Polynomial Time and Private Learning of Unbounded Gaussian Mixture Models
Authors: Jamil Arbas, Hassan Ashtiani, Christopher Liaw
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We study the problem of privately estimating the parameters of d-dimensional Gaussian Mixture Models (GMMs) with k components. For this, we develop a technique to reduce the problem to its non-private counterpart. This allows us to privatize existing non-private algorithms in a blackbox manner, while incurring only a small overhead in the sample complexity and running time. As the main application of our framework, we develop an (ε, δ)-differentially private algorithm to learn GMMs using the non-private algorithm of Moitra & Valiant (2010) as a blackbox. Consequently, this gives the first sample complexity upper bound and first polynomial time algorithm for privately learning GMMs without any boundedness assumptions on the parameters. As part of our analysis, we prove a tight (up to a constant factor) lower bound on the total variation distance of high-dimensional Gaussians which can be of independent interest. |
| Researcher Affiliation | Collaboration | Jamil Arbas * 1 Hassan Ashtiani * 1 2 Christopher Liaw * 3 1Mc Master University 2Vector Institute 3Google. |
| Pseudocode | Yes | Algorithm 1 Private Populous Estimator; Algorithm 2 GMM Masking Mechanism |
| Open Source Code | No | The paper does not contain any statement about making its source code available or provide a link to a code repository. |
| Open Datasets | No | The paper is theoretical and does not conduct experiments on a specific dataset. It refers to "independent samples" in the problem definition but provides no concrete dataset information or access. |
| Dataset Splits | No | The paper is theoretical and does not describe empirical experiments, thus it does not provide dataset split information for training, validation, or testing. |
| Hardware Specification | No | The paper does not mention any specific hardware used for running experiments. |
| Software Dependencies | No | The paper does not provide specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not describe empirical experiments with specific hyperparameters or training configurations. |