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Applying Machine Learning to the Problem of Choosing a Heuristic to Select the Variable Ordering for Cylindrical Algebraic Decomposition [chapter]

Zongyan Huang, Matthew England, David Wilson, James H. Davenport, Lawrence C. Paulson, James Bridge
2014 Lecture Notes in Computer Science  
In this paper we use machine learning (specifically a support vector machine) to select between heuristics for choosing a variable ordering, outperforming each of the separate heuristics.  ...  Machine learning is the process of fitting a computer model to a complex function based on properties learned from measured data.  ...  The authors thank the anonymous referees for useful comments which improved the paper.  ... 
doi:10.1007/978-3-319-08434-3_8 fatcat:h7ea2kvf3rgzbek3f3xplsu5ze

Comparing machine learning models to choose the variable ordering for cylindrical algebraic decomposition [article]

Matthew England, Dorian Florescu
2019 arXiv   pre-print
We address the problem of selecting the variable ordering for cylindrical algebraic decomposition (CAD), an important algorithm in Symbolic Computation.  ...  The present work extends to have ML select the variable ordering directly, and to try a wider variety of ML techniques.  ...  Acknowledgements The authors are supported by EPSRC Project EP/R019622/1: Embedding Machine Learning within Quantifier Elimination Procedures.  ... 
arXiv:1904.11061v1 fatcat:mavnkb7pjbc3lgkabxrgo4zd2a

Applying Machine Learning to Heuristics for Real Polynomial Constraint Solving [chapter]

Christopher W. Brown, Glenn Christopher Daves
2020 Lecture Notes in Computer Science  
We consider a specific choice-point in the algorithm for constructing an open Non-uniform Cylindrical Algebraic Decomposition (NuCAD) for a conjunction of constraints, and we learn a heuristic for making  ...  We hope that the approach we take to learning this heuristic, which is not a natural fit to machine learning, can be applied effectively to other choices in constraint solving algorithms.  ...  Parts of this work were supported by National Science Foundation Grant 1525896.  ... 
doi:10.1007/978-3-030-52200-1_29 fatcat:f5gxdztdkva5hgprwlnjmuxnqy

Experience with Heuristics, Benchmarks & Standards for Cylindrical Algebraic Decomposition [article]

Matthew England, James H. Davenport
2016 arXiv   pre-print
To start this learning process we summarise our experience with heuristic development for the computer algebra algorithm Cylindrical Algebraic Decomposition.  ...  ISSAC '15, pp. 1-6, ACM, 2015] the author identified the use of sophisticated heuristics as a technique that the Satisfiability Checking community excels in and from which it is likely the Symbolic Computation  ...  Thanks also to the anonymous referees for their comments which improved the paper. Most of the work surveyed here was supported by EPSRC grant EP/J003247/1.  ... 
arXiv:1609.09269v1 fatcat:yhfamipsvnfupnf6ebfgtvxqru

Machine Learning for Mathematical Software [chapter]

Matthew England
2018 Lecture Notes in Computer Science  
However, recent results for quantifier elimination suggest that, given enough example problems, there is scope for machine learning tools like Support Vector Machines to improve the performance of Computer  ...  However, algorithms and implementations often come with a range of choices which have no effect on the mathematical correctness of the end result but a great effect on the resources required to find it  ...  The author is now supported by EPSRC grant EP/R019622/1.  ... 
doi:10.1007/978-3-319-96418-8_20 fatcat:f53ce6zd6bdgfels5tqn5s37nq

Using Machine Learning to Improve Cylindrical Algebraic Decomposition

Zongyan Huang, Matthew England, David J. Wilson, James Bridge, James H. Davenport, Lawrence C. Paulson
2019 Mathematics in Computer Science  
In this paper we apply it in two case studies: the first to select between heuristics for choosing a CAD variable ordering; the second to identify when a CAD problem instance would benefit from Gröbner  ...  Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields.  ...  , and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s11786-019-00394-8 fatcat:zbww4kstzjdqvdvfe3x5ymvct4

From Individuals to Populations: A Symbolic Process Algebra Approach to Epidemiology

Chris McCaig, Rachel Norman, Carron Shankland
2009 Mathematics in Computer Science  
In this paper we apply it in two case studies: the first to select between heuristics for choosing a CAD variable ordering; the second to identify when a CAD problem instance would benefit from Gröbner  ...  Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields.  ...  , and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s11786-008-0066-2 fatcat:zheeoezu3jhydaw7ant6jk4tke

Algorithmically generating new algebraic features of polynomial systems for machine learning [article]

