Quizz 4: Information Geometry

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

1. The statistical distribution p(x;θ) belonging the name of exponential families are:
a) log-concave
b) log-convex
c) neither
2. Exponential families can be recovered by the maximum entropy estimate method. Who pioneered that approach?
a) T. Cover
b) S. Kullback
c) H. Jeyffreys
d) E. T. Jaynes

3. Finding the distribution that has maximal entropy over the set of linear constraints is equivalent to finding the I-projection of the uniform distribution onto the constraints. Who pioneered the geometric approach of I-projection?
a) S.-i. Amari
b) I. Csiszar
c) N. Chentsov
4. The Kullback-Leibler divergence can be lower bounded using the variational metric. What is the generic name for designing such an inequality
Cramer-Rao inequality
Bhattacharyya inequality
Pinsker inequality
Bayes inequality
5. Both Renyi entropies (extensive) and Tsallis entropies (non-extensive) generalizing Shannon entropy, can be interpreted using a biparameter family of entropies. Mittal, and Sharma and Taneja independently published papers in which year?
6. Give a famous example of exponential families in statistical physics:
Einstein model
Botzlmann model
Ising model
Gibbs model

7. In physics, EM means electro-magnetism. But what does this acronym mean in statistics/computer science:
empirical minimization
emipirical maximization
extended minimization
expectation maximization

8. In statistical physics, what does a Gibbs distribution mean?
a Markov Random Field
a Conditional Random Field
a Hidden Markov Model
an exponential family

9. In 1957, E.T. Jaynes came up with two papers introducing the novel MaxEnt statistical inference scheme for thermodynamics. Jaynes started his PhD with Oppenheimer but aborted, he then restarted a PhD with Eugene Wigner. What are the first names of E. T.?
Edgard Thompson
Edwin Thompson
Edgard Thomason
Edwin Thomason

10. Quasi-arithmetic means were independently studied by Kolmogorov and Nagumo. What is the firstname of Nagumo in the original paper
M. Nagumo, ¨Uber eine klasse der mittelwerte, Japan. J. Math., 7 (1930) 71–79.


© July 2010 Frank Nielsen, All rights reserved.