arXiv：cs.LG· Fabian Galis, Darian Onchis, Pedro Real Jurado·· 3 小时前AI 评分28
Ψ-Resilience：基于一维拓扑信号的无模型特征重要性方法
$\Psi$-Resilience: Model-Free Feature Importance from 1D Topological Signals
AI 导读
研究者提出 Ψ-Resilience，一种无需预测模型的特征重要性方法，通过估计类条件密度并沿特征轴取逐点绝对差构建类分歧景观，再用该一维信号的 0 维持续同调定义韧性泛函，聚合在用户设定稳健尺度内幸存的拓扑特征。在具有已知真实重要性的合成数据上，其 Spearman 秩相关最高达 0.8，与 SHAP、互信息等方法表现相当；在无真实标签的真实数据集上相关性最高达 0.9。
正文
Abstract:We introduce $\Psi$-Resilience, a model-free feature importance method that derives explanations directly from the data itself via 1D topological signals. Our method constructs a class-disagreement landscape by estimating class-conditional densities and taking their pointwise absolute difference along the feature axis. Then, the 0-dimensional persistence of this 1D signal defines a resilience functional that aggregates only those topological features that survive perturbations up to a robustness scale which is set by the user. This gives us a context-robust importance score that is inherently auditable via the underlying 1D landscapes and their persistence. We evaluate our method on both synthetic and real datasets. On synthetic generators with specified ground-truth importance, $\Psi$-Resilience recovers the ranking of features with high fidelity, achieving Spearman rank correlations up to 0.8 and performing competitively with multiple feature importance methods, including SHAP and mutual information. On real datasets with no known ground truth, our technique agrees with these methods, with correlations up to 0.9. These results show that $\Psi$-Resilience is a stable explanation method that enables rigorous, distribution-level auditing of feature importance without relying on a predictive model.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.02299 [cs.LG] |
| (or arXiv:2610.02299v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.02299 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Fabian Galis [view email]
[v1]
Thu, 1 Oct 2026 17:51:40 UTC (129 KB)
来源：arXiv：cs.LG · arxiv.org