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Symbolic regression is a kind of machine learning consisting of the construction of models by symbolically constructing formulas and testing how well they describe a training data set. It is essentially a search process to find a workable formula, using some criteria to decide which of two is "better", the effectiveness of the search depending upon the this evaluation ability. Given this general strategy, a wide variety of techniques are used, which include those common in modern AI, such as neural networks.
This is in contrast to statistical regression, which develops a finished formula by numerically calculating the best coefficients to plug into a pre-selected parameterized formula. Manipulating symbols potentially explores a much wider set of candidate models, which is so wide that it presents its own challenges.