conditional neural process

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Introduction

To train a model effectively, deep neural networks require large datasets. To mitigate this data efficiency problem, learning in two phases is one approach : the first phase learns the statistics of a generic domain without committing to a specific learning task; the second phase learns a function for a specific task, but does so using only a small number of data points by exploiting the domain-wide statistics already learned.

For example, consider a data set [math] \{x_i, y_i\} [/math] with evaluations [math]y_i = f(x_i) [/math] for some unknown function [math]f[/math]. Assume [math]g[/math] is an approximating function of f. The aim is yo minimize the loss between [math]f[/math] and [math]g[/math] on the entire space [math]X[/math]. In practice, the routine is evaluated on a finite set of observations.

In this work, they proposed a family of models that represent solutions to the supervised problem, and ab end-to-end training approach to learning them, that combine neural networks with features reminiscent if Gaussian Process. They call this family of models Conditional Neural Processes.


Model

Let training set be [math] O = \{x_i, y_i\}_{i = 0} ^ n-1[/math], and test set be [math] T = \{x_i, y_i\}_{i = n} ^ {n + m - 1}[/math].

We assume the outputs are obtained by the following steps :

P be a probability distribution over functions [math] F : X \to Y[/math]