Adversarial Subspace Generation for Outlier Detection in High-Dimensional Data
Transactions on Machine Learning Research (TMLR)
Given a domain $\mathcal X$ that is a union of submanifolds $\lbrace S_i \rbrace_{i=1}^d$, how do you recover each one? We answer this in the axis-parallel case, where $\mathcal X \subseteq \mathbb R^d$ and every $S_i$ is generated by canonical vectors---think lines and planes parallel to the axes.
We first build the theoretical framework: Myopic Subspace Theory (MST) describes probability measures on $\mathcal X = \cup_{i=1}^d S_i$ through their marginals on each submanifold. On top of MST we build V-GAN, the first non-parametric probabilistic method for subspace selection---a generative model that, instead of images or text, generates the maps $\mathcal X \to S_i$. Across 42 real-world datasets, ensembles built on V-GAN subspaces improve one-class classification significantly over the competition.
Cite
@ARTICLE{cribeiro25adversarial,
AUTHOR = {Jose Cribeiro-Ramallo and Federico Matteucci and Paul Enciu and Alexander Jenke and Vadim Arzamasov and Thorsten Strufe and Klemens B{\"o}hm},
TITLE = {Adversarial Subspace Generation for Outlier Detection in High-Dimensional Data},
JOURNAL = {Transactions on Machine Learning Research},
YEAR = {2025},
}