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Molecular subtypes of breast cancer are important references to personalized clinical treatment. For cost and labor savings, only one of the patient's paraffin blocks is usually selected for subsequent immunohistochemistry (IHC) to obtain molecular subtypes. Inevitable sampling error is risky due to tumor heterogeneity and could result in a delay in treatment. Molecular subtype prediction from conventional H&E pathological whole slide images (WSI) using AI method is useful and critical to assist pathologists pre-screen proper paraffin block for IHC. It's a challenging task since only WSI level labels of molecular subtypes can be obtained from IHC. Gigapixel WSIs are divided into a huge number of patches to be computationally feasible for deep learning. While with coarse slide-level labels, patch-based methods may suffer from abundant noise patches, such as folds, overstained regions, or non-tumor tissues. A weakly supervised learning framework based on discriminative patch selecting and multi-instance learning was proposed for breast cancer molecular subtype prediction from H&E WSIs. Firstly, co-teaching strategy was adopted to learn molecular subtype representations and filter out noise patches. Then, a balanced sampling strategy was used to handle the imbalance in subtypes in the dataset. In addition, a noise patch filtering algorithm that used local outlier factor based on cluster centers was proposed to further select discriminative patches. Finally, a loss function integrating patch with slide constraint information was used to finetune MIL framework on obtained discriminative patches and further improve the performance of molecular subtyping. The experimental results confirmed the effectiveness of the proposed method and our models outperformed even senior pathologists, with potential to assist pathologists to pre-screen paraffin blocks for IHC in clinic.