Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes
This work addresses prediction in stationary stochastic processes for applications like spatio-temporal data modeling, offering incremental improvements over existing Neural Processes.
The authors tackled the problem of predicting stationary stochastic processes by proposing the Convolutional Neural Process (ConvNP), which incorporates translation equivariance and dependencies in predictive distributions, and introduced a maximum-likelihood objective to improve performance. They demonstrated strong results on tasks including 1D regression, image completion, and real-world spatio-temporal data, with empirical performance gains.
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.