Probabilistic Explanations for Linear Models

• URL: http://arxiv.org/abs/2501.00154v1
• Date: Mon, 30 Dec 2024 21:59:16 GMT
• Title: Probabilistic Explanations for Linear Models
• Authors: Bernardo Subercaseaux, Marcelo Arenas, Kuldeep S Meel,
• Abstract summary: Formal XAI focuses on providing explanations with mathematical guarantees for the decisions made by machine learning models. We show that $(delta, epsilon)$-SR, a simple relaxation of $delta$-SRs, can be computed efficiently over linear models.
• Score: 35.437057227703846
• License:
• Abstract: Formal XAI is an emerging field that focuses on providing explanations with mathematical guarantees for the decisions made by machine learning models. A significant amount of work in this area is centered on the computation of "sufficient reasons". Given a model $M$ and an input instance $\vec{x}$, a sufficient reason for the decision $M(\vec{x})$ is a subset $S$ of the features of $\vec{x}$ such that for any instance $\vec{z}$ that has the same values as $\vec{x}$ for every feature in $S$, it holds that $M(\vec{x}) = M(\vec{z})$. Intuitively, this means that the features in $S$ are sufficient to fully justify the classification of $\vec{x}$ by $M$. For sufficient reasons to be useful in practice, they should be as small as possible, and a natural way to reduce the size of sufficient reasons is to consider a probabilistic relaxation; the probability of $M(\vec{x}) = M(\vec{z})$ must be at least some value $\delta \in (0,1]$, for a random instance $\vec{z}$ that coincides with $\vec{x}$ on the features in $S$. Computing small $\delta$-sufficient reasons ($\delta$-SRs) is known to be a theoretically hard problem; even over decision trees--traditionally deemed simple and interpretable models--strong inapproximability results make the efficient computation of small $\delta$-SRs unlikely. We propose the notion of $(\delta, \epsilon)$-SR, a simple relaxation of $\delta$-SRs, and show that this kind of explanation can be computed efficiently over linear models.

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