We study the problem of collaboratively learning least squares estimates for $m$ agents. Each agent observes a different subset of the features$\unicode{x2013}$e.g., containing data collected from sensors of varying resolution. Our goal is to determine how to coordinate the agents in order to produce the best estimator for each agent. We propose a distributed, semi-supervised algorithm Collab, consisting of three steps: local training, aggregation, and distribution. Our procedure does not require communicating the labeled data, making it communication efficient and useful in settings where the labeled data is inaccessible. Despite this handicap, our procedure is nearly asymptotically local minimax optimal$\unicode{x2013}$even among estimators allowed to communicate the labeled data such as imputation methods. We test our method on real and synthetic data.

我们研究了协作学习最小二乘估计的问题，提出了一种分布式半监督算法Collab，该算法包含三个步骤：本地训练、聚合和分发。我们的方法在没有标记数据的情况下无需通信，具有良好的通信效率，适用于无法获取标记数据的环境。尽管如此，我们的方法几乎渐近局部最小值，并可用于需要通信标记数据的估计方法，如填充方法。我们在真实数据和合成数据上对我们的方法进行了测试。

协同学习结构缺失数据的线性模型