| Title:
|
A note on how Rényi entropy can create a spectrum of probabilistic merging operators (English) |
| Author:
|
Adamčík, Martin |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
55 |
| Issue:
|
4 |
| Year:
|
2019 |
| Pages:
|
605-617 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we present a result that relates merging of closed convex sets of discrete probability functions respectively by the squared Euclidean distance and the Kullback-Leibler divergence, using an inspiration from the Rényi entropy. While selecting the probability function with the highest Shannon entropy appears to be a convincingly justified way of representing a closed convex set of probability functions, the discussion on how to represent several closed convex sets of probability functions is still ongoing. The presented result provides a perspective on this discussion. Furthermore, for those who prefer the standard minimisation based on the squared Euclidean distance, it provides a connection to a probabilistic merging operator based on the Kullback-Leibler divergence, which is closely connected to the Shannon entropy. (English) |
| Keyword:
|
probabilistic merging |
| Keyword:
|
information geometry |
| Keyword:
|
Kullback–Leibler divergence |
| Keyword:
|
Rényi entropy |
| MSC:
|
52A99 |
| MSC:
|
52C99 |
| idZBL:
|
Zbl 07177906 |
| idMR:
|
MR4043538 |
| DOI:
|
10.14736/kyb-2019-4-0605 |
| . |
| Date available:
|
2020-01-10T14:20:58Z |
| Last updated:
|
2020-04-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147959 |
| . |
| Reference:
|
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