Differentially Private Data Analysis of Social Networks via Restricted Sensitivity (1208.4586v2)

Abstract: We introduce the notion of restricted sensitivity as an alternative to global and smooth sensitivity to improve accuracy in differentially private data analysis. The definition of restricted sensitivity is similar to that of global sensitivity except that instead of quantifying over all possible datasets, we take advantage of any beliefs about the dataset that a querier may have, to quantify over a restricted class of datasets. Specifically, given a query f and a hypothesis H about the structure of a dataset D, we show generically how to transform f into a new query f_H whose global sensitivity (over all datasets including those that do not satisfy H) matches the restricted sensitivity of the query f. Moreover, if the belief of the querier is correct (i.e., D is in H) then f_H(D) = f(D). If the belief is incorrect, then f_H(D) may be inaccurate. We demonstrate the usefulness of this notion by considering the task of answering queries regarding social-networks, which we model as a combination of a graph and a labeling of its vertices. In particular, while our generic procedure is computationally inefficient, for the specific definition of H as graphs of bounded degree, we exhibit efficient ways of constructing f_H using different projection-based techniques. We then analyze two important query classes: subgraph counting queries (e.g., number of triangles) and local profile queries (e.g., number of people who know a spy and a computer-scientist who know each other). We demonstrate that the restricted sensitivity of such queries can be significantly lower than their smooth sensitivity. Thus, using restricted sensitivity we can maintain privacy whether or not D is in H, while providing more accurate results in the event that H holds true.

• The paper introduces "restricted sensitivity," a novel concept for differentially private data analysis that leverages dataset characteristics to potentially improve accuracy in social networks.
• It proposes a mechanism to construct a modified query whose global sensitivity matches the restricted sensitivity within a dataset hypothesis, with efficient methods for bounded-degree social graphs.
• Numerical results demonstrate that restricted sensitivity can significantly lower noise for important queries on social networks, such as subgraph counting, compared to traditional sensitivity measures.

An Expert Perspective on Differentially Private Data Analysis of Social Networks via Restricted Sensitivity

The paper under discussion explores the enhancement of accuracy in differentially private data analysis within social networks through a novel concept termed "restricted sensitivity." Unlike global and smooth sensitivity, restricted sensitivity capitalizes on presumed characteristics of datasets, allowing sensitivity considerations only over a subset of plausible datasets informed by such beliefs. This strategic approach seeks to provide improved accuracy while steadfastly maintaining differential privacy.

Overview and Methodology

The authors introduce a transformative mechanism for a given query $f$ and hypothesis $H$, constructing a modified query $f_H$ that aligns its global sensitivity with the query's restricted sensitivity within $H$. Notably, if the hypothesis $H$ accurately represents the dataset $D$, then $f_H(D)$ corresponds equivalently to $f(D)$.

The paper's methodology emphasizes social networks, represented by graphs and vertex attributes, as the practical playground for these theoretical endeavors. Despite the potentially high computational demands of the generic procedure, the paper outlines efficient techniques for scenarios where $\mathcal{H}$ is defined as bounded-degree graphs. Specifically, it offers projection-based techniques to construct $f_{\cal H}$ efficiently for critical subclasses of queries, such as subgraph counting and local profile queries. In such contexts, the restricted sensitivity can substantially undercut smooth sensitivity, allowing privacy assurances with augmented accuracy, should the dataset fall within the confines of the hypothesis.

Implications and Numerical Results

Practical implications arise prominently in the scenario where social networks, modeled as graphs, produce numerous natural queries whose global and smooth sensitivities are non-trivial. This paper's framework, particularly within the vertex adjacency model, allows for significant noise reduction. As an illustrative point, the restricted sensitivity of subgraph counting queries can be considerably lower than their smooth counterparts, with restricted sensitivity $RS_{f}(H_k) \leq k^{|P|-1}$ compared to high smooth sensitivity when assumptions of $H_k$ hold true.

The results provided substantiate the significance of restricted sensitivity not just in theory but in real applications by lowering the sensitivity for bounded-degree graph hypotheses. Through computational enhancements like efficient projection mappings, the paper's approach stands ready to reduce noise addition in queries, directly impacting the fidelity of the results.

Future Applications and Conclusion

The paper’s promising results hint at several prospective research avenues. The methodologies could be extended to other structural hypotheses beyond bound-degree, perhaps even tailored to specific social networks characteristics. Moreover, exploring uses of restricted sensitivity across broader AI applications or differentially private mechanisms remains a route brimming with potential.

In conclusion, the research sets a noteworthy precedent for leveraging domain-specific beliefs within social networks to reinforce privacy efforts while boosting data accuracy. This contribution is a significant step in refining mechanisms employed in the sensitive analysis of social networks, opening paths for future advancements in AI, particularly as privacy regulations become increasingly stringent.