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described by multiple instances (e.g., image patches) and simultaneously associated with multiple labels. Existing MIML methods are useful in many applications but most of which suffer from relatively low accuracy and training efficiency due to several issues: i) the inter-label correlations(i.e., the probabilistic correlations between the multiple labels corresponding to an object) are neglected; ii) the inter-instance correlations (i.e., the probabilistic correlations of different instances in predicting the object label) cannot be learned directly (or jointly) with other types of correlations due to the missing instance labels; iii) diverse inter-correlations (e.g., inter-label correlations, inter-instance correlations) can only be learned in multiple stages. To resolve these issues, a new single-stage framework called broad multi-instance multi-label learning (BMIML) is proposed. In BMIML, there are three innovative modules: i) an auto-weighted label enhancement learning (AWLEL) based on broad learning system (BLS) is designed, which simultaneously and efficiently captures the inter-label correlations while traditional BLS cannot; ii) A specific MIML neural network called scalable multi-instance probabilistic regression (SMIPR) is constructed to effectively estimate the inter-instance correlations using the object label only, which can provide additional probabilistic information for learning; iii) Finally, an interactive decision optimization (IDO) is designed to combine and optimize the results from AWLEL and SMIPR and form a single-stage framework. Experiments show that BMIML is highly competitive to (or even better than) existing methods in accuracy and much faster than most MIML methods even for large medical image data sets (> 90K images).