  Sparse learning is a very important tool for mining useful information and
patterns from high dimensional data. Non-convex non-smooth regularized learning
problems play essential roles in sparse learning, and have drawn extensive
attentions recently. We design a family of stochastic proximal gradient methods
by applying arbitrary sampling to solve the empirical risk minimization problem
with a non-convex and non-smooth regularizer. These methods draw mini-batches
of training examples according to an arbitrary probability distribution when
computing stochastic gradients. A unified analytic approach is developed to
examine the convergence and computational complexity of these methods, allowing
us to compare the different sampling schemes. We show that the independent
sampling scheme tends to improve performance over the commonly-used uniform
sampling scheme. Our new analysis also derives a tighter bound on convergence
speed for the uniform sampling than the best one available so far. Empirical
evaluations demonstrate that the proposed algorithms converge faster than the
state of the art.
