Fast multiple instance learning via L1,2 logistic regression

In this paper, we develop an efficient logistic regression model for multiple instance learning that combines L 1 and L 2 regularisation techniques. An L 1 regularised logistic regression model is first learned to find out the sparse pattern of the features. To train the L 1 model efficiently, we employ a convex differentiable approximation of the L 1 cost function which can be solved by a quasi Newton method. We then train an L 2 regularised logistic regression model only on the subset of features with nonzero weights returned by the L 1 logistic regression. Experimental results demonstrate the utility and efficiency of the proposed approach compared to a number of alternatives.