Revisiting Differentially Private Regression: Lessons From Learning Theory and their Consequences
This addresses the privacy-utility tradeoff problem for practitioners needing accurate private models, though it reveals a security tradeoff.
The paper tackles the poor accuracy of differentially private linear regression models by connecting differential privacy with stable learning theory, showing that output perturbation achieves accurate models even at ε=0.1 on medical data, but also finds this makes models more vulnerable to inversion attacks.
Private regression has received attention from both database and security communities. Recent work by Fredrikson et al. (USENIX Security 2014) analyzed the functional mechanism (Zhang et al. VLDB 2012) for training linear regression models over medical data. Unfortunately, they found that model accuracy is already unacceptable with differential privacy when $\varepsilon = 5$. We address this issue, presenting an explicit connection between differential privacy and stable learning theory through which a substantially better privacy/utility tradeoff can be obtained. Perhaps more importantly, our theory reveals that the most basic mechanism in differential privacy, output perturbation, can be used to obtain a better tradeoff for all convex-Lipschitz-bounded learning tasks. Since output perturbation is simple to implement, it means that our approach is potentially widely applicable in practice. We go on to apply it on the same medical data as used by Fredrikson et al. Encouragingly, we achieve accurate models even for $\varepsilon = 0.1$. In the last part of this paper, we study the impact of our improved differentially private mechanisms on model inversion attacks, a privacy attack introduced by Fredrikson et al. We observe that the improved tradeoff makes the resulting differentially private model more susceptible to inversion attacks. We analyze this phenomenon formally.