In this paper, we propose a new systematic design method of a regularization parameter for
L1-norm minimization problem by using statistics of noise. We consider
L1 regularized linear regression and
L1 regularized logistic regression as the minimization and we analyze a relationship between their regularization parameters and system parameters. In the case of
L1 regularized linear regression, we show that a condition of the regularization parameter is given by LMI parameterized by a covariance matrix of measurement noise. Also in the case of
L1 regularized logistic regression, we show that the regularization parameter satisfies LMI described by a variance of a modeling error of a logistic model. Since the proposed design method requires a value of second moment of noise, we estimate the value by a sample covariance matrix. We demonstrate the effectiveness of the proposed method by numerical simulations, in which we use random systems and real data sets to evaluate the proposed method.
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