Skip navigation
  • Home
  • Browse
    • Communities
      & Collections
    • Browse Items by:
    • Publication Date
    • Author
    • Title
    • Subject
    • Department
  • Sign on to:
    • My MacSphere
    • Receive email
      updates
    • Edit Profile


McMaster University Home Page
  1. MacSphere
  2. Open Access Dissertations and Theses Community
  3. Open Access Dissertations and Theses
Please use this identifier to cite or link to this item: 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 SizeFormat 
Arbas_Jamil_M_202402_M.Sc.pdf
Open Access
614.92 kBAdobe PDFView/Open
Show full item record Statistics


Items in MacSphere are protected by copyright, with all rights reserved, unless otherwise indicated.

Sherman Centre for Digital Scholarship     McMaster University Libraries
©2022 McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4L8 | 905-525-9140 | Contact Us | Terms of Use & Privacy Policy | Feedback

Report Accessibility Issue