Dimensionality Reduction via Program Induction

This work proposes a machine learning algorithm for inductive synthesis of programs. The objective of the algorithm is to learn a distribution over programs that evaluate to a given constant. The algorithm searches for programs in a bottomup fashion, going directly from the data to the program, in contrast to recent, similar work that adopts a generate-and-test approach. I use this algorithm to perform density estimation upon strings. Then, I show that the estimated density can be used to perform two distinct kinds of dimensionality reduction upon strings: one, converting strings in to real-valued vectors; and two, converting strings to compressive symbolic descriptions. The goals of this work are to demonstrate a bottom-up approach to program induction, and to evaluate two types of dimensionality reduction suggested by this bottom-up approach.