Draft : February 28 , 2008 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...

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

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...

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. These factors destroy the doubly stochastic property of the matrix and an iterative procedure is needed to re-normalize the rows and columns. Even thou...

ar X iv : 0 80 3 . 28 39 v 1 [ m at h . ST ] 1 9 M ar 2 00 8 AGGREGATION BY EXPONENTIAL WEIGHTING , SHARP ORACLE INEQUALITIES AND SPARSITY

We study the problem of aggregation under the squared loss in the model of regression with deterministic design. We obtain sharp PAC-Bayesian risk bounds for aggregates defined via exponential weights, under general assumptions on the distribution of errors and on the functions to aggregate. We then apply these results to derive sparsity oracle inequalities.