{"ID":5551909,"CreatedAt":"2026-07-02T01:54:51.863792489Z","UpdatedAt":"2026-07-04T01:45:22.703757252Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.00376","arxiv_id":"2607.00376","title":"Distributed Prediction under Heterogeneity with Unidentifiable Parameter","abstract":"Predicting a response based on covariates is a fundamental problem in statistics and machine learning. However, profound difficulties arise when the underlying low-dimensional structural parameters are unidentifiable, as typified in dimension reduction contexts. Specifically,estimating these non-identifiable parameters inherently introduces severe nonconvexity. In distributed settings, this difficulty is further compounded by the challenges of data heterogeneity and communication cost. To overcome these intertwined barriers, we propose a novel distributed semiparametric framework. We formulate an adaptive homogeneity pursuit utilizing a trace-similarity penalty to effectively address data heterogeneity. To resolve the ensuing severe nonconvexity and communication bottlenecks, we introduce an invex relaxation technique coupled with a multi-step local update algorithm, ensuring stable convergence to global optimality with significantly reduced communication overhead. Theoretically, we establish a non-asymptotic model-free prediction error bound and prove that our estimator achieves a two-phase minimax optimal convergence rate and an sharper model-free prediction error bound. Furthermore, we provide theoretical guarantees for algorithmic convergence and communication efficiency. Extensive simulations and a real-world multi-center medical application validate the superiority of our method.","short_abstract":"Predicting a response based on covariates is a fundamental problem in statistics and machine learning. However, profound difficulties arise when the underlying low-dimensional structural parameters are unidentifiable, as typified in dimension reduction contexts. Specifically,estimating these non-identifiable parameters...","url_abs":"https://arxiv.org/abs/2607.00376","url_pdf":"https://arxiv.org/pdf/2607.00376v1","authors":"[\"Erbo Li\",\"Zhaojun Hu\",\"Ting Wei\",\"Yifan Sun\",\"Liping Zhu\"]","published":"2026-07-01T03:20:57Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"math.OC\",\"math.ST\"]","methods":"[]","has_code":false}