Improving the Variance of Differentially Private Randomized Experiments through Clustering
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866908381668704256 |
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| author | Javanmard, Adel Mirrokni, Vahab Pouget-Abadie, Jean |
| author_facet | Javanmard, Adel Mirrokni, Vahab Pouget-Abadie, Jean |
| contents | Estimating causal effects from randomized experiments is only possible if participants are willing to disclose their potentially sensitive responses. Differential privacy, a widely used framework for ensuring an algorithms privacy guarantees, can encourage participants to share their responses without the risk of de-anonymization. However, many mechanisms achieve differential privacy by adding noise to the original dataset, which reduces the precision of causal effect estimation. This introduces a fundamental trade-off between privacy and variance when performing causal analyses on differentially private data. In this work, we propose a new differentially private mechanism, "Cluster-DP", which leverages a given cluster structure in the data to improve the privacy-variance trade-off. While our results apply to any clustering, we demonstrate that selecting higher-quality clusters, according to a quality metric we introduce, can decrease the variance penalty without compromising privacy guarantees. Finally, we evaluate the theoretical and empirical performance of our Cluster-DP algorithm on both real and simulated data, comparing it to common baselines, including two special cases of our algorithm: its unclustered version and a uniform-prior version. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_00957 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Improving the Variance of Differentially Private Randomized Experiments through Clustering Javanmard, Adel Mirrokni, Vahab Pouget-Abadie, Jean Machine Learning Cryptography and Security Methodology Estimating causal effects from randomized experiments is only possible if participants are willing to disclose their potentially sensitive responses. Differential privacy, a widely used framework for ensuring an algorithms privacy guarantees, can encourage participants to share their responses without the risk of de-anonymization. However, many mechanisms achieve differential privacy by adding noise to the original dataset, which reduces the precision of causal effect estimation. This introduces a fundamental trade-off between privacy and variance when performing causal analyses on differentially private data. In this work, we propose a new differentially private mechanism, "Cluster-DP", which leverages a given cluster structure in the data to improve the privacy-variance trade-off. While our results apply to any clustering, we demonstrate that selecting higher-quality clusters, according to a quality metric we introduce, can decrease the variance penalty without compromising privacy guarantees. Finally, we evaluate the theoretical and empirical performance of our Cluster-DP algorithm on both real and simulated data, comparing it to common baselines, including two special cases of our algorithm: its unclustered version and a uniform-prior version. |
| title | Improving the Variance of Differentially Private Randomized Experiments through Clustering |
| topic | Machine Learning Cryptography and Security Methodology |
| url | https://arxiv.org/abs/2308.00957 |