## Abstract

In this paper, we study the hard and soft support vector regression techniques applied to a set of n linear measurements of the form y_{i} = β^{T}_{?} x_{i} + n_{i} where β_{?} is an unknown vector, (x_{i})^{n}_{i=1} are the feature vectors and (n_{i})^{n}_{i=1} model the noise. Particularly, under some plausible assumptions on the statistical distribution of the data, we characterize the feasibility condition for the hard support vector regression in the regime of high dimensions and, when feasible, derive an asymptotic approximation for its risk. Similarly, we study the test risk for the soft support vector regression as a function of its parameters. Our results are then used to optimally tune the parameters intervening in the design of hard and soft support vector regression algorithms. Based on our analysis, we illustrate that adding more samples may be harmful to the test performance of support vector regression, while it is always beneficial when the parameters are optimally selected. Such a result reminds a similar phenomenon observed in modern learning architectures according to which optimally tuned architectures present a decreasing test performance curve with respect to the number of samples.

Original language | English (US) |
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Title of host publication | Proceedings of the 38th International Conference on Machine Learning, ICML 2021 |

Publisher | Mathematical Research Press |

Pages | 9671-9680 |

Number of pages | 10 |

ISBN (Electronic) | 9781713845065 |

State | Published - 2021 |

Event | 38th International Conference on Machine Learning, ICML 2021 - Virtual, Online Duration: Jul 18 2021 → Jul 24 2021 |

### Publication series

Name | Proceedings of Machine Learning Research |
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Volume | 139 |

ISSN (Electronic) | 2640-3498 |

### Conference

Conference | 38th International Conference on Machine Learning, ICML 2021 |
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City | Virtual, Online |

Period | 07/18/21 → 07/24/21 |

### Bibliographical note

Publisher Copyright:Copyright © 2021 by the author(s)

## ASJC Scopus subject areas

- Artificial Intelligence
- Software
- Control and Systems Engineering
- Statistics and Probability