We study the classification problem under the two-component anisotropic sub-Gaussian mixture model in high dimensions and in the non-asymptotic setting. First, we derive lower bounds and matching upper bounds for the minimax risk of classification in this framework. We also show that in the high-dimensional regime, the linear discriminant analysis classifier turns out to be sub-optimal in the minimax sense. Next, we give precise characterization of the risk of classifiers based on solutions of $\ell_2$-regularized least squares problem. We deduce that the interpolating solutions may outperform the regularized classifiers under mild assumptions on the covariance structure of the noise, and present concrete examples of this phenomenon. Our analysis also demonstrates robustness of interpolation to certain models of corruption. To the best of our knowledge, this peculiar fact has not yet been investigated in the rapidly growing literature related to interpolation. We conclude that interpolation is not only benign but can also be optimal, and in some cases robust.

Learning representations for individual instances when only bag-level labels are available is a fundamental challenge in multiple instance learning (MIL). Recent works have shown promising results using contrastive self-supervised learning (CSSL), which learns to push apart representations corresponding to two different randomly-selected instances. Unfortunately, in real-world applications such as medical image classification, there is often class imbalance, so randomly-selected instances mostly belong to the same majority class, which precludes CSSL from learning inter-class differences. To address this issue, we propose a novel framework, Iterative Self-paced Supervised Contrastive Learning for MIL Representations (ItS2CLR), which improves the learned representation by exploiting instance-level pseudo labels derived from the bag-level labels. The framework employs a novel self-paced sampling strategy to ensure the accuracy of pseudo labels. We evaluate ItS2CLR on three medical datasets, showing that it improves the quality of instance-level pseudo labels and representations, and outperforms existing MIL methods in terms of both bag and instance level accuracy.11Code is available at https://github.com/Kangningthu/ItS2CLR

Deep learning in the presence of noisy annotations has been studied extensively in classification, but much less in segmentation tasks. In this work, we study the learning dynamics of deep segmentation networks trained on inaccurately annotated data. We observe a phenomenon that has been previously reported in the context of classification: the networks tend to first fit the clean pixel-level labels during an “early-learning” phase, before eventually memorizing the false annotations. However, in contrast to classification, memorization in segmentation does not arise simultaneously for all semantic categories. Inspired by these findings, we propose a new method for segmentation from noisy annotations with two key elements. First, we detect the beginning of the memorization phase separately for each category during training. This allows us to adaptively correct the noisy annotations in order to exploit early learning. Second, we incorporate a regularization term that enforces consistency across scales to boost robustness against annotation noise. Our method outperforms standard approaches on a medical-imaging segmentation task where noises are synthesized to mimic human annotation errors. It also provides robustness to realistic noisy annotations present in weakly-supervised semantic segmentation, achieving state-of-the-art results on PASCAL VOC 2012.11Code is available at https://github.com/Kangningthu/ADELE

Medical images differ from natural images in significantly higher resolutions and smaller regions of interest. Because of these differences, neural network architectures that work well for natural images might not be applicable to medical image analysis. In this work, we propose a novel neural network model to address these unique properties of medical images. This model first uses a low-capacity, yet memory-efficient, network on the whole image to identify the most informative regions. It then applies another higher-capacity network to collect details from chosen regions. Finally, it employs a fusion module that aggregates global and local information to make a prediction. While existing methods often require lesion segmentation during training, our model is trained with only image-level labels and can generate pixel-level saliency maps indicating possible malignant findings. We apply the model to screening mammography interpretation: predicting the presence or absence of benign and malignant lesions. On the NYU Breast Cancer Screening Dataset, our model outperforms (AUC = 0.93) ResNet-34 and Faster R-CNN in classifying breasts with malignant findings. On the CBIS-DDSM dataset, our model achieves performance (AUC = 0.858) on par with state-of-the-art approaches. Compared to ResNet-34, our model is 4.1x faster for inference while using 78.4% less GPU memory. Furthermore, we demonstrate, in a reader study, that our model surpasses radiologist-level AUC by a margin of 0.11.

We present a deep convolutional neural network for breast cancer screening exam classification, trained, and evaluated on over 200000 exams (over 1000000 images). Our network achieves an AUC of 0.895 in predicting the presence of cancer in the breast, when tested on the screening population. We attribute the high accuracy to a few technical advances. 1) Our network's novel two-stage architecture and training procedure, which allows us to use a high-capacity patch-level network to learn from pixel-level labels alongside a network learning from macroscopic breast-level labels. 2) A custom ResNet-based network used as a building block of our model, whose balance of depth and width is optimized for high-resolution medical images. 3) Pretraining the network on screening BI-RADS classification, a related task with more noisy labels. 4) Combining multiple input views in an optimal way among a number of possible choices. To validate our model, we conducted a reader study with 14 readers, each reading 720 screening mammogram exams, and show that our model is as accurate as experienced radiologists when presented with the same data. We also show that a hybrid model, averaging the probability of malignancy predicted by a radiologist with a prediction of our neural network, is more accurate than either of the two separately. To further understand our results, we conduct a thorough analysis of our network's performance on different subpopulations of the screening population, the model's design, training procedure, errors, and properties of its internal representations. Our best models are publicly available at https://github.com/nyukat/breast_cancer_classifier.

Breast density classification is an essential part of breast cancer screening. Although a lot of prior work considered this problem as a task for learning algorithms, to our knowledge, all of them used small and not clinically realistic data both for training and evaluation of their models. In this work, we explored the limits of this task with a data set coming from over 200,000 breast cancer screening exams. We used this data to train and evaluate a strong convolutional neural network classifier. In a reader study, we found that our model can perform this task comparably to a human expert.