개인 정보 보호 PAC 학습은 유한한 리틀스톤 차원을 의미한다.
📝 원문 정보
- Title: Private PAC learning implies finite Littlestone dimension
- ArXiv ID: 1806.00949
- 발행일: 2019-03-11
- 저자: Noga Alon and Roi Livni and Maryanthe Malliaris and Shay Moran
📝 초록 (Abstract)
우리는 Littlestone 차원이 $d$인 클래스 $H$에 대해 모든 근사적으로 차등 사생활 알고리즘이 $\Omega\bigl(\log^*(d)\bigr)$ 개의 예시를 필요로 한다는 것을 보여줍니다. 이 결과의 부산물로, $\mathbb{N}$ 상에서의 임계값 클래스가 사생활 방식으로 학습될 수 없다는 것이 증명됩니다; 이는 [Bun et al., 2015, Feldman and Xiao, 2015]에 의해 제기된 개방적인 질문을 해결합니다. 모든 유한 Littlestone 차원의 클래스가 근사적으로 차등 사생활 알고리즘으로 학습될 수 있는지 여부는 여전히 개방적입니다.💡 논문 핵심 해설 (Deep Analysis)
This paper delves into the intricacies of private machine learning by focusing on the sample complexity required for differentially private PAC (Probably Approximately Correct) learning algorithms. The central question revolves around understanding how many samples are minimally needed to ensure that a class can be learned in a way that preserves privacy.The authors introduce and analyze the concept of Littlestone dimension, which quantifies the complexity of a hypothesis space $H$. By establishing this connection between the Littlestone dimension and sample complexity, they prove that any approximately differentially private learning algorithm for a class with Littlestone dimension $d$ requires $\Omega(\log^*(d))$ samples. This result not only provides theoretical grounding but also resolves an open question regarding whether thresholds over natural numbers can be learned privately.
The significance of this work lies in its contribution to the broader field of privacy-preserving machine learning, offering a clearer understanding of the trade-offs between privacy and learnability. The findings suggest that while some classes might require fewer samples to maintain privacy, others may inherently demand more due to their complexity, as measured by Littlestone dimension.