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We consider a scenario where different learners hold datasets with potentially distinct variables, and their observations can be aligned by a nonprivate identifier. Their collaboration faces the following difficulties: first, learners may need to keep data values or even variable names undisclosed due to, e.g. commercial interest or privacy regulations; second, there are restrictions on the number of transmission rounds between them due to e.g. communication costs. To address these challenges, we develop a two-stage assisted learning architecture for an agent, Alice, to seek assistance from another agent, Bob. In the first stage, we propose a privacy-aware hypothesis testing-based screening method for Alice to decide on the usefulness of the data from Bob, in a way that only requires Bob to transmit sketchy data. Once Alice recognizes Bob\u2019s usefulness, Alice and Bob move to the second stage, where they jointly apply a synergistic iterative model training procedure. With limited transmissions of summary statistics, we show that Alice can achieve the oracle performance as if the training were from centralized data, both theoretically and numerically.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkaf062","type":"journal-article","created":{"date-parts":[[2025,9,10]],"date-time":"2025-09-10T11:50:04Z","timestamp":1757505004000},"page":"657-676","source":"Crossref","is-referenced-by-count":0,"title":["Additive-Effect Assisted Learning"],"prefix":"10.1093","volume":"88","author":[{"given":"Jiawei","family":"Zhang","sequence":"first","affiliation":[{"name":"Dr. Bing Zhang Department of Statistics, University of Kentucky , 725 Rose Street, Lexington, KY 40536-0082 ,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuhong","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Statistics, University of Minnesota , 224 Church St SE, Minneapolis, MN 55455 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