## AbstractThe type of L1 norm regularization used in Lasso and related methods typically yields sparse parameter estimates where most of the estimates are equal to zero. We study a class of estimators obtained by applying a linear transformation on the parameter vector before evaluating the L1 norm. The resulting "transformed Lasso" yields estimates that are "smooth" in a way that depends on the applied transformation. The optimization problem is convex and can be solved efficiently using existing tools. We present two examples: the Haar transform which corresponds to variable length Markov chain (context-tree) models, and the Walsh-Hadamard transform which corresponds to linear combinations of XOR (parity) functions of binary input features.
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