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Award ID contains: 2003035

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  1. ; ; (, Transactions on machine learning research)
    Accepted Manuscript Full Text Available
  2. ; ; (, 2023 IEEE Information Theory Workshop (ITW))
    Full Text Available 
  3. ; ; ; (, IEEE Transactions on Information Theory)
    Full Text Available 
  4. ; ; (, IEEE Transactions on Neural Networks and Learning Systems)
    Full Text Available 
  5. ; ; ; ; (, International Conference on Learning Representations (ICLR) 2023)
    Accepted Manuscript Full Text Available
  6. ; ; ; ; (, IEEE Journal on Selected Areas in Information Theory)
    Full Text Available 
  7. ; ; ; (, IEEE Journal on Selected Areas in Information Theory)
    Full Text Available 
  8. ; ; ; ; ; (, Thirty-ninth International Conference on Machine Learning)
    Accepted Manuscript Full Text Available
  9. ; ; (, IEEE/ACM Transactions on Networking)
    null (Ed.)
    Full Text Available 
  10. ; ; (, Entropy)
    null (Ed.)
    We study convex empirical risk minimization for high-dimensional inference in binary linear classification under both discriminative binary linear models, as well as generative Gaussian-mixture models. Our first result sharply predicts the statistical performance of such estimators in the proportional asymptotic regime under isotropic Gaussian features. Importantly, the predictions hold for a wide class of convex loss functions, which we exploit to prove bounds on the best achievable performance. Notably, we show that the proposed bounds are tight for popular binary models (such as signed and logistic) and for the Gaussian-mixture model by constructing appropriate loss functions that achieve it. Our numerical simulations suggest that the theory is accurate even for relatively small problem dimensions and that it enjoys a certain universality property. 
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