Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes
Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes
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发表时间：
2020-07
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通讯作者：
Andrew Y. K. Foong;W. Bruinsma;Jonathan Gordon;Yann Dubois;James Requeima;Richard E. Turner
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作者：
Andrew Y. K. Foong;W. Bruinsma;Jonathan Gordon;Yann Dubois;James Requeima;Richard E. Turner
平稳随机过程(SP)是许多概率模型的重要组成部分，例如离网时空数据的概率模型。它们使潜在物理现象的统计对称性得以利用，从而有助于推广。这类模型中的预测可以看作是从观测数据集到预测性SP的平移等变映射，强调平稳性和等方差之间的密切关系。在此基础上，我们提出了卷积神经过程(ConvNP)，它赋予神经过程(NP)平移等差性，并扩展卷积条件NP以允许预测分布中的依赖。后者使ConvNP能够部署在需要相干样本的环境中，例如汤普森采样或条件图像完成。此外，我们提出了一种新的最大似然目标来代替NPS中的标准ELBO目标，它在概念上简化了框架，并从经验上提高了性能。我们用真实的时空数据展示了ConvNPs在一维回归、图像完成和各种任务上的强大性能和泛化能力。
Stationary stochastic processes (SPs) are a key component of many probabilistic models, such as those for off-the-grid spatio-temporal data. They enable the statistical symmetry of underlying physical phenomena to be leveraged, thereby aiding generalization. Prediction in such models can be viewed as a translation equivariant map from observed data sets to predictive SPs, emphasizing the intimate relationship between stationarity and equivariance. Building on this, we propose the Convolutional Neural Process (ConvNP), which endows Neural Processes (NPs) with translation equivariance and extends convolutional conditional NPs to allow for dependencies in the predictive distribution. The latter enables ConvNPs to be deployed in settings which require coherent samples, such as Thompson sampling or conditional image completion. Moreover, we propose a new maximum-likelihood objective to replace the standard ELBO objective in NPs, which conceptually simplifies the framework and empirically improves performance. We demonstrate the strong performance and generalization capabilities of ConvNPs on 1D regression, image completion, and various tasks with real-world spatio-temporal data.