Generative-Discriminative Low Rank Decomposition for Medical Imaging Applications

In this thesis, we propose a method that can be used to extract biomarkers from medical images toward early diagnosis of abnormalities. Surge of demand for biomarkers and availability of medical images in the recent years call for accurate, repeatable, and interpretable approaches for extracting meaningful imaging features. However, extracting such information from medical images is a challenging task because the number of pixels (voxels) in a typical image is in order of millions while even a large sample-size in medical image dataset does not usually exceed a few hundred. Nevertheless, depending on the nature of an abnormality, only a parsimonious subset of voxels is typically relevant to the disease; therefore various notions of sparsity are exploited in this thesis to improve the generalization performance of the prediction task. We propose a novel discriminative dimensionality reduction method that yields good classification performance on various datasets without compromising the clinical interpretability of the results. This is achieved by combining the modelling strength of generative learning framework and the classification performance of discriminative learning paradigm. Clinical interpretability can be viewed as an additional measure of evaluation and is also helpful in designing methods that account for the clinical prior such as association of certain areas in a brain to a particular cognitive task or connectivity of some brain regions via neural fibres. We formulate our method as a large-scale optimization problem to solve a constrained matrix factorization. Finding an optimal solution of the large-scale matrix factorization renders off-the-shelf solver computationally prohibitive; therefore, we designed an efficient algorithm based on the proximal method to address the computational bottle-neck of the optimization problem. Our formulation is readily extended for different scenarios such as cases where a large cohort of subjects has uncertain or no class labels (semi-supervised learning) or a case where each subject has a battery of imaging channels (multi-channel), \etc. We show that by using various notions of sparsity as feasible sets of the optimization problem, we can encode different forms of prior knowledge ranging from brain parcellation to brain connectivity

Generative-Discriminative Complementary Learning

Majority of state-of-the-art deep learning methods are discriminative approaches, which model the conditional distribution of labels given inputs features. The success of such approaches heavily depends on high-quality labeled instances, which are not easy to obtain, especially as the number of candidate classes increases. In this paper, we study the complementary learning problem. Unlike ordinary labels, complementary labels are easy to obtain because an annotator only needs to provide a yes/no answer to a randomly chosen candidate class for each instance. We propose a generative-discriminative complementary learning method that estimates the ordinary labels by modeling both the conditional (discriminative) and instance (generative) distributions. Our method, we call Complementary Conditional GAN (CCGAN), improves the accuracy of predicting ordinary labels and can generate high-quality instances in spite of weak supervision. In addition to the extensive empirical studies, we also theoretically show that our model can retrieve the true conditional distribution from the complementarily-labeled data