Pushing for the Extreme: Estimation of Poisson Distribution from Low Count Unreplicated Data—How Close Can We Get?
Studies of learning algorithms typically concentrate on situations where potentially ever growing training sample is available. Yet, there can be situations (e.g., detection of differentially expressed genes on unreplicated data or estimation of time delay in non-stationary gravitationally lensed ph...
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| Format: | Article |
| Language: | English |
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MDPI AG
2013-04-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/15/4/1202 |
| _version_ | 1798042129927241728 |
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| author | Peter Tiňo |
| author_facet | Peter Tiňo |
| author_sort | Peter Tiňo |
| collection | DOAJ |
| description | Studies of learning algorithms typically concentrate on situations where potentially ever growing training sample is available. Yet, there can be situations (e.g., detection of differentially expressed genes on unreplicated data or estimation of time delay in non-stationary gravitationally lensed photon streams) where only extremely small samples can be used in order to perform an inference. On unreplicated data, the inference has to be performed on the smallest sample possible—sample of size 1. We study whether anything useful can be learnt in such extreme situations by concentrating on a Bayesian approach that can account for possible prior information on expected counts. We perform a detailed information theoretic study of such Bayesian estimation and quantify the effect of Bayesian averaging on its first two moments. Finally, to analyze potential benefits of the Bayesian approach, we also consider Maximum Likelihood (ML) estimation as a baseline approach. We show both theoretically and empirically that the Bayesian model averaging can be potentially beneficial. |
| first_indexed | 2024-04-11T22:31:14Z |
| format | Article |
| id | doaj.art-8f6adec22d094096938a576768d36ecc |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T22:31:14Z |
| publishDate | 2013-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-8f6adec22d094096938a576768d36ecc2022-12-22T03:59:25ZengMDPI AGEntropy1099-43002013-04-011541202122010.3390/e15041202Pushing for the Extreme: Estimation of Poisson Distribution from Low Count Unreplicated Data—How Close Can We Get?Peter TiňoStudies of learning algorithms typically concentrate on situations where potentially ever growing training sample is available. Yet, there can be situations (e.g., detection of differentially expressed genes on unreplicated data or estimation of time delay in non-stationary gravitationally lensed photon streams) where only extremely small samples can be used in order to perform an inference. On unreplicated data, the inference has to be performed on the smallest sample possible—sample of size 1. We study whether anything useful can be learnt in such extreme situations by concentrating on a Bayesian approach that can account for possible prior information on expected counts. We perform a detailed information theoretic study of such Bayesian estimation and quantify the effect of Bayesian averaging on its first two moments. Finally, to analyze potential benefits of the Bayesian approach, we also consider Maximum Likelihood (ML) estimation as a baseline approach. We show both theoretically and empirically that the Bayesian model averaging can be potentially beneficial.http://www.mdpi.com/1099-4300/15/4/1202Poisson distributionunreplicated dataBayesian learningexpected Kullback–Leibler divergence |
| spellingShingle | Peter Tiňo Pushing for the Extreme: Estimation of Poisson Distribution from Low Count Unreplicated Data—How Close Can We Get? Entropy Poisson distribution unreplicated data Bayesian learning expected Kullback–Leibler divergence |
| title | Pushing for the Extreme: Estimation of Poisson Distribution from Low Count Unreplicated Data—How Close Can We Get? |
| title_full | Pushing for the Extreme: Estimation of Poisson Distribution from Low Count Unreplicated Data—How Close Can We Get? |
| title_fullStr | Pushing for the Extreme: Estimation of Poisson Distribution from Low Count Unreplicated Data—How Close Can We Get? |
| title_full_unstemmed | Pushing for the Extreme: Estimation of Poisson Distribution from Low Count Unreplicated Data—How Close Can We Get? |
| title_short | Pushing for the Extreme: Estimation of Poisson Distribution from Low Count Unreplicated Data—How Close Can We Get? |
| title_sort | pushing for the extreme estimation of poisson distribution from low count unreplicated data how close can we get |
| topic | Poisson distribution unreplicated data Bayesian learning expected Kullback–Leibler divergence |
| url | http://www.mdpi.com/1099-4300/15/4/1202 |
| work_keys_str_mv | AT petertino pushingfortheextremeestimationofpoissondistributionfromlowcountunreplicateddatahowclosecanweget |