Longitudinal Deep Kernel Gaussian Process Regression
Longitudinal Deep Kernel Gaussian Process Regression
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DOI：
10.1609/aaai.v35i10.17038
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发表时间：
2020-05
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影响因子：
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通讯作者：
Junjie Liang;Yanting Wu;Dongkuan Xu;Vasant G Honavar
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文献类型：
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作者：
Junjie Liang;Yanting Wu;Dongkuan Xu;Vasant G Honavar
高斯过程为纵向数据的预测建模提供了一个有吸引力的框架，即从一组个体随时间的不规则采样，稀疏观察。然而，这些方法有两个主要缺点：(i)它们依赖于特别的启发式或昂贵的试错来选择有效的核，（ii）它们不能处理数据中的多级相关结构。为了克服这些限制，我们引入了纵向深度核高斯过程回归（L-DKGPR），可以完全自动化地从纵向数据中发现复杂的多层相关结构。具体来说，L-DKGPR使用一种新颖的深度核学习方法，将深度神经网络的表达能力与非参数核方法的灵活性相结合，消除了对特别启发式或试错的需要。L-DKGPR利用一种同时适应时变和定常效应的新型加性核，有效地学习了多层相关。我们提出了一种利用潜在空间诱导点和变分推理训练L-DKGPR的有效算法。在几个基准数据集上进行的大量实验结果表明，L-DKGPR显著优于最先进的纵向数据分析（LDA）方法。
Gaussian processes offer an attractive framework for predictive modeling from longitudinal data, \ie irregularly sampled, sparse observations from a set of individuals over time. However, such methods have two key shortcomings: (i) They rely on ad hoc heuristics or expensive trial and error to choose the effective kernels, and (ii) They fail to handle multilevel correlation structure in the data. We introduce Longitudinal deep kernel Gaussian process regression (L-DKGPR) to overcome these limitations by fully automating the discovery of complex multilevel correlation structure from longitudinal data. Specifically, L-DKGPR eliminates the need for ad hoc heuristics or trial and error using a novel adaptation of deep kernel learning that combines the expressive power of deep neural networks with the flexibility of non-parametric kernel methods. L-DKGPR effectively learns the multilevel correlation with a novel additive kernel that simultaneously accommodates both time-varying and the time-invariant effects. We derive an efficient algorithm to train L-DKGPR using latent space inducing points and variational inference. Results of extensive experiments on several benchmark data sets demonstrate that L-DKGPR significantly outperforms the state-of-the-art longitudinal data analysis (LDA) methods.