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Activity Number:
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120
- Challenges and Recent Advances in Private Data Analysis
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Type:
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Topic-Contributed
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Date/Time:
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Monday, August 9, 2021 : 1:30 PM to 3:20 PM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract #317106
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Title:
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The Cost of Privacy in Generalized Linear Models: Algorithms and Minimax Lower Bounds
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Author(s):
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Yichen Wang* and Tony Cai and Linjun Zhang
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Companies:
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University of Pennsylvania and University of Pennsylvania and Rutgers University
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Keywords:
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Abstract:
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In this paper, we propose differentially private algorithms for parameter estimation in both low-dimensional and high-dimensional sparse generalized linear models (GLMs) by constructing private versions of projected gradient descent. We show that the proposed algorithms are nearly rate-optimal by characterizing their statistical performance and establishing privacy-constrained minimax lower bounds for GLMs. The lower bounds are obtained via a novel technique, which is based on Stein's Lemma and generalizes the tracing attack technique for privacy-constrained lower bounds. This lower bound argument can be of independent interest as it is applicable to general parametric models. Simulated and real data experiments are conducted to demonstrate the numerical performance of our algorithms.
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Authors who are presenting talks have a * after their name.
