Proof of a Combinatorial Conjecture Coming from the PAC-Bayesian Machine   Learning Theory
  We give a proof of a conjecture of A. Lacasse in his doctoral thesis which has applications in machine learning algorithms. The proof relies on some interesting binomial sums identities introduced by Abel (1839), and on their generalization to the multinomial case by Hurwitz (1902). 
Malik Younsi
math.CO