  We theoretically investigate the convergence rate and support consistency
(i.e., correctly identifying the subset of non-zero coefficients in the large
sample limit) of multiple kernel learning (MKL). We focus on MKL with block-l1
regularization (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 the
true kernel combination is sparse, we show a sharper convergence rate of the
block-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 being
consistent than block-l1 MKL. For the case where the optimal kernel combination
is not exactly sparse, we prove that elastic-net MKL can achieve a faster
convergence rate than the block-l1 and block-l2 MKL methods by carefully
controlling the balance between the block-l1and block-l2 regularizers. Thus,
our theoretical results overall suggest the use of elastic-net regularization
in MKL.
