### Abstract

Sliced Normal (SN) distributions are a generalization of Gaussian distributions where the quadratic argument of the exponential is replaced with a sum of squares polynomial. SNs may be used to represent the distribution of a diverse set of random variables including multi-modal, non-symmetric, and skewed distributions. Unfortunately, the likelihood function of a SN includes a normalization constant and the inclusion of this normalization constant makes the likelihood a non-convex function of the hyperparameters which define the SN. In previous work, suboptimal fitting of the hyperparameters was performed by transforming the given data into a higher dimensional monomial basis and selecting the optimal hyperparameters of a Gaussian fit in this space. However, this approach did not account for the effect of lifting on the normalization constant. Indeed, it was observed that as the number of monomials is increased the likelihood of the Sliced Normal can decrease. In this paper, we increase the likelihood of Sliced Normals found using the previous method by developing a convex formulation which scales the covariance matrix of the Gaussian fit such that the likelihood of the Sliced Normal is maximized. The result is significant improvements of the log likelihood of fitted SN distributions, including a significant increase, especially for problems with 500+ monomials.

Original language | English (US) |
---|---|

Title of host publication | 2020 American Control Conference, ACC 2020 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 4478-4483 |

Number of pages | 6 |

ISBN (Electronic) | 9781538682661 |

DOIs | |

State | Published - Jul 2020 |

Event | 2020 American Control Conference, ACC 2020 - Denver, United States Duration: Jul 1 2020 → Jul 3 2020 |

### Publication series

Name | Proceedings of the American Control Conference |
---|---|

Volume | 2020-July |

ISSN (Print) | 0743-1619 |

### Conference

Conference | 2020 American Control Conference, ACC 2020 |
---|---|

Country | United States |

City | Denver |

Period | 7/1/20 → 7/3/20 |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

## Fingerprint Dive into the research topics of 'A Convex Optimization Approach to Improving Suboptimal Hyperparameters of Sliced Normal Distributions'. Together they form a unique fingerprint.

## Cite this

*2020 American Control Conference, ACC 2020*(pp. 4478-4483). [9147403] (Proceedings of the American Control Conference; Vol. 2020-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC45564.2020.9147403