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http://hdl.handle.net/11375/28364
Title: | Polynomial time and private learning of unbounded Gaussian Mixture Models |
Authors: | Arbas, Jamil |
Advisor: | Ashtiani, Hassan |
Department: | Computer Science |
Keywords: | Differential Privacy;Gaussian Mixture Models |
Publication Date: | 2023 |
Abstract: | We develop a technique for privately estimating the parameters of a mixture distribution by reducing the problem to its non-private counterpart. This technique allows us to privatize existing non-private algorithms in a BlackBox manner while only incurring a small overhead in sample complexity and running time. As the main application of our framework, we develop an algorithm for privately learning mixtures of Gaussians using the non-private algorithm of Moitra and Valiant [MV10] as a BlackBox and incurs only a polynomial time overhead in the sample complexity and computational complexity. As a result, this gives the first sample complexity upper bound and the first polynomial time algorithm in d for learning the parameters of the Gaussian Mixture Models privately without requiring any boundedness assumptions on the parameters. To prove the results we introduced Private Populous Estimator (PPE) which is a generalized version of the one used in [AL22] to achieve (ϵ, δ)-differential privacy. We also develop a new masking mechanism for a single Gaussian component. Then we introduce a general recipe to turn a masking mechanism for a component into a masking mechanism for mixtures. |
URI: | http://hdl.handle.net/11375/28364 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Arbas_Jamil_M_202402_M.Sc.pdf | 614.92 kB | Adobe PDF | View/Open |
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