We present a tuning-free and computationally simple solution for multivariate reduced rank regression, based on the recently introduced signal subspace matching (SSM) metric. Unlike the existing solutions, which solve simultaneously for the rank and the value of the coefficient matrix, our solution decouples the two tasks. First, the rank of the coefficient matrix is determined using the SSM metric, and then the coefficient matrix is determined by ordinary least squares. We prove the consistency of the solution for the high signal-to-noise-ratio limit, and also for the large-sample limit, conditioned on the noise being white. Experimental results, demonstrating the performance of the SSM solution, are included.

中文翻译：

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通过信号子空间匹配进行多元降序回归

基于最近引入的信号子空间匹配（SSM）指标，我们提出了一种无需调整且计算简单的多元降阶回归解决方案。与同时求解系数矩阵的秩和值的现有解决方案不同，我们的解决方案将这两个任务解耦。首先，使用SSM度量确定系数矩阵的秩，然后通过普通最小二乘法确定系数矩阵。我们证明了解决方案对于高信噪比限制以及大样本限制的一致性，条件是噪声为白噪声。其中包括展示 SSM 解决方案性能的实验结果。