Accelerating Understanding of Scientific Experiments with End to End Symbolic Regression

We consider the problem of learning free-form symbolic expressions from raw data, such as that produced by an experiment in any scientific domain. Accurate and interpretable models of scientific phenomena are the cornerstone of scientific research. Simple yet interpretable models, such as linear or logistic regression and decision trees often lack predictive accuracy. Alternatively, accurate blackbox models such as deep neural networks provide high predictive accuracy, but do not readily admit human understanding in a way that would enrich the scientific theory of the phenomenon. Many great breakthroughs in science revolve around the development of parsimonious equational models with high predictive accuracy, such as Newton's laws, universal gravitation, and Maxwell's equations. Previous work on automating the search of equational models from data combine domain-specific heuristics as well as computationally expensive techniques, such as genetic programming and Monte-Carlo search. We develop a deep neural network (MACSYMA) to address the symbolic regression problem as an end-to-end supervised learning problem. MACSYMA can generate symbolic expressions that describe a dataset. The computational complexity of the task is reduced to the feedforward computation of a neural network. We train our neural network on a synthetic dataset consisting of data tables of varying length and varying levels of noise, for which the neural network must learn to produce the correct symbolic expression token by token. Finally, we validate our technique by running on a public dataset from behavioral science.