### Abstract

In our prior work we explored the different ML models that could be used, and how to identify suitable features of the input polynomials. In the present paper we both repeat our prior experiments on problems which have more variables (and thus exponentially more possible orderings), and examine the metric which our ML classifiers targets. The natural metric is computational runtime, with classifiers trained to pick the ordering which minimises this. However, this leads to the situation were models do not distinguish between any of the non-optimal orderings, whose runtimes may still vary dramatically. In this paper we investigate a modification to the cross-validation algorithms of the classifiers so that they do distinguish these cases, leading to improved results.

Original language | English |
---|---|

Title of host publication | Mathematical Aspects of Computer and Information Sciences 2019 |

Subtitle of host publication | Proc. MACIS 2019 |

Publisher | Springer International Publishing |

Number of pages | 16 |

Publication status | Accepted/In press - 12 Nov 2019 |

Event | Mathematical Aspects of Computer and Information Sciences 2019 - Istanbul, Turkey Duration: 13 Nov 2019 → 15 Nov 2019 |

### Publication series

Name | Lecture Notes in Computer Science |
---|

### Conference

Conference | Mathematical Aspects of Computer and Information Sciences 2019 |
---|---|

Abbreviated title | MACIS 2019 |

Country | Turkey |

City | Istanbul |

Period | 13/11/19 → 15/11/19 |

### Fingerprint

### Keywords

- Machine Learning
- cross-validation
- Computer Algebra
- Symbolic Computation
- Cylindrical Algebraic Decomposition

### Cite this

*Mathematical Aspects of Computer and Information Sciences 2019: Proc. MACIS 2019*(Lecture Notes in Computer Science). Springer International Publishing.

**Improved cross-validation for classifiers that make algorithmic choices to minimise runtime without compromising output correctness.** / Florescu, Dorian; England, Matthew.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Mathematical Aspects of Computer and Information Sciences 2019: Proc. MACIS 2019.*Lecture Notes in Computer Science, Springer International Publishing, Mathematical Aspects of Computer and Information Sciences 2019, Istanbul, Turkey, 13/11/19.

}

TY - CHAP

T1 - Improved cross-validation for classifiers that make algorithmic choices to minimise runtime without compromising output correctness

AU - Florescu, Dorian

AU - England, Matthew

PY - 2019/11/12

Y1 - 2019/11/12

N2 - Our topic is the use of machine learning to improve software by making choices which do not compromise the correctness of the output, but do affect the time taken to produce such output. We are particularly concerned with computer algebra systems (CASs), and in particular, our experiments are for selecting the variable ordering to use when performing a cylindrical algebraic decomposition of n-dimensional real space with respect to the signs of a set of polynomials.In our prior work we explored the different ML models that could be used, and how to identify suitable features of the input polynomials. In the present paper we both repeat our prior experiments on problems which have more variables (and thus exponentially more possible orderings), and examine the metric which our ML classifiers targets. The natural metric is computational runtime, with classifiers trained to pick the ordering which minimises this. However, this leads to the situation were models do not distinguish between any of the non-optimal orderings, whose runtimes may still vary dramatically. In this paper we investigate a modification to the cross-validation algorithms of the classifiers so that they do distinguish these cases, leading to improved results.

AB - Our topic is the use of machine learning to improve software by making choices which do not compromise the correctness of the output, but do affect the time taken to produce such output. We are particularly concerned with computer algebra systems (CASs), and in particular, our experiments are for selecting the variable ordering to use when performing a cylindrical algebraic decomposition of n-dimensional real space with respect to the signs of a set of polynomials.In our prior work we explored the different ML models that could be used, and how to identify suitable features of the input polynomials. In the present paper we both repeat our prior experiments on problems which have more variables (and thus exponentially more possible orderings), and examine the metric which our ML classifiers targets. The natural metric is computational runtime, with classifiers trained to pick the ordering which minimises this. However, this leads to the situation were models do not distinguish between any of the non-optimal orderings, whose runtimes may still vary dramatically. In this paper we investigate a modification to the cross-validation algorithms of the classifiers so that they do distinguish these cases, leading to improved results.

KW - Machine Learning

KW - cross-validation

KW - Computer Algebra

KW - Symbolic Computation

KW - Cylindrical Algebraic Decomposition

M3 - Chapter

T3 - Lecture Notes in Computer Science

BT - Mathematical Aspects of Computer and Information Sciences 2019

PB - Springer International Publishing

ER -