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.