Counterfactual Explanations for Arbitrary Regression Models
arXiv:2106.15212
Abstract
We present a new method for counterfactual explanations (CFEs) based on Bayesian optimisation that applies to both classification and regression models. Our method is a globally convergent search algorithm with support for arbitrary regression models and constraints like feature sparsity and actionable recourse, and furthermore can answer multiple counterfactual questions in parallel while learning from previous queries. We formulate CFE search for regression models in a rigorous mathematical framework using differentiable potentials, which resolves robustness issues in threshold-based objectives. We prove that in this framework, (a) verifying the existence of counterfactuals is NP-complete; and (b) that finding instances using such potentials is CLS-complete. We describe a unified algorithm for CFEs using a specialised acquisition function that composes both expected improvement and an exponential-polynomial (EP) family with desirable properties. Our evaluation on real-world benchmark domains demonstrate high sample-efficiency and precision.
arXiv comment20 pages, 5 figures, 3 tables
References in corpus (11)
- Practical Bayesian Optimization of Machine Learning Algorithms
- Categorical Reparameterization with Gumbel-Softmax
- Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations
- The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables
- Gaussian Process Optimization in the Bandit Setting: No Regret and Experimental Design
- Actionable Recourse in Linear Classification
- The Hidden Assumptions Behind Counterfactual Explanations and Principal Reasons
- Learning Model-Agnostic Counterfactual Explanations for Tabular Data
- Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers
- Fair lending needs explainable models for responsible recommendation
- On the computation of counterfactual explanations -- A survey