Differentially Private Algorithms for Learning Mixtures of Separated Gaussians
Authors: Gautam Kamath, Or Sheffet, Vikrant Singhal, Jonathan Ullman
NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this work, we give new algorithms for learning the parameters of a high-dimensional, well separated, Gaussian mixture model subject to the strong constraint of differential privacy. In particular, we give a differentially private analogue of the algorithm of Achlioptas and Mc Sherry (COLT 2005). Our algorithm has two key properties not achieved by prior work: (1) The algorithm s sample complexity matches that of the corresponding non-private algorithm up to lower order terms in a wide range of parameters. (2) The algorithm requires very weak a priori bounds on the parameters of the mixture. |
| Researcher Affiliation | Academia | Gautam Kamath David R. Cheriton School of Computer Science University of Waterloo Waterloo, ON, Canada N2L 3G1 g@csail.mit.edu Or Sheffet Department of Computer Science, Faculty of Exact Sciences Bar-Ilan University Ramat-Gan, 5290002 Israel or.sheffet@biu.ac.il Vikrant Singhal Khoury College of Computer Sciences Northeastern University 360 Huntington Ave., Boston, MA 02115 singhal.vi@husky.neu.edu Jonathan Ullman Khoury College of Computer Sciences Northeastern University 360 Huntington Ave., Boston, MA 02115 jullman@ccs.neu.edu |
| Pseudocode | Yes | Algorithm 1: Private Gaussian Mixture Partitioning RPGMP(X; k, R, wmin, σmin, σmax, ε, δ) Algorithm 2: Privately Learn Gaussian Mixture PGME(X; k, R, wmin, σmin, σmax, ε, δ, β) |
| Open Source Code | No | The paper does not provide any links to open-source code or explicitly state that code is available. |
| Open Datasets | No | The paper is theoretical and focuses on algorithmic design and analysis of sample complexity, rather than empirical evaluation on a specific publicly available dataset. |
| Dataset Splits | No | The paper is theoretical and does not describe dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper is theoretical and does not mention any hardware specifications for running experiments. |
| Software Dependencies | No | The paper is theoretical and provides algorithms in pseudocode but does not specify any software dependencies with version numbers for implementation. |
| Experiment Setup | No | The paper is theoretical and does not describe experimental setup details such as hyperparameters or training configurations. |