Lock Eric F
Division of Biostatistics, University of Minnesota.
J Comput Graph Stat. 2018;27(3):638-647. doi: 10.1080/10618600.2017.1401544. Epub 2018 Jun 6.
We propose a framework for the linear prediction of a multi-way array (i.e., a tensor) from another multi-way array of arbitrary dimension, using the contracted tensor product. This framework generalizes several existing approaches, including methods to predict a scalar outcome from a tensor, a matrix from a matrix, or a tensor from a scalar. We describe an approach that exploits the multiway structure of both the predictors and the outcomes by restricting the coefficients to have reduced CP-rank. We propose a general and efficient algorithm for penalized least-squares estimation, which allows for a ridge ( ) penalty on the coefficients. The objective is shown to give the mode of a Bayesian posterior, which motivates a Gibbs sampling algorithm for inference. We illustrate the approach with an application to facial image data. An R package is available at https://github.com/lockEF/MultiwayRegression.
我们提出了一个框架，用于使用收缩张量积从任意维度的另一个多路数组（即张量）对多路数组进行线性预测。该框架推广了几种现有方法，包括从张量预测标量结果、从矩阵预测矩阵或从标量预测张量的方法。我们描述了一种通过将系数限制为具有降低的CP秩来利用预测变量和结果的多路结构的方法。我们提出了一种用于惩罚最小二乘估计的通用且高效的算法，该算法允许对系数进行岭（ ）惩罚。目标被证明给出了贝叶斯后验的模式，这激发了一种用于推理的吉布斯采样算法。我们通过将该方法应用于面部图像数据来说明。可在https://github.com/lockEF/MultiwayRegression获得一个R包。
