Deep Multi-View Learning via Task-Optimal CCA

Canonical Correlation Analysis (CCA) is widely used for multimodal data analysis and, more recently, for discriminative tasks such as multi-view learning; however, it makes no use of class labels. Recent CCA methods have started to address this weakness but are limited in that they do not simultaneously optimize the CCA projection for discrimination and the CCA projection itself, or they are linear only. We address these deficiencies by simultaneously optimizing a CCA-based and a task objective in an end-to-end manner. Together, these two objectives learn a non-linear CCA projection to a shared latent space that is highly correlated and discriminative. Our method shows a significant improvement over previous state-of-the-art (including deep supervised approaches) for cross-view classification, regularization with a second view, and semi-supervised learning on real data.

Receiver Operating Characteristic Curves and Confidence Bands for Support Vector Machines

Many problems that appear in biomedical decision making, such as diagnosing disease and predicting response to treatment, can be expressed as binary classification problems. The costs of false positives and false negatives vary across application domains and receiver operating characteristic (ROC) curves provide a visual representation of this trade-off. Nonparametric estimators for the ROC curve, such as a weighted support vector machine (SVM), are desirable because they are robust to model misspecification. While weighted SVMs have great potential for estimating ROC curves, their theoretical properties were heretofore underdeveloped. We propose a method for constructing confidence bands for the SVM ROC curve and provide the theoretical justification for the SVM ROC curve by showing that the risk function of the estimated decision rule is uniformly consistent across the weight parameter. We demonstrate the proposed confidence band method and the superior sensitivity and specificity of the weighted SVM compared to commonly used methods in diagnostic medicine using simulation studies. We present two illustrative examples: diagnosis of hepatitis C and a predictive model for treatment response in breast cancer.

Multiple Instance Learning for Heterogeneous Images: Training a CNN for Histopathology

Multiple instance (MI) learning with a convolutional neural network enables end-to-end training in the presence of weak image-level labels. We propose a new method for aggregating predictions from smaller regions of the image into an image-level classification by using the quantile function. The quantile function provides a more complete description of the heterogeneity within each image, improving image-level classification. We also adapt image augmentation to the MI framework by randomly selecting cropped regions on which to apply MI aggregation during each epoch of training. This provides a mechanism to study the importance of MI learning. We validate our method on five different classification tasks for breast tumor histology and provide a visualization method for interpreting local image classifications that could lead to future insights into tumor heterogeneity.