Fractional Divergence of Probability Densities
The divergence or relative entropy between probability densities is examined. Solutions that minimise the divergence between two distributions are usually “trivial” or unique. By using a fractional-order formulation for the divergence with respect to the parameters, the distance between probability...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-10-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/1/1/8 |
| _version_ | 1818407729766596608 |
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| author | Aris Alexopoulos |
| author_facet | Aris Alexopoulos |
| author_sort | Aris Alexopoulos |
| collection | DOAJ |
| description | The divergence or relative entropy between probability densities is examined. Solutions that minimise the divergence between two distributions are usually “trivial” or unique. By using a fractional-order formulation for the divergence with respect to the parameters, the distance between probability densities can be minimised so that multiple non-trivial solutions can be obtained. As a result, the fractional divergence approach reduces the divergence to zero even when this is not possible via the conventional method. This allows replacement of a more complicated probability density with one that has a simpler mathematical form for more general cases. |
| first_indexed | 2024-12-14T09:32:28Z |
| format | Article |
| id | doaj.art-797ac7b3bde846cbae50e8eb53253c9e |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-12-14T09:32:28Z |
| publishDate | 2017-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-797ac7b3bde846cbae50e8eb53253c9e2022-12-21T23:08:02ZengMDPI AGFractal and Fractional2504-31102017-10-0111810.3390/fractalfract1010008fractalfract1010008Fractional Divergence of Probability DensitiesAris Alexopoulos0P.O. Box 123AA, Adelaide, SA 5000, AustraliaThe divergence or relative entropy between probability densities is examined. Solutions that minimise the divergence between two distributions are usually “trivial” or unique. By using a fractional-order formulation for the divergence with respect to the parameters, the distance between probability densities can be minimised so that multiple non-trivial solutions can be obtained. As a result, the fractional divergence approach reduces the divergence to zero even when this is not possible via the conventional method. This allows replacement of a more complicated probability density with one that has a simpler mathematical form for more general cases.https://www.mdpi.com/2504-3110/1/1/8divergencefractional divergenceprobability densities |
| spellingShingle | Aris Alexopoulos Fractional Divergence of Probability Densities Fractal and Fractional divergence fractional divergence probability densities |
| title | Fractional Divergence of Probability Densities |
| title_full | Fractional Divergence of Probability Densities |
| title_fullStr | Fractional Divergence of Probability Densities |
| title_full_unstemmed | Fractional Divergence of Probability Densities |
| title_short | Fractional Divergence of Probability Densities |
| title_sort | fractional divergence of probability densities |
| topic | divergence fractional divergence probability densities |
| url | https://www.mdpi.com/2504-3110/1/1/8 |
| work_keys_str_mv | AT arisalexopoulos fractionaldivergenceofprobabilitydensities |