For all models, we follow Le et al.

Neural Information Processing Systems http://nips.cc/

The dynamics of simple decisions are well understood and modeled as a class of random walk models [e.g.

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.

The dynamics of simple decisions are well understood and modeled as a class of random walk models (e.g. Laming, 1968; Ratcliff, 1978; Busemeyer and Townsend, 1993; Usher and McClelland, 2001; Bogacz et al., 2006). However, most real-life decisions include a rich and dynamically-changing influence of additional information we call context. In this work, we describe a computational theory of decision making under dynamically shifting context. We show how the model generalizes the dominant existing model of fixed-context decision making (Ratcliff, 1978) and can be built up from a weighted combination of fixed-context decisions evolving simultaneously. We also show how the model generalizes re- cent work on the control of attention in the Flanker task (Yu et al., 2009). Finally, we show how the model recovers qualitative data patterns in another task of longstanding psychological interest, the AX Continuous Performance Test (Servan-Schreiber et al., 1996), using the same model parameters.