Interpreting Deep Learning for cell differentiation. Supervised and Unsupervised models viewed through the lens of information and perturbation theory.
"Predicting the future isn't magic, it's artificial intelligence" Dave Waters. In the last decades there has been an unprecedented growth in the field of machine learning, and particularly within deep learning models. The combination of big data and computational power has nurtured the evolution of a variety of new methods to predict and interpret future scenarios. These data centric models can achieve exceptional performances on specific tasks, with their prediction boundaries continuously expanding towards new and more complex challenges. However, the model complexity often translates into a lack of interpretability from a scientific c perspective, it is not trivial to identify the factors involved in final outcomes. Explainability may not always be a requirement for some machine learning tasks, specially when it comes in detriment of performance power. But for some applications, such as biological discoveries or medical diagnostics, understanding the output and determining factors that influence decisions is essential. In this thesis we develop both a supervised and unsupervised approach to map from genotype to phenotype. We emphasise the importance of interpretability and feature extraction from the models, by identifying relevant genes for cell differentiation. We then continue to explore the rules and mechanisms behind the models from a theoretical perspective. Using information theory to explain the learning process and applying perturbation theory to transform the results into a generalisable representation. We start by building a supervised approach to mapping cell profiles from genotype to phenotype, using single cell RNA-Seq data. We leverage non-linearities among gene expressions to identify cellular levels of differentiation. The ambiguity and even absence of labels in most biological studies instigated the development of novel unsupervised techniques, leading to a new general and biologically interpretable framework based on Variational Autoencoders. The application and validation of the methods has proven to be successful, but questions regarding the learning process and generative nature of the results remained unanswered. I use information theory to define a new approach to interpret training and the converged solutions of our models. The variational and generative nature of Autoencoders provides a platform to develop general models. Their results should extrapolate and allow generalisation beyond the boundaries of the observed data. To this extent, we introduce for the first time a new interpretation of the embedded generative functions through Perturbation Theory. The embedding multiplicity is addressed by transforming the distributions into a new set of generalisable functions, while characterising their energy spectrum under a particular energy landscape. We outline the combination of theoretical and machine learning based methods, for moving towards interpretable and generalisable models. Developing a theoretical framework to map from genotype to phenotype, we provide both supervised and unsupervised tools to operate over single cell RNA-Seq. data. We have generated a pipeline to identify relevant genes and cell types through Variational Autoencoders (VAEs), validating reconstructed gene expressions to prove the generative performance of the embeddings. The new interpretation of the information learned and extracted by the models de fines a label independent evaluation, particularly useful for unsupervised learning. Lastly, we introduce a novel transformation of the generative embeddings based on quantum and perturbation theory. Our contributions can and have been extended to new datasets, according to the nature of the tasks being explored. For instance, the combination of unsupervised learning and information theory can be applied to a variety of biological or medical data. We have trained several VAE models with additional cancer and metabolic data, proving to extract meaningful representations of the data. The perturbation theory transformation of the embedding can also lead to future research on the generative potential of Variational Autoencoders through a physics perspective, combining statistical and quantum mechanics. We believe that machine learning will only continue its fast expansion and growth through the development of more generalisable more interpretable models. "Prediction is very difficult, especially if it's about the future" Niels Bohr
Artificial Intelligence, Unsupervised Learning, Variational Autoencoders, Single Cell RNA-Seq, Information Theory, Generative methods
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