[Paper Review] Towards Probabilistic Verification of Machine Unlearning

David Sommer, Liwei Song+2 more|arXiv (Cornell University)|Mar 9, 2020

Adversarial Robustness in Machine LearningComputer Science52 references36 citations

TL;DR

The paper proposes a probabilistic framework to verify machine unlearning in MLaaS using backdoor data poisoning, formalizing verification as a hypothesis test and showing high-confidence detection with practical participation levels.

ABSTRACT

The right to be forgotten, also known as the right to erasure, is the right of individuals to have their data erased from an entity storing it. The status of this long held notion was legally solidified recently by the General Data Protection Regulation (GDPR) in the European Union. Consequently, there is a need for mechanisms whereby users can verify if service providers comply with their deletion requests. In this work, we take the first step in proposing a formal framework to study the design of such verification mechanisms for data deletion requests -- also known as machine unlearning -- in the context of systems that provide machine learning as a service (MLaaS). Our framework allows the rigorous quantification of any verification mechanism based on standard hypothesis testing. Furthermore, we propose a novel backdoor-based verification mechanism and demonstrate its effectiveness in certifying data deletion with high confidence, thus providing a basis for quantitatively inferring machine unlearning. We evaluate our approach over a range of network architectures such as multi-layer perceptrons (MLP), convolutional neural networks (CNN), residual networks (ResNet), and long short-term memory (LSTM), as well as over 5 different datasets. We demonstrate that our approach has minimal effect on the ML service's accuracy but provides high confidence verification of unlearning. Our proposed mechanism works even if only a handful of users employ our system to ascertain compliance with data deletion requests. In particular, with just 5% of users participating, modifying half their data with a backdoor, and with merely 30 test queries, our verification mechanism has both false positive and false negative ratios below $10^{-3}$. We also show the effectiveness of our approach by testing it against an adaptive adversary that uses a state-of-the-art backdoor defense method.

Motivation & Objective

• Formalize machine unlearning verification as a hypothesis testing problem to quantify compliance with deletion requests.
• Introduce a backdoor-based mechanism where privacy-focused users poison a fraction of data to create verifiable traces.
• Provide theoretical guarantees and closed-form expressions for verification confidence under different server behaviors (adaptive/non-adaptive).
• Empirically validate the approach across multiple datasets and architectures showing high confidence with limited participation and test queries.

Proposed method

• Model unlearning verification as a hypothesis test comparing deleted vs. undeleted data scenarios.
• Use user-specific backdoor poisoning to create detectable traces in models trained on poisoned data.
• Define p and q as the backdoor success probabilities under H1 (not deleted) and H0 (deleted) respectively.
• Derive a closed-form expression for deletion confidence rho_A,alpha(s,n) based on binomial distributions and the test threshold.
• Analyze estimation of p and q from limited queries and provide relaxation for single-user scenarios.
• Evaluate across five datasets (EMNIST, FEMNIST, CIFAR10, ImageNet, AG News) and four architectures (MLP, CNN, ResNet, LSTM).

Experimental results

Research questions

• RQ1 Can a backdoor-based strategy enable high-confidence verification of data deletion in MLaaS?
• RQ2 How many backdoored test samples (n) and what participation fraction (f_user) are needed to achieve low false positive/negative rates?
• RQ3 How does an adaptive server defense against backdoors affect verification performance?
• RQ4 Do results generalize across diverse datasets and model architectures?
• RQ5 How can multiple privacy enthusiasts jointly improve verification without harming model utility?

Key findings

• The proposed backdoor-based mechanism achieves low false positive and false negative rates (below 1e-3) with 50% poisoned data and 30 test queries in their experiments.
• Across 5 datasets and 4 architectures, the approach demonstrates high verification confidence while maintaining model accuracy.
• An adaptive server employing backdoor defenses reduces backdoor success rates but remains capable of high-confidence unlearning verification.
• Even with only 5% participating users, the framework remains effective, and combining multiple users improves verification performance.
• The paper provides closed-form analytic expressions for deletion confidence and discusses practical estimation of p and q in real settings.