Supplementary Material: Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes

We first review the notation introduced in the main body for convenience. S denote a context and target set respectively. Later, as is common in recent meta-learning approaches, we will consider predicting the target set from the context set Garnelo et al. [3, 4]. The measurable sets of Σ are those which can be specified by the values of the function at a countable subset I X of its input locations. Since in practice we only ever observe data at a finite number of points, this is sufficient for our purposes. Hence we may think of these stochastic processes as defined by their finite-dimensional marginals. We now define what it means to condition on observations of the stochastic process P. Let p(y|X) denote the density with respect to Lebesgue measure of the finite marginal of P with index set X (we assume these densities always exist). Strictly speaking, this is non-standard terminology, since P is the law of a stochastic process.