Abstract
In many fields including control systems society, sparse estimations are attracting the most attention. Especially, L1 regularized linear regression is applied to many applications because it is easy to deal with. However, in calculations using all measurement data at once, the more number of measurement becomes, the lager computational costs become. In this paper, we propose a recursive algorithm for the L1 regularized linear regression. In order to derive the proposed recursive algorithm, we introduce upper and lower bounds of a criterion of the L1 regularized linear regression. Moreover, we show that we can solve a minimization problem of the both bounds analytically and recursively, and we use the analytic solutions as an approximate solution of the L1 regularized linear regression. We demonstrate the effectiveness of the proposed method by numerical simulations, in which we use random systems to evaluate the proposed method.
