Theory and application of neural and graphical models in early cancer diagnostics

Abstract

With the recent availability of large training datasets and graphics processing units (GPUs), we address challenges in the application of graphical models and neural networks to prediction sensitive areas such as healthcare. We begin by presenting our work in the context of learning graphical models from biological data. Namely, we present a combinatorial perspective of Markov Equivalence Classes (MECs), which defines the size of solution spaces when attempting to learn a graphical model from data. Through our analysis, we show that the size of these MECs can be exponential with respect to features of the graph (such as average degree). We then switch contexts to address the challenge of developing interpretable complex models. Namely, we present a variational-inference-motivated neural network, PatchNet, that provides visual interpretability, and we present the application of our network to the Describable Textures Dataset (DTD), the ISIC-ISBI Melanoma Classification Challenge, and cell nucleus data.