We study the problem of learning a hierarchical tree representation of data from labeled samples, taken from an arbitrary (and possibly adversarial) distribution. Consider a collection of data tuples labeled according to their hierarchical structure. The smallest number of such tuples required in order to be able to accurately label subsequent tuples is of interest for data collection in machine learning. We present optimal sample complexity bounds for this problem in several learning settings, including (agnostic) PAC learning and online learning. Our results are based on tight bounds of the Natarajan and Littlestone dimensions of the associated problem. The corresponding tree classifiers can be constructed efficiently in near-linear time.

Glaucoma is one of the most prevalent ophthalmic diseases, affecting millions of individuals worldwide. Current computational methods for glaucoma diagnosis leverage convolutional neural networks (CNNs) to analyze retinal fundus images in order to determine the presence of glaucoma. We evaluate the generalizability of a standard CNN by performing cross-dataset evaluation in which the models are tested on images from a separate data source and show that the model experience a significant drop off in this evaluation method. We introduce a multimodal approach that segments the optic disc (OD) and optic cup (OC) sections from fundus images and calculates the vertical optic cup to disc ratio (vCDR) and the eccentricity of the OD and OC regions. It then makes a diagnosis using these numerical features in conjunction with the standard CNN embedding extracted from the image. In the cross-dataset evaluation, the proposed model achieves an average accuracy increase of 2.63% over a standard CNN across all datasets. Code and data are available at: github.com/glaucomamultimodal/glaucoma-diagnosis.

Glioblastoma Multiforme (GBM) is a malignant brain cancer forming around 48% of all brain and Central Nervous System (CNS) cancers. It is estimated that annually over 13,000 deaths occur in the US due to GBM, making it crucial to have early diagnosis systems that can lead to predictable and effective treatment. The most common treatment after GBM diagnosis is chemotherapy, which works by sending rapidly dividing cells to apoptosis. However, this form of treatment is not effective when the MGMT promoter sequence is unmethy-lated, and instead leads to severe side effects decreasing patient survivability. Therefore, it is important to be able to identify the MGMT promoter methylation status before deciding on the treatment plan. In this research, we aim to detect the methylation status through non-invasive magnetic resonance imaging (MRI) based machine learning (ML) models. This is accomplished using the Brain Tumor Segmentation (BraTS) 2021 dataset, which was recently used for an international Kaggle competition. We built a novel ML model termed as the Intermediate State Generator which was used to normalize the slice thicknesses of all MRI scans. With further improvements, our model was able to achieve performance significantly (p < 0.05) better than the best performing Kaggle model with a 5.5% increase in average cross-validation accuracy. This improvement could potentially lead to a more informed choice of chemotherapy as a treatment option, prolonging lives of thousands of patients with GBM each year.

Melanoma is one of the most fatal forms of skin cancer and is often very difficult to differentiate from other benign skin lesions. However, if detected at its early stages, it can almost always be cured. Researchers and data scientists have studied this disease in-depth with the help of large datasets containing high-quality dermascopic images, such as those assembled by the International Skin Imaging Collaboration (ISIC). However, these images often lack diversity and over-represent patients with very common skin features such as light skin and having no visible body hair. In this study, we introduce a novel architecture called LatentNet which automatically detects overrepresented features and reduces their weights during training. We tested our model on four distinct categories - three skin color levels corresponding to Type I, II, and III on the Fitzpatrick Scale, and images containing visible hair. We then compared the accuracy against the conventional Deep Convolutional Neural Network (DCNN) model trained using the standard approach (i.e. without detecting over-represented features) and containing the same hyperparameters as the LatentNet. The LatentNet showed significant performance improvement over the standard DCNN model. Differences in average performance between the models were statistically significant $(p \lt 0.05)$, suggesting that the proposed model successfully reduced bias amongst the tested categories. LatentNet is the first architecture that addresses racial and other sources of bias in deep-learning based Melanoma diagnosis.