Book Review: High-dimensional statistics: A non-asymptotic viewpoint

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Protection Against Reconstruction and Its Applications in Private Federated Learning (2018, background): “By volume arguments, there are -packings of S d − 1 (in (cid:96) 2 ) of cardinality at least 2 d (cf. [64]).”
How Much Does Your Data Exploration Overfit? Controlling Bias via Information Usage (2015, background): “: [35] Given a zero-mean random variable Y , Suppose there is a constant c ≥ 1 and Gaussian random variable Z ∼ N (0, τ 2) such that P(|Y | ≥ s) ≤ c(P(|Z | ≥ s)) for all s ≥ 0.”
Improved OOD Generalization via Adversarial Training and Pre-training (2021, background): “…in the last inequality is upper bonded by t j =2 ξ j which is a sum of martingale difference, and | ξ j | ≤ 2 G 2 , a simple Azuma-Hoeffding’s inequality based on bounded martingale difference (Corollary 2.20 in (Wainwright, 2019)) can give a O (1 / √ t ) convergence rate in the high probability.”
FedSplit: An algorithmic framework for fast federated optimization (2020, result): “In the regime n j d considered here, known results in non-asymptotic random matrix theory (e.g. [29]) guarantee that the matrix A T j A j will be well-conditioned.”
On the Sample Complexity of Stability Constrained Imitation Learning (2021, methodology): “This follows from standard uniform convergence results, see e.g., Wainwright [40].”