论文标题
最佳准叶叶山脉降低了等级回归，而响应不完整
Optimal quasi-Bayesian reduced rank regression with incomplete response
论文作者
论文摘要
降低等级回归的目的是将多个响应变量连接到多个预测指标。该模型非常受欢迎，尤其是在生物统计学中，可以重新使用对个体的多次测量以预测多个输出。不幸的是，此类数据集中常常缺少数据，因此很难使用标准估计工具。在本文中，我们研究了响应矩阵不完整的等级回归减少的问题。我们提出了一种准巴约西亚的方法来解决这个问题，从某种意义上说，可能性被准类替代。我们提供紧密的甲骨文不平等，证明我们的方法适应了系数矩阵的等级。我们描述了一种用于计算后平均值的Langevin Monte Carlo算法。关于合成和实际数据的数值比较表明，我们的方法具有通过交叉验证选择等级的最先进的竞争，有时会导致改进。
The aim of reduced rank regression is to connect multiple response variables to multiple predictors. This model is very popular, especially in biostatistics where multiple measurements on individuals can be re-used to predict multiple outputs. Unfortunately, there are often missing data in such datasets, making it difficult to use standard estimation tools. In this paper, we study the problem of reduced rank regression where the response matrix is incomplete. We propose a quasi-Bayesian approach to this problem, in the sense that the likelihood is replaced by a quasi-likelihood. We provide a tight oracle inequality, proving that our method is adaptive to the rank of the coefficient matrix. We describe a Langevin Monte Carlo algorithm for the computation of the posterior mean. Numerical comparison on synthetic and real data show that our method are competitive to the state-of-the-art where the rank is chosen by cross validation, and sometimes lead to an improvement.
