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 L₁ and L₂ regularisation techniques. An L₁ regularised logistic regression model is first learned to find out the sparse pattern of the features. To train the L₁ model efficiently, we employ a convex differentiable approximation of the L₁ cost function which can be solved by a quasi Newton method. We then train an L₂ regularised logistic regression model only on the subset of features with nonzero weights returned by the L₁ logistic regression. Experimental results demonstrate the utility and efficiency of the proposed approach compared to a number of alternatives.