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The selection of the penalty functional is critical for the performance of a regularized learning algorithm, and thus lq-regularizer (1 &#x2264; q &#x2264; 2) deserves special attention. We consider the regularized least-squares regression learning algorithm for the non-identical and weakly dependent samples. The dependent samples satisfy the polynomially &#x03B2;-mixing condition and the sequence of the non-identical sampling marginal measures converges to a probability measure exponentially in the dual of a Ho&#x0308;lder space. We conduct the rigorous unified error analysis and derive the satisfactory learning rates of the algorithm by the stepping stone technique in the error decomposition and the independent-blocks technique in the sample error estimates.

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Error Analysis of Least-Squares <inline-formula> <tex-math notation="LaTeX">$l^{^{q}}$ </tex-math></inline-formula>-Regularized Regression Learning Algorithm With the Non-Identical and Dependent Samples

Error Analysis of Least-Squares $l^{^{q}}$ -Regularized Regression Learning Algorithm With the Non-Identical and Dependent Samples