On the chi square and higher-order chi distances for approximating f-Divergences

IEEE Signal Processing Letters

Volumn 21, Issue 1, 2014, Pages 10-13

  Nielsen, Frank ^a   Nock, Richard ^b  

^a SONY COMPUTER SCIENCE LABORATORIES INC   (Japan)

^b UAG CEREGMIA ^*  (France)

Author keywords

Chi square distance; exponential families; Kullback Leibler divergence; statistical divergences; Taylor series

Indexed keywords

ANALYTIC FORMULA; CHI SQUARE DISTANCE; CLOSED-FORM FORMULAE; EXPONENTIAL FAMILY; KULLBACK LEIBLER DIVERGENCE; STATISTICAL DISTRIBUTION; STATISTICAL DIVERGENCES; TAYLOR EXPANSIONS;

ELECTRICAL ENGINEERING; SIGNAL PROCESSING; TAYLOR SERIES;

POISSON DISTRIBUTION;

EID: 84888265445     PISSN: 10709908     EISSN: None     Source Type: Journal    
DOI: 10.1109/LSP.2013.2288355     Document Type: Article

References (11)

1. T.M. Cover and J.A. Thomas, Elements of Information Theory. New York, NY, USA: Wiley-Interscience, 1991.
2. F. Österreicher, "Distances based on the perimeter of the risk set of a testing problem," Austrian J. Statist., vol. 42, no. 1, p. 3.19, 2013.
3. S.-i. Amari, "Alpha-divergence is unique, belonging to both-divergence and Bregman divergence classes," IEEE Trans. Inf. Theory, vol. 55, no. 11, pp. 4925-4931, 2009.
4. S. Amari and H. Nagaoka, Methods of Information Geometry. Cambridge, U.K.: Oxford Univ. Press, 2000.
5. M. Khosravifard, D. Fooladivanda, and T. A. Gulliver, "Confliction of the convexity and metric properties in-divergences," IEICE Trans. Fund. Electron. Commun. Comput. Sci. , vol. 9, pp. 1848-1853, 2007.
6. N. Barnett, P. Cerone, S. Dragomir, and A. Sofo, "Approximating Csiszár-divergence by the use of taylor's formula with integral remainder," Math. Inequal. Applicat., vol. 5, no. 3, pp. 417-434, 2002.
7. T. Kanamori, T. Suzuki, and M. Sugiyama, "-divergence estimation and two-sample homogeneity test under semiparametric density-ratio models," IEEE Trans. Inf. Theory, vol. 58, no. 2, pp. 708-720, 2012.
8. L. D. Brown, Fundamentals of Statistical Exponential Families: With Applications in Statistical Decision Theory. Beachwood, OH, USA: Inst. Math. Statist., 1986.
9. A. Cichocki and S.-i. Amari, "Families of alpha-beta-and gammadivergences: Flexible and robust measures of similarities," Entropy, vol. 12, no. 6, pp. 1532-1568, 2010.
10. D. C. Brody, "A note on exponential families of distributions," J. Phys. A: Math. Gen., vol. 40, pp. 691-695, 2007.
11. F. Nielsen and S. Boltz, "The Burbea-Rao and Bhattacharyya centroids," IEEE Trans. Inf. Theory, vol. 57, no. 8, pp. 5455-5466, 2011.