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We theoretically investigate the convergence rate and support consistency(i.e., correctly identifying the subset of non-zero coefficients in the largesample limit) of multiple kernel learning (MKL). We focus on MKL with block-l1regularization (inducing sparse kernel combination), block-l2 regularization(inducing uniform kernel combination), and elastic-net regularization(including both block-l1 and block-l2 regularization). For the case where thetrue kernel combination is sparse, we show a sharper convergence rate of theblock-l1 and elastic-net MKL methods than the existing rate for block-l1 MKL.We further show that elastic-net MKL requires a milder condition for beingconsistent than block-l1 MKL. For the case where the optimal kernel combinationis not exactly sparse, we prove that elastic-net MKL can achieve a fasterconvergence rate than the block-l1 and block-l2 MKL methods by carefullycontrolling the balance between the block-l1and block-l2 regularizers. Thus,our theoretical results overall suggest the use of elastic-net regularizationin MKL.

Sharp Convergence Rate and Support Consistency of Multiple Kernel Learning with Sparse and Dense Regularization