Tensor Gaussian Process with Contraction for Multi-Channel Imaging Analysis
Tensor Gaussian Process with Contraction for Multi-Channel Imaging Analysis
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发表时间：
2023-01
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通讯作者：
Hu Sun;W. Manchester;Meng-yao Jin;Yang Liu;Y. Chen
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作者：
Hu Sun;W. Manchester;Meng-yao Jin;Yang Liu;Y. Chen
多通道成像数据是天文学和生物学等科学领域中流行的数据格式。这些 3D 张量数据的结构化信息和高维性使得分析成为统计学家和从业者感兴趣但具有挑战性的主题。尤其是低秩标量对张量回归模型受到了广泛关注，并在 Yu 等人（2018）中被重新表述为具有多线性核的张量高斯过程（Tensor-GP）模型。在本文中，我们通过引入一种称为张量收缩的集成降维技术来扩展 Tensor-GP 模型，并将 Tensor-GP 用于多通道成像数据的标量张量回归任务。这是由高维多通道成像数据的太阳耀斑预测问题引起的。我们首先估计每个数据张量的潜在的、尺寸减小的张量，然后对潜在张量数据应用多线性 Tensor-GP 进行预测。我们在进行张量收缩时引入各向异性全变分正则化以获得稀疏且平滑的潜在张量。然后，我们提出了一种用于估计的交替近端梯度下降算法。我们通过广泛的模拟研究验证了我们的方法，并将其应用于太阳耀斑预测问题。
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 introducing an integrative 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.