Dorian Florescu, Matthew England
2019 arXiv   pre-print
Our focus is selecting the variable ordering for cylindrical algebraic decomposition (CAD), an important algorithm implemented in several CASs, and now also SMT-solvers.  ...  Such choices are candidates for machine learning (ML) approaches, however, there are difficulties in applying standard ML techniques, such as the efficient identification of ML features from input data  ...  Acknowledgements This work is supported by EPSRC Project EP/R019622/1: Embedding Machine Learning within Quantifier Elimination Procedures.  ... 
arXiv:1906.01455v1 fatcat:lpyiksuzzzbc3a3qfoxsnz6jna

A machine learning based software pipeline to pick the variable ordering for algorithms with polynomial inputs [article]

Dorian Florescu, Matthew England
2020 arXiv   pre-print
In the past we experimented with one such choice: the variable ordering to use when building a Cylindrical Algebraic Decomposition (CAD).  ...  We are interested in the application of Machine Learning (ML) technology to improve mathematical software.  ...  Acknowledgements This work is funded by EPSRC Project EP/R019622/1: Embedding Machine Learning within Quantifier Elimination Procedures. We thank the anonymous referees for their comments.  ... 
arXiv:2005.11251v1 fatcat:7xhxvkgkpfcz3mjjvr6uem7bmq

A Machine Learning Based Software Pipeline to Pick the Variable Ordering for Algorithms with Polynomial Inputs [chapter]

Dorian Florescu, Matthew England
2020 Lecture Notes in Computer Science  
In the past we experimented with one such choice: the variable ordering to use when building a Cylindrical Algebraic Decomposition (CAD).  ...  We are interested in the application of Machine Learning (ML) technology to improve mathematical software.  ...  This work is funded by EPSRC Project EP/R019622/1: Embedding Machine Learning within Quantifier Elimination Procedures. We thank the anonymous referees for their comments.  ... 
doi:10.1007/978-3-030-52200-1_30 fatcat:mkrpckkoxnevpdiynqfwny6rhu

Foreword

James H. Davenport, Laura Kovacs, Daniela Zaharie
2019 Mathematics in Computer Science  
: (i) selection between heuristics for choosing a CAD variable ordering; (ii) identification of CAD problem instances which would benefit from Gröbner Basis preconditioning.  ...  The approach is based on learning a matching between problem features and heuristics to be applied (e.g. choice of variable ordering) and its performance is experimentally illustrated for two case studies  ...  The work of Laura Kovács is supported by the ERC Starting Grant 2014 SYMCAR 639270, the Wallenberg Academy Fellowship 2014 TheProSE and the Austrian FWF project W1255-N23.  ... 
doi:10.1007/s11786-019-00411-w fatcat:d4rv4kog6zbv5b4ocfl2jwmpdy

Choosing a Variable Ordering for Truth-Table Invariant Cylindrical Algebraic Decomposition by Incremental Triangular Decomposition [chapter]

Matthew England, Russell Bradford, James H. Davenport, David Wilson
2014 Lecture Notes in Computer Science  
Cylindrical algebraic decomposition (CAD) is a key tool for solving problems in real algebraic geometry and beyond.  ...  Like all CAD algorithms the user must provide a variable ordering which can have a profound impact on the tractability of a problem.  ...  RC-TTICAD was developed by Changbo Chen, Marc Moreno Maza and the present authors.  ... 
doi:10.1007/978-3-662-44199-2_68 fatcat:gj5u2g4osncwfp46e3er34plby

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

Dorian Florescu, Matthew England
2019 arXiv   pre-print
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  ...  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.  ...  Acknowledgements This work is funded by EPSRC Project EP/R019622/1: Embedding Machine Learning within Quantifier Elimination Procedures.  ... 
arXiv:1911.12672v1 fatcat:ozm7omqywna2hkaeubiio2edrm

Using Machine Learning to Decide When to Precondition Cylindrical Algebraic Decomposition with Groebner Bases

Zongyan Huang, Matthew England, James H. Davenport, Lawrence C. Paulson
2016 2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)  
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields.  ...  In the present paper we investigate whether machine learning, specifically a support vector machine (SVM), may be used to identify those CAD problems which benefit from GB preconditioning.  ...  Acknowledgements Thanks to David Wilson and James Bridge, our collaborators on [41] , for useful conversations on the topic of machine learning to optimise computer algebra.  ... 
doi:10.1109/synasc.2016.020 dblp:conf/synasc/HuangEDP16 fatcat:ckolngesnbewhk67ovxs23hzw4

Using Machine Learning to Improve Cylindrical Algebraic Decomposition [article]

Zongyan Huang, Matthew England, David Wilson, James H. Davenport, and Lawrence C. Paulson
2018 arXiv   pre-print
In this paper we apply it in two case studies: the first to select between heuristics for choosing a CAD variable ordering; the second to identify when a CAD problem instance would benefit from Groebner  ...  Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields.  ...  The authors acknowledge both the anonymous referees of the present paper, and those of [66] and [65] , whose comments also helped improve this article.  ... 
arXiv:1804.10520v1 fatcat:nfgkcdi535ejtixmn6iyt4w5cu
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