  Users have the right to have their data deleted by third-party learned
systems, as codified by recent legislation such as the General Data Protection
Regulation (GDPR) and the California Consumer Privacy Act (CCPA). Such data
deletion can be accomplished by full re-training, but this incurs a high
computational cost for modern machine learning models. To avoid this cost, many
approximate data deletion methods have been developed for supervised learning.
Unsupervised learning, in contrast, remains largely an open problem when it
comes to (approximate or exact) efficient data deletion. In this paper, we
propose a density-ratio-based framework for generative models. Using this
framework, we introduce a fast method for approximate data deletion and a
statistical test for estimating whether or not training points have been
deleted. We provide theoretical guarantees under various learner assumptions
and empirically demonstrate our methods across a variety of generative methods.
