Robust Personalized Federated Learning with Sparse Penalization
带稀疏惩罚的稳健个性化联邦学习AI 解读 ↓
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带稀疏惩罚的稳健个性化联邦学习AI 解读 ↓
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Federated learning (FL) is an emerging topic due to its advantage in collaborative learning with distributed data. Due to the heterogeneity in the local data-generating mechanism, it is important to consider personalization when developing federated learning methods. In this work, we propose a personalized federated learning (PFL) method to address the robust regression problem. Specifically, we aim to learn the regression weight by solving a Huber loss with the sparse fused penalty. Additionally, we designed our personalized federated learning for robust and sparse regression (PerFL-RSR) algorithm to solve the estimation problem in the federated system efficiently. Theoretically, we show that the proposed PerFL-RSR reaches a convergence rate of O(1/T), and the proposed estimator is statistically consistent. Thorough experiments and real data analysis are conducted to corroborate the theoretical results of our proposed personalized federated learning method. Supplementary materials for this article are available online including a standardized description of the materials available for reproducing the work.
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Many multivariate time series arise on networks where relationships between variables depend on physical or more general distances. Standard vector autoregressive models struggle in such settings due to their quadratic parameter growth, while generalised network autoregressive (GNAR) models offer a parsimonious alternative by explicitly incorporating network structures. Existing GNAR formulations assume fixed weights, typically uniform or reciprocal distances, which may not…
近端估计与推断
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组间不平衡下的风险异质性稳健推断
Population-level heterogeneity is ubiquitous in biomedical data, where differences across demographic or clinical subgroups can substantially alter risk patterns. For example, in intensive care unit (ICU) studies, the mortality risk associated with specific admission diagnoses can vary across ethnic groups. Existing approaches for detecting risk heterogeneity are often sensitive to baseline model misspecification and regularization bias, both of which commonly arise in…
凸正则化的谱依赖:右旋转不变设计下的基本极限
We study the fundamental limits of convex-regularized estimation in high-dimensional linear regression with right-rotationally invariant design matrices. We show that the asymptotic risks of convex-penalized least squares estimators are lower bounded by the risk of an approximate message passing algorithm known as Bayes VAMP, and we further characterize when the lower bound is attainable. As a technical ingredient in the proof of our lower bound theorem, we characterize the…
从图套索到原子范数:高维模式恢复
We study high-dimensional precision-matrix estimation with polyhedral atomic-norm penalties on the off-diagonal entries. This framework covers the graphical lasso, $\ell_\infty$-type penalties, SLOPE/OWL penalties, and penalties motivated by colored graphical models. We define the target pattern through the subdifferential face of the dual ball and derive sufficient conditions for exact pattern recovery from the sample covariance matrix. Our analysis introduces two geometric…