QUCE: The Minimisation and Quantification of Path-Based Uncertainty for Generative Counterfactual Explanations

TL;DR

QUCE addresses the interpretability gap in deep neural networks by minimizing path-based uncertainty in explanations and providing uncertainty quantification for counterfactuals. It introduces a three-term objective that jointly maximizes the likelihood of a target class, minimizes proximity distance, and minimizes uncertainty using a variational autoencoder framework, while relaxing the straight-line path constraint of traditional path-based methods. The method supports multiple paths and computes both path-level and counterfactual uncertainty, yielding explanations that align more closely with the data distribution as demonstrated on the Simulacrum, COVID infection, and Wisconsin Breast Cancer datasets. Experimental results show QUCE achieves lower path-based and counterfactual uncertainty and better reconstruction fidelity than DiCE and AGI baselines, indicating more reliable and realistic counterfactual explanations. The work contributes a cohesive framework that unites feature attribution with generative counterfactuals and lays groundwork for extending to noncontinuous features and automated parameter tuning in future work.

Abstract

Deep Neural Networks (DNNs) stand out as one of the most prominent approaches within the Machine Learning (ML) domain. The efficacy of DNNs has surged alongside recent increases in computational capacity, allowing these approaches to scale to significant complexities for addressing predictive challenges in big data. However, as the complexity of DNN models rises, interpretability diminishes. In response to this challenge, explainable models such as Adversarial Gradient Integration (AGI) leverage path-based gradients provided by DNNs to elucidate their decisions. Yet the performance of path-based explainers can be compromised when gradients exhibit irregularities during out-of-distribution path traversal. In this context, we introduce Quantified Uncertainty Counterfactual Explanations (QUCE), a method designed to mitigate out-of-distribution traversal by minimizing path uncertainty. QUCE not only quantifies uncertainty when presenting explanations but also generates more certain counterfactual examples. We showcase the performance of the QUCE method by comparing it with competing methods for both path-based explanations and generative counterfactual examples.

Figures (1)

• Figure 1: Here we illustrate two explanations produced on the Wisconsin Breast Cancer Dataset given by the proposed QUCE method. We observe how each feature influenced the change in the prediction as we attempted to generate a counterfactual example. This demonstrates how explanations are presented through the QUCE method, with the benefit of observing uncertainty in explanations presented. We see the left explanation has almost no uncertainty in generated explanation, whereas the right image demonstrates a large degree of uncertainty in the generated counterfactual explanation.

Theorems & Definitions (34)

• Definition 1: Counterfactual Example
• Definition 2: Counterfactual Generator
• Definition 3: Feature Attribution
• Definition 4: Counterfactual Feature Attribution
• Remark 1
• Definition 5: Proximity
• Definition 6: Counterfactual Uncertainty
• Definition 7: Feature-wise Counterfactual Uncertainty
• Definition 8: Counterfactual Explanation Uncertainty
• Proposition 1