# September 2012

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## Rolling Dice Mod 3

It is fairly obvious if you think about it and if you are a mathematician, but I was surprised by this theorem.

Theorem:  Roll any number of dice all of which can have any (finite) number of sides except at least one die which is the standard six sided die.  The probability that the sum is divisible by three is exactly 1/3.  Also, the probability that the sum is odd is exactly 1/2.

Corollary:  Roll any number of six sided dice. The probability that the sum is divisible by 3 is 1/3.  The probability that the sum is even is exactly 1/2.

## Machine Translation of Chinese

In “Exploitation of Machine Learning Techniques in Modelling Phrase Movements for Machine Translation“, Ni, Saunders, Szedmak, and Niranjan (2011) create a “phrase reordering model” for statistical machine translation.  They apply their method to a Chinese-English corpus to match phrases in each language.  They compare their method to well known maximum entropy methods, support vector machines, maximum margin regression, and max-margin structure learning while giving short summaries on how each method is applied.  I’m very impressed with their writing style and the content of the paper.  The concept of maximum margin regression (similar to SVM) is explored in “Learning via Linear Operators: Maximum Margin Regression; Multiclass and Multiview Learning at One-class Complexity” by Szedmak, and Shawe-Taylor, and Parado-Hernandez (2006).  Max-margin structure learning is described in “Max–margin markov networks” by Taskar, Guestrin, and Koller (NIPS 2003).