### Abstract

Hold-out and cross-validation are among the most useful methods for model selection and performance assessment of machine learning algorithms. In this paper, we present a computationally efficient algorithm for calculating the hold-out performance for sparse regularized least-squares (RLS) in case the method is already trained with the whole training set. The computational complexity of performing the hold-out is O(|H|^{3} + |H|^{2}n), where |H| is the size of the hold-out set and n is the number of basis vectors. The algorithm can thus be used to calculate various types of cross-validation estimates effectively. For example, when m is the number of training examples, the complexities of N-fold and leave-one-out cross-validations are O(m ^{3}/N^{2} + (m^{2}n)/N) and O(mn), respectively. Further, since sparse RLS can be trained in O(mn^{2}) time for several regularization parameter values in parallel, the fast hold-out algorithm enables efficient selection of the optimal parameter value

Original language | English |
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Title of host publication | Adaptive and Natural Computing Algorithms - 9th International Conference, ICANNGA 2009, Revised Selected Papers |

Subtitle of host publication | Lecture Notes in Computer Science |

Pages | 350-359 |

Number of pages | 10 |

Volume | 5495 |

DOIs | |

Publication status | Published - 2009 |

Externally published | Yes |

Event | 9th International Conference on Adaptive and Natural Computing Algorithms, ICANNGA 2009 - Kuopio, Finland Duration: 23 Apr 2009 → 25 Apr 2009 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 5495 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Conference

Conference | 9th International Conference on Adaptive and Natural Computing Algorithms, ICANNGA 2009 |
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Country | Finland |

City | Kuopio |

Period | 23/04/09 → 25/04/09 |

### Fingerprint

### Cite this

*Adaptive and Natural Computing Algorithms - 9th International Conference, ICANNGA 2009, Revised Selected Papers: Lecture Notes in Computer Science*(Vol. 5495, pp. 350-359). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5495 LNCS). https://doi.org/10.1007/978-3-642-04921-7_36

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*Adaptive and Natural Computing Algorithms - 9th International Conference, ICANNGA 2009, Revised Selected Papers: Lecture Notes in Computer Science.*vol. 5495, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5495 LNCS, pp. 350-359, 9th International Conference on Adaptive and Natural Computing Algorithms, ICANNGA 2009, Kuopio, Finland, 23/04/09. https://doi.org/10.1007/978-3-642-04921-7_36

**Efficient hold-out for subset of regressors.** / Pahikkala, Tapio; Suominen, Hanna; Boberg, Jorma; Salakoski, Tapio I.

Research output: A Conference proceeding or a Chapter in Book › Conference contribution

TY - GEN

T1 - Efficient hold-out for subset of regressors

AU - Pahikkala, Tapio

AU - Suominen, Hanna

AU - Boberg, Jorma

AU - Salakoski, Tapio I.

PY - 2009

Y1 - 2009

N2 - Hold-out and cross-validation are among the most useful methods for model selection and performance assessment of machine learning algorithms. In this paper, we present a computationally efficient algorithm for calculating the hold-out performance for sparse regularized least-squares (RLS) in case the method is already trained with the whole training set. The computational complexity of performing the hold-out is O(|H|3 + |H|2n), where |H| is the size of the hold-out set and n is the number of basis vectors. The algorithm can thus be used to calculate various types of cross-validation estimates effectively. For example, when m is the number of training examples, the complexities of N-fold and leave-one-out cross-validations are O(m 3/N2 + (m2n)/N) and O(mn), respectively. Further, since sparse RLS can be trained in O(mn2) time for several regularization parameter values in parallel, the fast hold-out algorithm enables efficient selection of the optimal parameter value

AB - Hold-out and cross-validation are among the most useful methods for model selection and performance assessment of machine learning algorithms. In this paper, we present a computationally efficient algorithm for calculating the hold-out performance for sparse regularized least-squares (RLS) in case the method is already trained with the whole training set. The computational complexity of performing the hold-out is O(|H|3 + |H|2n), where |H| is the size of the hold-out set and n is the number of basis vectors. The algorithm can thus be used to calculate various types of cross-validation estimates effectively. For example, when m is the number of training examples, the complexities of N-fold and leave-one-out cross-validations are O(m 3/N2 + (m2n)/N) and O(mn), respectively. Further, since sparse RLS can be trained in O(mn2) time for several regularization parameter values in parallel, the fast hold-out algorithm enables efficient selection of the optimal parameter value

UR - http://www.scopus.com/inward/record.url?scp=78650747993&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-04921-7_36

DO - 10.1007/978-3-642-04921-7_36

M3 - Conference contribution

SN - 3642049206

SN - 9783642049200

VL - 5495

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 350

EP - 359

BT - Adaptive and Natural Computing Algorithms - 9th International Conference, ICANNGA 2009, Revised Selected Papers

ER -