Quizz 3: Information: Theory and Geometry

by Frank NIELSEN
This is the third installment of the quizz series.
Check the 1st quizz first, or the second quizz
(As usual, I welcome comments and suggestions! -:) )

1. The f-divergences generalizing the Kullback-Leibler divergence have been independently studied by Imre Csiszar (1963) and Ali and Silvey (1966). The seminal paper of S. M. Ali and S. D. Silvey ("A general class of coefficients of divergence of one distribution from another". Journal of the Royal Statistical Society, Series B 28 (1): 131140.) is authored with the initials only : What are the first names of Ali and Silvey ?
a) Syed Mohammed Ali and Simon Daniel Silvey
b) Sabir Mumtaz Ali and Simon David Silvey
c) Syed Mumtaz Ali and Samuel David Silvey
2. Which family of distortion measures gives always homogeneous means (as average distance minimizers) ?
a) Bregman divergences
b) f-divergences
c) Burbea-Rao divergences
d) Prokhorov metrics

3. The median and mode of a distribution can be found as a ?
a) Bregman centroid
b) f-centroid
c) Burbea-Rao centroid
4. The Euclidean, elliptical and hyperbolic geometries are three examples of differential geometries that have been generalized and later termed:
Riemmanian geometry
Riemannian geometry
Riemanian geometry
Riemmannian geometry
5. The Jensen-Shannon divergence is a symmetric divergence (whose square root is a metric) that was thoroughly studied by Jianhua Lin in 1991. This fundamental information measure appeared in a former paper without being explicitly studied.
Jeffreys J divergence (1946)
Ali-Silvey divergence (1966)
Csiszar divergence (1967)
Jensen difference of Rao (1982)
6. Q: Who pionneered the study of alpha-divergences

7. In mathematics, the Bunyakovsky inequality is also known as the...
Cauchy-Schwartz inequality
Cauchy-Swcharz inequality
Cauchy-Schwarz inequality
Cochy-Schwarz inequality

8. The logarithmic mean is also known as the
Holder mean
Gini mean
Lehmer mean
Stolarsky mean

9. Which of the following statistical distribution does not belong to the exponential families?
Gaussian distribution
Cauchy distribution
Poisson distribution
Beta distribution

10. Regular exponential families are in bijection with one class of distortion measures. Which one?
regular Bregman divergences
regular f-divergences
regular Burbea-Rao divergences

© June 2010 Frank Nielsen, All rights reserved.