Private and Communication-Efficient Algorithms for Entropy Estimation
| Title: | Private and Communication-Efficient Algorithms for Entropy Estimation |
|---|---|
| Authors: | Bravo-Hermsdorff, Gecia, Busa-Fekete, Róbert, Ghavamzadeh, Mohammad, Medina, Andres Muñoz, Syed, Umar |
| Publication Year: | 2023 |
| Collection: | Computer Science Mathematics Statistics |
| Subject Terms: | Computer Science - Machine Learning, Computer Science - Cryptography and Security, Computer Science - Information Theory, Mathematics - Statistics Theory |
| More Details: | Modern statistical estimation is often performed in a distributed setting where each sample belongs to a single user who shares their data with a central server. Users are typically concerned with preserving the privacy of their samples, and also with minimizing the amount of data they must transmit to the server. We give improved private and communication-efficient algorithms for estimating several popular measures of the entropy of a distribution. All of our algorithms have constant communication cost and satisfy local differential privacy. For a joint distribution over many variables whose conditional independence is given by a tree, we describe algorithms for estimating Shannon entropy that require a number of samples that is linear in the number of variables, compared to the quadratic sample complexity of prior work. We also describe an algorithm for estimating Gini entropy whose sample complexity has no dependence on the support size of the distribution and can be implemented using a single round of concurrent communication between the users and the server. In contrast, the previously best-known algorithm has high communication cost and requires the server to facilitate interaction between the users. Finally, we describe an algorithm for estimating collision entropy that generalizes the best known algorithm to the private and communication-efficient setting. Comment: Originally published at the 36th Conference on Neural Information Processing Systems (NeurIPS 2022). This version corrects some errors in the original version |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2305.07751 |
| Accession Number: | edsarx.2305.07751 |
| Database: | arXiv |
| Description not available. |