Learning Permutations with Exponential Weights

Helmbold & Warmuth ( 2007 ) “ Learning Permutations with Exponential weights ”

Draft : September 10 , 2008 Learning Permutations with Exponential Weights ∗

We give an algorithm for the on-line learning of permutations. The algorithm maintains its uncertainty about the target permutation as a doubly stochastic weight matrix, and uses an efficient method for decomposing the weight matrix as a convex combination of permutations to make predictions. The weight matrix is updated by multiplying the current matrix entries by exponential factors, and an i...

Draft : February 28 , 2008 Learning Permutations with Exponential Weights ∗

We give an algorithm for learning a permutation on-line. The algorithm maintains its uncertainty about the target permutation as a doubly stochastic matrix. This matrix is updated by multiplying the current matrix entries by exponential factors which destroy the doubly stochastic property of the matrix, and an iterative procedure is needed to renormalize the rows and columns. Even though the re...

Consensus Ranking with Signed Permutations

Signed permutations (also known as the hyperoctahedral group) are used in modeling genome rearrangements. The algorithmic problems they raise are computationally demanding when not NP-hard. This paper presents a tractable algorithm for learning consensus ranking between signed permutations under the inversion distance. This can be extended to estimate a natural class of exponential models over ...

AVOIDANCE OF PARTIALLY ORDERED PATTERNS OF THE FORM k-σ-k

Sergey Kitaev [4] has shown that the exponential generating function for permutations avoiding the generalized pattern σ-k, where σ is a pattern without dashes and k is one greater than the largest element in σ, is determined by the exponential generating function for permutations avoiding σ. We show that the exponential generating function for permutations avoiding the partially ordered patter...