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The problem of learning a transduction, that is a string-to-string mapping, is a common problem arising in natural language processing and computational biology. Previous methods proposed for learning such mappings are based on classification techniques. This paper presents a new and general regression technique for learning transductions and reports the results of experiments showing its effectiveness. Our transduction learning consists of two phases: the estimation of a set of regression coefficients and the computation of the pre-image corresponding to this set of coefficients. A novel and conceptually cleaner formulation of kernel dependency estimation provides a simple framework for estimating the regression coefficients, and an efficient algorithm for computing the pre-image from the regression coefficients extends the applicability of kernel dependency estimation to output sequences. We report the results of a series of experiments illustrating the application of our regression technique for learning transductions.