Theoretical foundations

MOSAIKS is motivated by the goal of enabling generalizable and skillful SIML predictions. It achieves this by embedding images in a basis that is both descriptive (i.e., models trained using this single basis achieve high skill across diverse labels) and efficient (i.e., such skill is achieved using a relatively low-dimensional basis). The approach for this embedding relies on the theory of random kitchen sinks¹⁶, a method for feature generation that enables the linear approximation of arbitrary well-behaved functions. This is akin to the use of polynomial features or discrete Fourier transforms for function approximation generally, such as functions of one dimension. When users apply these features in linear regression, they identify linear weightings of these basis vectors important for predicting a specific set of labels. With inputs of high dimension, such as the satellite images we consider, it has been shown experimentally^17–19 and theoretically⁴³ that a randomly selected subspace of the basis often performs as well as the entire basis for prediction problems.