Modern mathematical machine learning approaches to problems in health and medicine: from deep learning to algebraic signal processing
Three different data science approaches will be explored on three very different problems that come from health. In the first problem we consider the prevalent challenge that poisson noise and compression plays in many real world medical imaging problems. We show that by taking a more generalized approach to traditional activation functions, standard deep learning architectures for computer vision can achieve higher accuracies in fewer epocs for images that exhibit poisson noise and high compression. In our second example, we consider the challenge of rigorously detecting epistasis in subsets of the genome to understand a specific phenotypic response. We show that using appropriate non-abelian fourier transforms creates a natural change of basis of the genome that significantly improves our ability to detect higher order gene interaction for a given phenotypic response. In the final example, we consider the problem of detecting Atrial Fibrillation in short time ECG recordings. We show that one can take a topological data analysis (TDA) approach to classification problem that yields comparable results to state of the art deep learning models.