  In this paper, we present a new adaptive feature scaling scheme for
ultrahigh-dimensional feature selection on Big Data. To solve this problem
effectively, we first reformulate it as a convex semi-infinite programming
(SIP) problem and then propose an efficient \emph{feature generating paradigm}.
In contrast with traditional gradient-based approaches that conduct
optimization on all input features, the proposed method iteratively activates a
group of features and solves a sequence of multiple kernel learning (MKL)
subproblems of much reduced scale. To further speed up the training, we propose
to solve the MKL subproblems in their primal forms through a modified
accelerated proximal gradient approach. Due to such an optimization scheme,
some efficient cache techniques are also developed. The feature generating
paradigm can guarantee that the solution converges globally under mild
conditions and achieve lower feature selection bias. Moreover, the proposed
method can tackle two challenging tasks in feature selection: 1) group-based
feature selection with complex structures and 2) nonlinear feature selection
with explicit feature mappings. Comprehensive experiments on a wide range of
synthetic and real-world datasets containing tens of million data points with
$O(10^{14})$ features demonstrate the competitive performance of the proposed
method over state-of-the-art feature selection methods in terms of
generalization performance and training efficiency.
