Multi-channel imaging data is a prevalent data format in scientific fields such as astronomy and biology. The structured information and the high dimensionality of these 3-D tensor data makes the analysis an intriguing but challenging topic for statisticians and practitioners. The low-rank scalar-on-tensor regression model, in particular, has received widespread attention and has been re-formulated as a tensor Gaussian Process (Tensor-GP) model with multi-linear kernel in Yu et al. (2018). In this paper, we extend the Tensor-GP model by integrating a dimensionality reduction technique, called tensor contraction, with a Tensor-GP for a scalar-on-tensor regression task with multi-channel imaging data. This is motivated by the solar flare forecasting problem with high dimensional multi-channel imaging data. We first estimate a latent, reduced-size tensor for each data tensor and then apply a multi-linear Tensor-GP on the latent tensor data for prediction. We introduce an anisotropic total-variation regularization when conducting the tensor contraction to obtain a sparse and smooth latent tensor. We then propose an alternating proximal gradient descent algorithm for estimation. We validate our approach via extensive simulation studies and applying it to the solar flare forecasting problem.
翻译:多通道成像数据是天文学和生物学等科学领域的普遍数据格式。这些三维强数据的结构化信息和高维度数据使分析成为统计人员和从业人员一个令人感兴趣但具有挑战性的专题。特别是低级的电压超强回归模型受到广泛关注,并被重新配制成高尔高西亚进程(Tensor-GP)模型,在尤等人(2018年)采用多线性内核(Tensor-GP)模型。在本文中,我们通过整合一个维度减少技术来扩展Tensor-GP模型,称为 " 高压收缩 " 模型,并配以多通道成成像素数据进行卡拉-电压收缩任务Tensor-GP。这是由高分辨率多频道成的太阳耀斑预测问题引发的。我们首先估计每个数据高压多线性阵列(2018年)的潜潜伏、缩小型阵列,然后将多线性Tensor-GGP模型用于预测。我们引入了一种全位性全面递减法,在进行高压性变压性变压研究时,然后通过静态变压法进行高压变现。我们提议,然后进行高压变压变压,然后进行高压变现。我们再研究,以便进行高压变压变压变压。