The main thesis of this work is that computers can be programmed to derive mathematical formula and relationships from data in an efficient, reproducible, and interpretable way. This problem is known as Symbolic Regression, the data driven search for mathematical relations as performed by a computer. In essence, this is a search over all possible equations to find those which best model the data on hand.
We propose Prioritized Grammar Enumeration (PGE) as a deterministic machine learning algorithm for solving Symbolic Regression. PGE works with a grammar’s rules and input data to prioritize the enumeration of expressions in that language. By making large reductions to the search space and introducing mechanisms for memoization, PGE can explore the space of all equations efficiently. Most notably, PGE provides reproducibility, a key aspect to any system used by scientists at large.
We then enhance the PGE algorithm in several ways. We enrich the equation equation types and application domains PGE can operate on. We deepen equation abstractions and relationships, add configuration to search operaters, and enrich the fitness metrics. We enable PGE to scale by decoupling the subroutines into a set of services.
Our algorithm experiments cover a range of problem types from a multitude of domains. Our experiments cover a variety of architectural and parameter configurations. Our results show PGE to have great promise and efficacy in automating the discovery of equations at the scales needed by tomorrow's scientific data problems.
Additionally, reproducibility has been a significant factor in the formulation and development of PGE. All supplementary materials, codes, and data can be found at github.com/verdverm/pypge.
|Commitee:||Chen, Yu, Madden, Patrick, Miller, Timothy|
|School:||State University of New York at Binghamton|
|School Location:||United States -- New York|
|Source:||DAI-B 77/11(E), Dissertation Abstracts International|
|Keywords:||Dynamic programming, Genetic programming, Machine learning, Symbolic regression|
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