A differentially private kernel two-sample test
Kernel two-sample testing is a useful statistical tool in determining whether data samples arise from different distributions without imposing any parametric assumptions on those distributions. However, raw data samples can expose sensitive information about individuals who participate in scientific...
| Main Authors: | , , , |
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| Format: | Conference item |
| Language: | English |
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Springer Nature
2020
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| _version_ | 1797051387027128320 |
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| author | Raj, A Law, HCL Sejdinovic, D Park, M |
| author_facet | Raj, A Law, HCL Sejdinovic, D Park, M |
| author_sort | Raj, A |
| collection | OXFORD |
| description | Kernel two-sample testing is a useful statistical tool in determining whether data samples arise from different distributions without imposing any parametric assumptions on those distributions. However, raw data samples can expose sensitive information about individuals who participate in scientific studies, which makes the current tests vulnerable to privacy breaches. Hence, we design a new framework for kernel twosample testing conforming to differential privacy constraints, in order to guarantee the privacy of subjects in the data. Unlike existing differentially private parametric tests that simply add noise to data, kernel-based testing imposes a challenge due to a complex dependence of test statistics on the raw data, as these statistics correspond to estimators of distances between representations of probability measures in Hilbert spaces. Our approach considers finite dimensional approximations to those representations. As a result, a simple chi squared test is obtained, where a test statistic depends on a mean and covariance of empirical differences between the samples, which we perturb for a privacy guarantee. We investigate the utility of our framework in two realistic settings and conclude that our method requires only a relatively modest increase in sample size to achieve a similar level of power to the non-private tests in both settings. |
| first_indexed | 2024-03-06T18:18:49Z |
| format | Conference item |
| id | oxford-uuid:05901228-958c-4d25-8c62-1a0dac73102d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:18:49Z |
| publishDate | 2020 |
| publisher | Springer Nature |
| record_format | dspace |
| spelling | oxford-uuid:05901228-958c-4d25-8c62-1a0dac73102d2022-03-26T08:57:54ZA differentially private kernel two-sample testConference itemhttp://purl.org/coar/resource_type/c_5794uuid:05901228-958c-4d25-8c62-1a0dac73102dEnglishSymplectic Elements at OxfordSpringer Nature2020Raj, ALaw, HCLSejdinovic, DPark, MKernel two-sample testing is a useful statistical tool in determining whether data samples arise from different distributions without imposing any parametric assumptions on those distributions. However, raw data samples can expose sensitive information about individuals who participate in scientific studies, which makes the current tests vulnerable to privacy breaches. Hence, we design a new framework for kernel twosample testing conforming to differential privacy constraints, in order to guarantee the privacy of subjects in the data. Unlike existing differentially private parametric tests that simply add noise to data, kernel-based testing imposes a challenge due to a complex dependence of test statistics on the raw data, as these statistics correspond to estimators of distances between representations of probability measures in Hilbert spaces. Our approach considers finite dimensional approximations to those representations. As a result, a simple chi squared test is obtained, where a test statistic depends on a mean and covariance of empirical differences between the samples, which we perturb for a privacy guarantee. We investigate the utility of our framework in two realistic settings and conclude that our method requires only a relatively modest increase in sample size to achieve a similar level of power to the non-private tests in both settings. |
| spellingShingle | Raj, A Law, HCL Sejdinovic, D Park, M A differentially private kernel two-sample test |
| title | A differentially private kernel two-sample test |
| title_full | A differentially private kernel two-sample test |
| title_fullStr | A differentially private kernel two-sample test |
| title_full_unstemmed | A differentially private kernel two-sample test |
| title_short | A differentially private kernel two-sample test |
| title_sort | differentially private kernel two sample test |
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