Lessons on Datasets and Paradigms in Machine Learning for Symbolic
  Computation: A Case Study on CAD
Tereso del Río Matthew England
Symbolic Computation algorithms and their implementation in computer algebra
systems often contain choices which do not affect the correctness of the output
but can significantly impact the resources required: such choices can benefit
from having them made separately for each problem via a machine learning model.
This study reports lessons on such use of machine learning in symbolic
computation, in particular on the importance of analysing datasets prior to
machine learning and on the different machine learning paradigms that may be
utilised. We present results for a particular case study, the selection of
variable ordering for cylindrical algebraic decomposition, but expect that the
lessons learned are applicable to other decisions in symbolic computation.
  We utilise an existing dataset of examples derived from applications which
was found to be imbalanced with respect to the variable ordering decision. We
introduce an augmentation technique for polynomial systems problems that allows
us to balance and further augment the dataset, improving the machine learning
results by 28\% and 38\% on average, respectively. We then demonstrate how the
existing machine learning methodology used for the problem $-$ classification
$-$ might be recast into the regression paradigm. While this does not have a
radical change on the performance, it does widen the scope in which the
methodology can be applied to make choices.