Many important tasks of large-scale recommender systems can be naturally cast
as testing multiple linear forms for noisy matrix completion. These problems,
however, present unique challenges because of the subtle bias-and-variance
tradeoff of and an intricate dependence among the estimated entries induced by
the low-rank structure. In this paper, we develop a general approach to
overcome these difficulties by introducing new statistics for individual tests
with sharp asymptotics both marginally and jointly, and utilizing them to
control the false discovery rate (FDR) via a data splitting and symmetric
aggregation scheme. We show that valid FDR control can be achieved with
guaranteed power under nearly optimal sample size requirements using the
proposed methodology. Extensive numerical simulations and real data examples
are also presented to further illustrate its practical merits.

通过引入新的统计量和利用数据分割和对称聚合方案，该研究开发了一种通用方法来控制多元线性形式的测试的误发现率，并展示了在几乎最优的样本量需求下可以实现有效的 FDR 控制和保证的功效。

嘈杂矩阵补全的线性形式多重检验

Multiple Testing of Linear Forms for Noisy Matrix Completion

We present Distributed Equivalent Substitution (DES) training, a novel
distributed training framework for large-scale recommender systems with dynamic
sparse features. DES introduces fully synchronous training to large-scale
recommendation system for the first time by reducing communication, thus making
the training of commercial recommender systems converge faster and reach better
CTR. DES requires much less communication by substituting the weights-rich
operators with the computationally equivalent sub-operators and aggregating
partial results instead of transmitting the huge sparse weights directly
through the network. Due to the use of synchronous training on large-scale Deep
Learning Recommendation Models (DLRMs), DES achieves higher AUC(Area Under
ROC). We successfully apply DES training on multiple popular DLRMs of
industrial scenarios. Experiments show that our implementation outperforms the
state-of-the-art PS-based training framework, achieving up to 68.7%
communication savings and higher throughput compared to other PS-based
recommender systems.

本文介绍了一种新的分布式训练框架 Distributed Equivalent Substitution（DES）进行大规模推荐系统的训练，采用同步训练的方式，采用子操作替代了权重操作，在结果聚合方面也采用聚合部分结果代替直接传输稀疏权重的方式，通过在工业场景下的多个流行的深度学习推荐模型中成功应用 DES 训练，展示了比其他基于 PS 的推荐系统更高的 AUC 值和更高的吞吐量，并实现了高达 68.7% 的通信开销节约。