PAC Learning from Positive Statistical Queries

Abstract The problem of privatizing statistical databases is a well-studied topic that has culminated with the notion of differential privacy. The complementary problem of securing these differentially private databases, however, has—as far as we know—not been considered in the past. While the security of private databases is in theory orthogonal to the problem of private statistical analysis (e.g., in the central model of differential privacy the curator is trusted) the recent real-world deployments of differentially-private systems suggest that it will become a problem of increasing importance. In this work, we consider the problem of designing encrypted databases (EDB) that support differentially-private statistical queries. More precisely, these EDBs should support a set of encrypted operations with which a curator can securely query and manage its data, and a set of private operations with which an analyst can privately analyze the data. Using such an EDB, a curator can securely outsource its database to an untrusted server (e.g., on-premise or in the cloud) while still allowing an analyst to privately query it. We show how to design an EDB that supports private histogram queries. As a building block, we introduce a differentially-private encrypted counter based on the binary mechanism of Chan et al. (ICALP, 2010). We then carefully combine multiple instances of this counter with a standard encrypted database scheme to support differentially-private histogram queries.

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A PAC Framework for Aggregating Agents’ Judgments

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v33i01.33012237 ◽

2019 ◽

Vol 33 ◽

pp. 2237-2244 ◽

Cited By ~ 1

Author(s):

Hanrui Zhang ◽

Vincent Conitzer

Keyword(s):

Objective Function ◽

Pac Learning ◽

Future Research ◽

Formal Learning ◽

Multiple Stakeholders

Specifying the objective function that an AI system should pursue can be challenging. Especially when the decisions to be made by the system have a moral component, input from multiple stakeholders is often required. We consider approaches that query them about their judgments in individual examples, and then aggregate these judgments into a general policy. We propose a formal learning-theoretic framework for this setting. We then give general results on how to translate classical results from PAC learning into results in our framework. Subsequently, we show that in some settings, better results can be obtained by working directly in our framework. Finally, we discuss how our model can be extended in a variety of ways for future research.

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On the Complexity of Learning a Class Ratio from Unlabeled Data

Journal of Artificial Intelligence Research ◽

10.1613/jair.1.12013 ◽

2020 ◽

Vol 69 ◽

Author(s):

Benjamin Fish ◽

Lev Reyzin

Keyword(s):

Computational Complexity ◽

Unlabeled Data ◽

Training Data ◽

Pac Learning ◽

Vc Dimension ◽

Standard Set

In the problem of learning a class ratio from unlabeled data, which we call CR learning, the training data is unlabeled, and only the ratios, or proportions, of examples receiving each label are given. The goal is to learn a hypothesis that predicts the proportions of labels on the distribution underlying the sample. This model of learning is applicable to a wide variety of settings, including predicting the number of votes for candidates in political elections from polls. In this paper, we formally define this class and resolve foundational questions regarding the computational complexity of CR learning and characterize its relationship to PAC learning. Among our results, we show, perhaps surprisingly, that for finite VC classes what can be efficiently CR learned is a strict subset of what can be learned efficiently in PAC, under standard complexity assumptions. We also show that there exist classes of functions whose CR learnability is independent of ZFC, the standard set theoretic axioms. This implies that CR learning cannot be easily characterized (like PAC by VC dimension).

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