惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

宝玉的分享
宝玉的分享
小众软件
小众软件
J
Java Code Geeks
I
InfoQ
奇客Solidot–传递最新科技情报
奇客Solidot–传递最新科技情报
腾讯CDC
L
LangChain Blog
博客园 - 司徒正美
量子位
Y
Y Combinator Blog
C
Check Point Blog
T
Tailwind CSS Blog
D
DataBreaches.Net
Blog — PlanetScale
Blog — PlanetScale
N
Netflix TechBlog - Medium
钛媒体:引领未来商业与生活新知
钛媒体:引领未来商业与生活新知
F
Fortinet All Blogs
云风的 BLOG
云风的 BLOG
A
About on SuperTechFans
B
Blog RSS Feed
酷 壳 – CoolShell
酷 壳 – CoolShell
大猫的无限游戏
大猫的无限游戏
V
V2EX
阮一峰的网络日志
阮一峰的网络日志

math.ST updates on arXiv.org

What is Learnable in Valiant's Theory of the Learnable? Learning Perturbations to Extrapolate Your LLM Byzantine-Robust Distributed Sparse Learning Revisited The Sample Complexity of Multiple Change Point Identification under Bandit Feedback A proximal gradient algorithm for composite log-concave sampling Model-based Bootstrap of Controlled Markov Chains Approximation of Maximally Monotone Operators : A Graph Convergence Perspective Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces MIST: Reliable Streaming Decision Trees for Online Class-Incremental Learning via McDiarmid Bound A Spectral Framework for Closed-Form Relative Density Estimation Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability Higher-Order Equilibrium Tracking for EM-Compressible Online Estimation Scaling Limits of Long-Context Transformers A Note on Non-Negative $L_1$-Approximating Polynomials Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning Linear Response Estimators for Singular Statistical Models Statistical inference with belief functions: A survey Robust stochastic first order methods in heavy-tailed noise via medoid mini-batch gradient sampling Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexity Adaptive auditing of AI systems with anytime-valid guarantees Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions Risk-Controlled Post-Processing of Decision Policies Covariate Balancing and Riesz Regression Should Be Guided by the Neyman Orthogonal Score in Debiased Machine Learning A Unified Pair-GRPO Family: From Implicit to Explicit Preference Constraints for Stable and General RL Alignment Time-Inhomogeneous Preconditioned Langevin Dynamics A Fine-Grained Understanding of Uniform Convergence for Halfspaces CITE: Anytime-Valid Statistical Inference in LLM Self-Consistency Ratio-based Loss Functions Optimal Confidence Band for Kernel Gradient Flow Estimator A renormalization-group inspired lattice-based framework for piecewise generalized linear models
Shrinkage to Infinity: Reducing Test Error by Inflating t...
Jake Freeman · 2025-10-22 · via math.ST updates on arXiv.org

Hastie et al. (2022) found that ridge regularization is essential in high dimensional linear regression $y=β^Tx + ε$ with isotropic co-variates $x\in \mathbb{R}^d$ and $n$ samples at fixed $d/n$. However, Hastie et al. (2022) also notes that when the co-variates are anisotropic and $β$ is aligned with the top eigenvalues of population covariance, the "situation is qualitatively different." In the present article, we make precise this observation for linear regression with highly anisotropic covariances and diverging $d/n$. We find (both theoretically and empirically) that simply scaling up (or inflating) the minimum $\ell_2$ norm interpolator by a constant greater than one can improve the generalization error. This is in sharp contrast to traditional regularization/shrinkage prescriptions. Moreover, we use a data-splitting technique to produce consistent estimators that achieve generalization error comparable to that of the optimally inflated minimum-norm interpolator. Our proof relies on matching upper and lower bounds for expectations of Gaussian random projections for a general class of anisotropic covariance matrices when $d/n\rightarrow \infty$.