论文标题
高维统计学习和推理的自适应加权方法
Adaptive weighted approach for high-dimensional statistical learning and inference
论文作者
论文摘要
我们为分布式学习系统下的高维参数提出了一个新的加权平均估计器，其中分配给每个坐标的权重与该坐标的本地估计值的差异完全成正比。该策略使新的估计器能够达到最小的平方误差，与当前最新的单发分布式学习方法相当。同时，新的加权方法的通信成本非常低，因为每个代理只需要将两个向量传输到中央服务器。结果，新提出的方法实现了最佳的统计效率，同时显着降低了沟通开销。我们通过研究估计的误差和渐近特性，以及一些模拟示例和实际数据分析的数值性能，进一步证明了新估计器的有效性。
We propose a new weighted average estimator for the high dimensional parameters under the distributed learning system, in which the weight assigned to each coordinate is precisely proportional to the inverse of the variance of the local estimates for that coordinate. This strategy empowers the new estimator to achieve a minimal mean squared error, comparable to the current state-of-the-art one-shot distributed learning methods. While at the same time, the new weighting approach maintains remarkably low communication costs, as each agent is required to transmit only two vectors to the central server. As a result, the newly proposed method achieves optimal statistical efficiency while significantly reducing communication overhead. We further demonstrate the effectiveness of the new estimator by investigating the error bound and the asymptotic properties of the estimation, as well as the numerical performance on some simulated examples and a real data analysis.
