Dergiler / Journal of New Results in Science / 2016 / Cilt: 5 - Sayı: 11

New Information Inequalities in Terms of Variational Distance and its Application

Sayfa
30–40
Yayın Tarihi
2016-08-31
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Asymptotic approximation on new generalized f- divergence is done as well.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this work, new information inequalities are obtained and characterized on new generalized f- divergence (introduced by Jain and Saraswat (2012)) in terms of the Variational distance and these inequalities have been taken for evaluating some new relations among well known divergences.
📊
Temel Bulgular & Veri:These new relations have been verified numerically by considering two discrete probability distributions: Binomial and Poisson.
💡
Sonuç & Katkı:Asymptotic approximation on new generalized f- divergence is done as well.
🔬Tür:Araştırma Makalesi
📍Kapsam:2012 Verileri
⚙️Değişkenler:Variational distance · new information inequalities · bounded variation

Abstract

In this work, new information inequalities are obtained and characterized on new generalized f- divergence (introduced by Jain and Saraswat (2012)) in terms of the Variational distance and these inequalities have been taken for evaluating some new relations among well known divergences. These new relations have been verified numerically by considering two discrete probability distributions: Binomial and Poisson. Asymptotic approximation on new generalized f- divergence is done as well.

🔖

Bu Makaleye Atıf Yap

JAİN, K. C., CHHABRA, P. (2016). New Information Inequalities in Terms of Variational Distance and its Application. Journal of New Results in Science, Cilt: 5 - Sayı: 11, 30–40. https://ajindex.com/articles/777899

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (15)

  1. M.B. Bassat, f- Entropies, probability of error and feature selection, Inform. Control, vol. 39, 1978, pp: 227-242.
  2. H.C. Chen, Statistical pattern recognition, Hoyderc Book Co., Rocelle Park, New York, 1973.
  3. C.K. Chow and C.N. Lin, Approximating discrete probability distributions with dependence trees, IEEE Trans. Inform. Theory, vol. 14, 1968, no 3, pp: 462-467.
  4. D. Dacunha- Castelle, Ecole d’Ete de Probabilites de, Saint-Flour VII-1977,
  5. Berlin, Heidelberg, New York: Springer, 1978.
  6. S.S. Dragomir, On the Ostrowski’s integral inequality for mappings of bounded variation and applications, RGMIA Res. Rep. Coll. 2 (1999) No.1, 73?80. S.S. Dragomir, V. Gluscevic, and C.E.M. Pearce, Approximation for the Csiszar f-divergence via midpoint inequalities, in inequality theory and applications - Y.J.Cho, J.K. Kim, and S.S. Dragomir (Eds.), Nova Science Publishers,
  7. Inc., Huntington, New York, Vol. 1, 2001, pp. 139-154.
  8. D.V. Gokhale and S. Kullback, Information in contingency Tables, New York, Marcel Dekker, 1978.
  9. K.C. Jain and P. Chhabra, Series of new information divergences, properties and corresponding series of metric spaces, International Journal of Innovative Research in Science, Engineering and Technology, vol. 3- no.5 (2014), pp: 12124- 12132. K.C. Jain and R.N. Saraswat, Some new information inequalities and its applications in information theory, International Journal of Mathematics Research, vol. 4, Number 3 (2012), pp. 295-307.
  10. L. Jones and C. Byrne, General entropy criteria for inverse problems with applications to data compression, pattern classification and cluster analysis, IEEE Trans. Inform. Theory, vol. 36, 1990, pp: 23-30.
  11. T. Kailath, The divergence and Bhattacharyya distance measures in signal selection, IEEE Trans. Comm. Technology, vol. COM-15, 1967, pp: 52-60.
  12. T.T. Kadota and L.A. Shepp, On the best finite set of linear observables for discriminating two Gaussian signals, IEEE Trans. Inform. Theory, vol. 13, 1967, pp: 288-294.
  13. D. Kazakos and T. Cotsidas, A decision theory approach to the approximation of discrete probability densities, IEEE Trans. Perform. Anal. Machine Intell., vol. 1, 1980, pp: 61-67.
  14. A.N. Kolmogorov, On the approximation of distributions of sums of independent summands by infinitely divisible distributions, Sankhya, 25, 159-174, 1963.
  15. F. Nielsen and S. Boltz, The Burbea-Rao and Bhattacharyya centroids, Apr. 2010, arxiv. K. Pearson, On the Criterion that a given system of deviations from the probable in the case of correlated