Probabilistic Linear Explanations

Problem

This work addresses a gap in the literature regarding probabilistic explainability specifically for continuous regression and binary classification tasks. The authors highlight the need for effective methods that can provide interpretable explanations while maintaining probabilistic rigor. The paper is a preprint and has not yet undergone peer review.

Method

The authors propose a unified framework for probabilistic explainability that leverages sparse, anchored linear models. Key components of the method include:

• Mapping: Instances are mapped to the Boolean hypercube, facilitating the interpretation of model outputs.
• Sparsity Budget: The framework enforces a prescribed sparsity budget denoted as $k$, which controls the number of features used in the explanation.
• Relevance Error: The minimization of relevance error is identified as a extit{Class NPPP}-hard problem when applied to neural networks, indicating the computational complexity involved in achieving optimal explanations.
• Surrogate Objective: The authors establish a relationship between relevance error and fidelity error, providing a theoretical foundation for their approach.
• Approaches: Two main techniques are employed:
  • Mixed Integer Programming (MIP): This method yields optimal empirical solutions with polynomial sample complexity, ensuring efficient computation of explanations.
  • Iterative Hard Thresholding (IHT): A polynomial-time algorithm that offers provable approximation guarantees, making it a viable alternative for generating explanations.

Results

The proposed method demonstrates a lower relevance error compared to state-of-the-art baselines, specifically LIME and MAPLE. However, the available text does not report quantitative results detailing the extent of improvement or specific metrics used in the evaluation.

Limitations

The authors do not report any limitations in their work. However, the absence of quantitative results may hinder the ability to fully assess the practical implications and performance of the proposed methods in diverse scenarios.

Why it matters

This research contributes to the field of interpretable machine learning by providing a robust framework for generating probabilistic explanations in regression and classification tasks. The implications of this work extend to enhancing the transparency of machine learning models, which is crucial for applications in sensitive domains such as healthcare and finance. By addressing the computational challenges associated with relevance error minimization, this framework may pave the way for more interpretable AI systems.