Supplement for: Unsupervised Learning by Program Synthesis

Unsupervised program synthesis is a domain-general framework for defining domain-specific program synthesis systems. For each domain, we expect the user to sketch a space of program hypotheses. For example, in a domain of regression problems the space of programs might include piecewise polynomials, and in a domain of visual concepts the space of programs might include graphics primitives. As part of the probabilistic framing of unsupervised program synthesis, the user must also write down a (prior) probability distribution over program inputs. Given the program sketch and prior program input probabilities, we give a domain-general algorithm that inductively synthesizes programs from noisy data sets where we have a model of the noise process. The general idea is to compile both the soft constraints of the probabilistic models and the hard constraints of the program space into a set of equations that an SMT solver can jointly reason over. Section 1.1 gives a heuristic overview of this compilation algorithm, while Section 1.2 formalizes the unsupervised program synthesis algorithm.