[Paper Review] On the computation of counterfactual explanations -- A survey

André Artelt, Barbara Hammer|arXiv (Cornell University)|Nov 15, 2019

Explainable Artificial Intelligence (XAI)21 references17 citations

TL;DR

This survey proposes model-specific methods for efficiently computing counterfactual explanations across diverse machine learning models, leveraging optimization techniques such as difference-of-convex programming and semi-definite programming to solve non-convex quadratically constrained quadratic programs (QCQPs). The key contribution is a systematic framework that improves computational efficiency and solution quality over model-agnostic approaches by exploiting model internals.

ABSTRACT

Due to the increasing use of machine learning in practice it becomes more and more important to be able to explain the prediction and behavior of machine learning models. An instance of explanations are counterfactual explanations which provide an intuitive and useful explanations of machine learning models. In this survey we review model-specific methods for efficiently computing counterfactual explanations of many different machine learning models and propose methods for models that have not been considered in literature so far.

Motivation & Objective

• To address the growing need for interpretable machine learning in high-stakes applications such as loan approval and predictive policing.
• To overcome the limitations of model-agnostic counterfactual methods, which are often computationally expensive and lack efficiency.
• To develop model-specific algorithms that exploit model internals to compute high-quality counterfactuals more efficiently.
• To extend existing methods to machine learning models not previously addressed in the literature.
• To provide a unified framework for computing counterfactuals via optimization, including non-convex QCQP and duality-based solutions.

Proposed method

• The paper formulates counterfactual generation as a constrained optimization problem minimizing a loss function for target prediction and a regularization term for proximity to the original input.
• It models the decision boundary of models with s.p.s.d. matrices, enabling representation of constraints as quadratic forms in the optimization problem.
• For non-convex QCQPs, the method applies the penalty convex-concave procedure (CCP) by approximating the concave part using first-order Taylor expansion around current iterates.
• It leverages duality theory to solve non-convex QCQPs with a single constraint by reformulating them as semi-definite programs (SDPs) with zero duality gap under strict feasibility.
• The approach uses difference-of-convex programming (DCP) to handle constraints defined as the difference of two convex quadratic forms.
• It enables efficient computation via iterative convex approximations, with initialization options including the original input or a feasible solution.

Experimental results

Research questions

• RQ1 How can counterfactual explanations be computed more efficiently by leveraging model-specific internal structures?
• RQ2 What optimization techniques are effective for solving non-convex QCQPs arising in counterfactual generation?
• RQ3 Can duality-based methods be applied to non-convex QCQPs to achieve exact or near-exact solutions?
• RQ4 Which machine learning models currently lack efficient counterfactual computation methods and how can they be addressed?
• RQ5 How do model-specific methods compare in quality and efficiency to model-agnostic approaches?

Key findings

• Model-specific methods significantly improve computational efficiency compared to model-agnostic approaches by utilizing model internals and tailored optimization.
• The penalty convex-concave procedure (CCP) provides a reliable approximation for non-convex QCQPs by iteratively solving convex subproblems.
• Non-convex QCQPs with a single constraint can be solved exactly via semi-definite programming (SDP) when strict feasibility is satisfied.
• The use of difference-of-convex programming (DCP) enables the formulation of complex decision boundaries as constraints in counterfactual optimization.
• The framework supports a wide range of models by expressing their decision boundaries through s.p.s.d. matrices, enabling systematic counterfactual computation.
• The method is generalizable and can be applied to models not previously considered in the literature, extending the scope of counterfactual explanation.