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In this paper, a L1 regularized linear regression based method is proposed to model the relationship between the linguistic features and prosodic parameters in Text-to-Speech (TTS) synthesis. By formulating prosodic prediction as a convex problem, it can be solved using very efficient numerical method. The performance can be similar to that of the Classification and Regression Tree (CART), a widely used approach for prosodic prediction. However, the computational load can be as low as 76% of that required by CART.