tabular datasets -- efficiently returns results that are closer to the original data manifold compared to three state-of-the-art methods, which are essential for realistic high-dimensional machine learning applications.