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Computer Science > Machine Learning

arXiv:2305.14311 (cs)
[Submitted on 23 May 2023]

Title:Statistical Indistinguishability of Learning Algorithms

Authors:Alkis Kalavasis, Amin Karbasi, Shay Moran, Grigoris Velegkas
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Abstract:When two different parties use the same learning rule on their own data, how can we test whether the distributions of the two outcomes are similar? In this paper, we study the similarity of outcomes of learning rules through the lens of the Total Variation (TV) distance of distributions. We say that a learning rule is TV indistinguishable if the expected TV distance between the posterior distributions of its outputs, executed on two training data sets drawn independently from the same distribution, is small. We first investigate the learnability of hypothesis classes using TV indistinguishable learners. Our main results are information-theoretic equivalences between TV indistinguishability and existing algorithmic stability notions such as replicability and approximate differential privacy. Then, we provide statistical amplification and boosting algorithms for TV indistinguishable learners.
Subjects: Machine Learning (cs.LG); Data Structures and Algorithms (cs.DS); Machine Learning (stat.ML)
Cite as: arXiv:2305.14311 [cs.LG]
  (or arXiv:2305.14311v1 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2305.14311

Submission history

From: Grigoris Velegkas [view email]
[v1] Tue, 23 May 2023 17:49:56 UTC (110 KB)
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