On the Interaction between Norm and Dimensionality: Multiple Regimes in Learning

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Smoothness, Low Noise and Fast Rates (2010, background): “This sheds further light on recent work on this phenomena by Liang and Srebro based on exact asymptotics of simpliﬁed situations [18].”
High-Dimensional Asymptotics of Prediction: Ridge Regression and Classification (2015, methodology): “The results (9) and (10) not only show that the scalings found by Liang and Srebro (2010) with Σ = I p × p hold for arbitrary Σ, but make explicit how the slopes depend on the limiting population spectral distribution.”
Asymptotically Optimal Regularization in Smooth Parametric Models (2009, background): “[26] shows that these analyses are complementary and actually capture different regimes of the learning curve.”
Tight Sample Complexity of Large-Margin Learning (2010, background): “As was recently shown by Liang and Srebro [2], the quantities on whi ch the sample complexity depends on for very smallǫ (in the classical statistics asymptotic regime) can be very different from those for moderate error rates, which are more relevant for machine le arning.”