Characterizing the Sample Complexity of Pure Private Learners

Authors: Amos Beimel, Kobbi Nissim, Uri Stemmer

JMLR 2019 | Venue PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We give a combinatorial characterization of the sample size sufficient and necessary to learn a class of concepts under pure differential privacy. This characterization is analogous to the well known characterization of the sample complexity of non-private learning in terms of the VC dimension of the concept class. We introduce the notion of probabilistic representation of a concept class, and our new complexity measure Rep Dim corresponds to the size of the smallest probabilistic representation of the concept class. We show that any private learning algorithm for a concept class C with sample complexity m implies Rep Dim(C) = O(m), and that there exists a private learning algorithm with sample complexity m = O(Rep Dim(C)).
Researcher Affiliation Academia Amos Beimel EMAIL Ben-Gurion University Kobbi Nissim EMAIL Georgetown University Uri Stemmer EMAIL Ben-Gurion University
Pseudocode No The paper describes algorithms (like the exponential mechanism and learning algorithms) but does not present them in structured pseudocode or algorithm blocks. It contains definitions, theorems, lemmas, and proofs.
Open Source Code No The paper discusses its license (CC-BY 4.0) and attribution requirements for the publication itself, but there is no explicit statement or link indicating the release of source code for the described methodology.
Open Datasets No The paper is theoretical and discusses 'concept classes' and 'distributions on Xd' abstractly. It does not refer to any specific named or publicly available datasets for empirical evaluation.
Dataset Splits No The paper does not present empirical experiments using specific datasets, therefore, there is no mention of dataset splits like training, testing, or validation sets.
Hardware Specification No The paper is theoretical and does not describe any experiments that would require specific hardware. Therefore, no hardware specifications are mentioned.
Software Dependencies No The paper is theoretical and does not describe any computational implementations. Consequently, there are no mentions of software dependencies with version numbers.
Experiment Setup No The paper is theoretical and does not include any experimental results or computational evaluations. Therefore, there is no 'Experimental Setup' section with hyperparameter values or training configurations.