Gaussian Mixture Estimation from Weighted Samples
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2021
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915223448846336 |
|---|---|
| author | Frisch, Daniel Hanebeck, Uwe D. |
| author_facet | Frisch, Daniel Hanebeck, Uwe D. |
| contents | We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac mixture density over a continuous domain with weighted components. Hence, Gaussian mixture fitting is viewed as density re-approximation. In order to speed up computation, an expectation-maximization method is proposed that properly considers not only the sample locations, but also the corresponding weights. It is shown that methods from literature do not treat the weights correctly, resulting in wrong estimates. This is demonstrated with simple counterexamples. The proposed method works in any number of dimensions with the same computational load as standard Gaussian mixture estimators for unweighted samples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_05109 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Gaussian Mixture Estimation from Weighted Samples Frisch, Daniel Hanebeck, Uwe D. Machine Learning Computer Vision and Pattern Recognition Systems and Control 62G07 We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac mixture density over a continuous domain with weighted components. Hence, Gaussian mixture fitting is viewed as density re-approximation. In order to speed up computation, an expectation-maximization method is proposed that properly considers not only the sample locations, but also the corresponding weights. It is shown that methods from literature do not treat the weights correctly, resulting in wrong estimates. This is demonstrated with simple counterexamples. The proposed method works in any number of dimensions with the same computational load as standard Gaussian mixture estimators for unweighted samples. |
| title | Gaussian Mixture Estimation from Weighted Samples |
| topic | Machine Learning Computer Vision and Pattern Recognition Systems and Control 62G07 |
| url | https://arxiv.org/abs/2106.05109 |