Differentially Private Explanations for Clusters

Abstract: The dire need to protect sensitive data has led to various flavors of privacy definitions. Among these, Differential privacy (DP) is considered one of the most rigorous and secure notions of privacy, enabling data analysis while preserving the privacy of data contributors. One of the fundamental tasks of data analysis is clustering , which is meant to unravel hidden patterns within complex datasets. However, interpreting clustering results poses significant challenges, and often necessitates an extensive analytical process. Interpreting clustering results under DP is even more challenging, as analysts are provided with noisy responses to queries, and longer, manual exploration sessions require additional noise to meet privacy constraints. While increasing attention has been given to clustering explanation frameworks that aim at assisting analysts by automatically uncovering the characteristics of each cluster, such frameworks may also disclose sensitive information within the dataset, leading to a breach in privacy. To address these challenges, we present DPClustX, a framework that provides explanations for black-box clustering results while satisfying DP. DPClustX takes as input the sensitive dataset alongside privately computed clustering labels, and outputs a global explanation, emphasizing prominent characteristics of each cluster while guaranteeing DP. We perform an extensive experimental analysis of DPClustX on real data, showing that it provides insightful and accurate explanations even under tight privacy constraints.

• The paper introduces DPClustX to generate clear and private explanations for clustering through low-sensitivity score functions and candidate set construction.
• It employs a one-shot top-k method and the exponential mechanism to balance noise addition and explanation quality, achieving results similar to non-private methods.
• The framework demonstrates robust applicability in privacy-sensitive fields like healthcare and finance, enhancing transparency in unsupervised learning.

Differentially Private Explanations for Clusters

The paper "Differentially Private Explanations for Clusters" introduces a framework, DPClustX, designed to generate explanations for clustering results while adhering to differential privacy (DP) constraints. The necessity for such a framework stems from the increasing importance of privacy-preserving data analysis, especially with the prevalence of sensitive data across various domains such as healthcare and finance. Clustering, a fundamental data analysis task, is particularly challenging to explain under DP due to the inherent noise added to protect individual privacy, which often obfuscates the clarity of clustering outputs.

Framework Overview

DPClustX is aimed at providing insightful explanations for black-box clustering methods. Black-box clustering algorithms often produce results that are difficult to interpret because they offer limited transparency regarding the reasoning behind the groupings. The framework seeks to address this gap by offering explanations that are both informative and privacy-preserving.

The core innovations of DPClustX are threefold:

1. Low-Sensitivity Score Functions: Traditional measures of clustering explanation quality, such as interestingness, sufficiency, and diversity, tend to be highly sensitive. DPClustX offers low-sensitivity variants of these functions to enable their use under DP without significant loss of explanatory power or drastic distortion due to noise.
2. Candidate Set Construction: The framework efficiently constructs a pool of high-quality candidate attributes for each cluster, leveraging the one-shot top-k mechanism to privately select these attributes based on their suitability to explain the assigned clusters.
3. Privacy-Preserving Attribute Combination Selection: Using the exponential mechanism, DPClustX selects the top attribute combination from the candidate sets, balancing privacy constraints with the need for interpretability. Noise is added strategically only during the selection process, preserving most of the privacy budget for actual histogram generation of the selected attributes.

Experimental Evaluation

The experimental analysis demonstrates that DPClustX competently balances privacy and explanation quality across various datasets (US Census, Diabetes, and Stack Overflow Developer Survey) and clustering techniques. The results show that DPClustX can achieve comparable explanation quality to non-private methods when using a modest privacy budget. Moreover, the framework consistently selected attributes closely aligned with those chosen in the non-private setting, highlighting its robustness in maintaining interpretability under DP constraints.

Implications and Future Directions

DPClustX is a significant step forward in the field of privacy-preserving data analysis. Its ability to generate clear and privacy-respecting explanations for clustering algorithms can be particularly valuable in domains with stringent privacy requirements, such as healthcare and finance.

However, there are avenues for further research and enhancement:

• Multiple Explanations per Cluster: Extending the framework to support multiple explanations per cluster could offer richer insights but would require efficient management of complexity.
• Higher-Dimensional Histograms: Exploring multi-dimensional histograms may provide deeper analysis capabilities but pose challenges in terms of interpretability and complexity under DP.
• Discretization Effects: Evaluating the impact of different binning strategies on the framework's performance could further refine histogram accuracy and utility.

Overall, DPClustX lays the groundwork for advancements in privacy-preserving machine learning, particularly in making unsupervised learning models more transparent and trustworthy while maintaining rigorous privacy standards.