A Gaussian Mixture Model for Multiple Instance Learning With Both Bag‐ and Instance‐Level Features

The core challenge of multiple instance learning (MIL) is to predict bag‐level labels with partially or completely unobserved instance‐level labels. Most existing methods focus on instance‐level features and ignore commonly available bag‐level covariates. To address this issue, this paper proposes a novel Gaussian mixture model (GMM) framework that fuses both bag‐ and instance‐level features. The framework introduces an instance‐level background class to characterize instances weakly related to the target topic. It models the two types of features with separate Gaussian distributions and fuses cross‐level information by combining the bag‐level label distribution with the conditional distribution of instance‐level labels. For parameter estimation, a two‐step strategy is adopted: Bag‐level parameters are obtained in closed form, while instance‐level parameters are estimated by maximum likelihood via the EM algorithm. Numerical simulations verify the consistency of the proposed estimator, and the proposed method achieves substantially higher prediction accuracy than the baseline GMM (using only single‐level features) and classical MIL methods. Experiments on a real‐world government service hotline dataset show that the method achieves an average AUC of 0.8920, markedly outperforming competing methods. These results indicate that fusing dual‐level features and explicitly modelling background patterns can effectively improve bag‐level label prediction.