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The prediction of translation initiation sites (TISs) in eukaryotic mRNAs has been a challenging problem in computational molecular biology. In this paper, we present a new algorithm to recognize TISs with a very high accuracy. Our algorithm includes two novel ideas. First, we introduce a class of new sequence-similarity kernels based on string editing, called edit kernels, for use with support vector machines (SVMs) in a discriminative approach to predict TISs. The edit kernels are simple and have significant biological and probabilistic interpretations. Although the edit kernels are not positive definite, it is easy to make the kernel matrix positive definite by adjusting the parameters. Second, we convert the region of an input mRNA sequence downstream to a putative TIS into an amino acid sequence before applying SVMs to avoid the high redundancy in the genetic code. The algorithm has been implemented and tested on previously published data. Our experimental results on real mRNA data show that both ideas improve the prediction accuracy greatly and that our method performs significantly better than those based on neural networks and SVMs with polynomial kernels or Salzberg kernels.