Sample Complexity Bounds for Differentially Private Learning.

Area of Science:

• Machine Learning
• Computer Science
• Data Privacy

Background:

• Privacy-preserving classification aims to train models without compromising individual data privacy.
• Differential privacy offers a strong guarantee for individual privacy in machine learning.
• Understanding sample complexity is crucial for efficient private learning algorithms.

Purpose of the Study:

• To investigate the sample requirements for differentially private learning with infinite hypothesis classes on continuous data.
• To identify limitations of existing private learning paradigms in this context.
• To propose and analyze alternative approaches for achieving accurate and private classification.

Main Methods:

• Theoretical analysis of sample complexity for differentially private learning algorithms.
• Development of upper bounds for sample requirements using reference distributions.
• Investigation of label-privacy as a relaxation of differential privacy.

Main Results:

• Demonstrated that finite sample differentially private learning fails for infinite hypothesis classes on continuous distributions.
• Established an upper bound on sample complexity dependent on distribution similarity when using a reference distribution.
• Derived a lower bound for learning with label-privacy.

Conclusions:

• Distribution-free differentially private learning is not possible for infinite hypothesis classes with continuous data.
• Leveraging prior knowledge of data distributions or relaxing privacy to label-privacy are viable strategies.
• These findings inform the design of more efficient and practical privacy-preserving machine learning systems.