Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.00154 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916546873393152 |
|---|---|
| author | Subercaseaux, Bernardo Arenas, Marcelo Meel, Kuldeep S |
| author_facet | Subercaseaux, Bernardo Arenas, Marcelo Meel, Kuldeep S |
| contents | 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 $δ\in (0,1]$, for a random instance $\vec{z}$ that coincides with $\vec{x}$ on the features in $S$. Computing small $δ$-sufficient reasons ($δ$-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 $δ$-SRs unlikely. We propose the notion of $(δ, ε)$-SR, a simple relaxation of $δ$-SRs, and show that this kind of explanation can be computed efficiently over linear models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00154 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Probabilistic Explanations for Linear Models Subercaseaux, Bernardo Arenas, Marcelo Meel, Kuldeep S Artificial Intelligence Computational Complexity 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 $δ\in (0,1]$, for a random instance $\vec{z}$ that coincides with $\vec{x}$ on the features in $S$. Computing small $δ$-sufficient reasons ($δ$-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 $δ$-SRs unlikely. We propose the notion of $(δ, ε)$-SR, a simple relaxation of $δ$-SRs, and show that this kind of explanation can be computed efficiently over linear models. |
| title | Probabilistic Explanations for Linear Models |
| topic | Artificial Intelligence Computational Complexity |
| url | https://arxiv.org/abs/2501.00154 |