# The Gaussian Discriminant Variational Autoencoder (GdVAE): A Self-Explainable Model with Counterfactual Explanations

arXiv: https://arxiv.org/abs/2409.12952 · HTML: https://mlsanity.com/paper/2409.12952/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 53 references that are in the map.
- First posted on arXiv 19 Sep 2024.

## Builds on (most cited first, 30 of 40)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [Towards Robust Interpretability with Self-Explaining Neural Networks](https://mlsanity.com/paper/1806.07538/) (2018)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Counterfactual Visual Explanations](https://mlsanity.com/paper/1904.07451/) (2019)
- [Unsupervised Discovery of Interpretable Directions in the GAN Latent Space](https://mlsanity.com/paper/2002.03754/) (2020)
- [The Variational Fair Autoencoder](https://mlsanity.com/paper/1511.00830/) (2015)
- [GANalyze: Toward Visual Definitions of Cognitive Image Properties](https://mlsanity.com/paper/1906.10112/) (2019)
- [Explaining in Style: Training a GAN to explain a classifier in StyleSpace](https://mlsanity.com/paper/2104.13369/) (2021)
- [Semantic Hierarchy Emerges in Deep Generative Representations for Scene Synthesis](https://mlsanity.com/paper/1911.09267/) (2019)
- [Controlling generative models with continuous factors of variations](https://mlsanity.com/paper/2001.10238/) (2020)
- [NODE-GAM: Neural Generalized Additive Model for Interpretable Deep Learning](https://mlsanity.com/paper/2106.01613/) (2021)
- [Diffusion Models for Counterfactual Explanations](https://mlsanity.com/paper/2203.15636/) (2022)
- [Explanation by Progressive Exaggeration](https://mlsanity.com/paper/1911.00483/) (2019)
- [A Rigorous Study of Integrated Gradients Method and Extensions to Internal Neuron Attributions](https://mlsanity.com/paper/2202.11912/) (2022)
- [Guided Variational Autoencoder for Disentanglement Learning](https://mlsanity.com/paper/2004.01255/) (2020)
- [A Disentangling Invertible Interpretation Network for Explaining Latent Representations](https://mlsanity.com/paper/2004.13166/) (2020)
- [A Causal View on Robustness of Neural Networks](https://mlsanity.com/paper/2005.01095/) (2020)
- [Consistency Regularization for Variational Auto-Encoders](https://mlsanity.com/paper/2105.14859/) (2021)
- [STEEX: Steering Counterfactual Explanations with Semantics](https://mlsanity.com/paper/2111.09094/) (2021)
- [Class-Incremental Learning with Generative Classifiers](https://mlsanity.com/paper/2104.10093/) (2021)
- [DISSECT: Disentangled Simultaneous Explanations via Concept Traversals](https://mlsanity.com/paper/2105.15164/) (2021)
- [Consistent Counterfactuals for Deep Models](https://mlsanity.com/paper/2110.03109/) (2021)
- [Learning Disentangled Representation by Exploiting Pretrained Generative Models: A Contrastive Learning View](https://mlsanity.com/paper/2102.10543/) (2021)
- [ProtoVAE: A Trustworthy Self-Explainable Prototypical Variational Model](https://mlsanity.com/paper/2210.08151/) (2022)

## Built on by (most cited first, 5 of 5)

- [A Comprehensive Survey on Self-Interpretable Neural Networks](https://mlsanity.com/paper/2501.15638/) (2025)
- [Looking in the mirror: A faithful counterfactual explanation method for interpreting deep image classification models](https://mlsanity.com/paper/2509.16822/) (2025)
- [MaskDiME: Adaptive Masked Diffusion for Precise and Efficient Visual Counterfactual Explanations](https://mlsanity.com/paper/2602.18792/) (2026)
- [Counterfactual Explanations in Medical Imaging: Exploring SPN-Guided Latent Space Manipulation](https://mlsanity.com/paper/2507.19368/) (2025)
- [MedDiME: Efficient Latent Diffusion with Adaptive Masking for Medical Counterfactual Generation](https://mlsanity.com/paper/2609.15647/) (2026)

## Abstract (arXiv)

Visual counterfactual explanation (CF) methods modify image concepts, e.g, shape, to change a prediction to a predefined outcome while closely resembling the original query image. Unlike self-explainable models (SEMs) and heatmap techniques, they grant users the ability to examine hypothetical "what-if" scenarios. Previous CF methods either entail post-hoc training, limiting the balance between transparency and CF quality, or demand optimization during inference. To bridge the gap between transparent SEMs and CF methods, we introduce the GdVAE, a self-explainable model based on a conditional variational autoencoder (CVAE), featuring a Gaussian discriminant analysis (GDA) classifier and integrated CF explanations. Full transparency is achieved through a generative classifier that leverages class-specific prototypes for the downstream task and a closed-form solution for CFs in the latent space. The consistency of CFs is improved by regularizing the latent space with the explainer function. Extensive comparisons with existing approaches affirm the effectiveness of our method in producing high-quality CF explanations while preserving transparency. Code and models are public.