  (Mini-batch) Stochastic Gradient Descent is a popular optimization method
which has been applied to many machine learning applications. But a rather high
variance introduced by the stochastic gradient in each step may slow down the
convergence. In this paper, we propose the antithetic sampling strategy to
reduce the variance by taking advantage of the internal structure in dataset.
Under this new strategy, stochastic gradients in a mini-batch are no longer
independent but negatively correlated as much as possible, while the mini-batch
stochastic gradient is still an unbiased estimator of full gradient. For the
binary classification problems, we just need to calculate the antithetic
samples in advance, and reuse the result in each iteration, which is practical.
Experiments are provided to confirm the effectiveness of the proposed method.
