A Query-Optimal Algorithm for Finding Counterfactuals

• URL: http://arxiv.org/abs/2207.07072v1
• Date: Thu, 14 Jul 2022 17:21:13 GMT
• Title: A Query-Optimal Algorithm for Finding Counterfactuals
• Authors: Guy Blanc, Caleb Koch, Jane Lange, Li-Yang Tan
• Abstract summary: We design an algorithm for finding counterfactuals with strong theoretical guarantees on its performance. [ S(f)O(Delta_f(xstar))cdot log d] queries to $f$ and returns an sl optimal counterfactual for $xstar$.
• Score: 14.934032347716995
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We design an algorithm for finding counterfactuals with strong theoretical guarantees on its performance. For any monotone model $f : X^d \to \{0,1\}$ and instance $x^\star$, our algorithm makes \[ {S(f)^{O(\Delta_f(x^\star))}\cdot \log d}\] queries to $f$ and returns {an {\sl optimal}} counterfactual for $x^\star$: a nearest instance $x'$ to $x^\star$ for which $f(x')\ne f(x^\star)$. Here $S(f)$ is the sensitivity of $f$, a discrete analogue of the Lipschitz constant, and $\Delta_f(x^\star)$ is the distance from $x^\star$ to its nearest counterfactuals. The previous best known query complexity was $d^{\,O(\Delta_f(x^\star))}$, achievable by brute-force local search. We further prove a lower bound of $S(f)^{\Omega(\Delta_f(x^\star))} + \Omega(\log d)$ on the query complexity of any algorithm, thereby showing that the guarantees of our algorithm are essentially optimal.

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