  Convolutional deep sets are the architecture of a deep neural network (DNN)
that can model stationary stochastic process. This architecture uses the kernel
smoother and the DNN to construct the translation equivariant functional
representations, and thus reflects the inductive bias of the stationarity into
DNN. However, since this architecture employs the kernel smoother known as the
non-parametric model, it may produce ambiguous representations when the number
of data points is not given sufficiently. To remedy this issue, we introduce
Bayesian convolutional deep sets that construct the random translation
equivariant functional representations with stationary prior. Furthermore, we
present how to impose the task-dependent prior for each dataset because a
wrongly imposed prior forms an even worse representation than that of the
kernel smoother. We validate the proposed architecture and its training on
various experiments with time-series and image datasets.
