Utilizing nonnegative tensor factorization methods for inference, model selection, and analysis in supervised learning

This thesis focuses on utilizing nonnegative tensor factorization (NTF) methods in various areas of supervised learning. We start with the introduction of a probabilistic NTF framework that can accommodate a wide range of modeling assumptions while maintaining algorithmic efficiency during inference. The flexibility provided by this framework is then utilized for inference, model selection, and analysis in various supervised learning problems. In the first of these scenarios, we use this approach to effectively model time series with nested, complex seasonalities, ensuring accuracy and interpretability. We then propose a novel method for learning to defer to an expert based on the output of a machine learning model in classification problems, and show that NTF can be utilized to extend this method to arbitrarily complex settings. Afterwards, we investigate when and why deep neural networks' parameters become compressible, and use the aforementioned NTF framework to help analyze how these dynamics are reflected in the representation space. In addition to making independent contributions to various areas of supervised learning, our work shows that, coupled with a convenient modeling approach, NTF can be beneficial for a wide range of supervised learning problems.