Efficient probabilistic inference and Bayesian non-parametrics with applications in phylogenetics and cancer genomics

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The fields of computational and statistical phylogenetics are concerned with the modelling and inference of evolutionary relationships. These fields have grown rapidly in recent years due to important advances in sequencing technologies. Many challenges, however, remain. One such example arises in the area of cancer phylogenetics, and relates to the characterization of evolutionary dynamics within cancer tumours. More specifically, the challenge arises from the need to characterize the evolution of individual cancer cells, where researchers are presented with mixtures of multiple sub-populations of cancer cells that have acquired different sets of mutations. At present, the core challenges in phylogenetics are computational and statistical in nature. This is not only true in the cancer phylogenetics example just referred to, but also in many other cases where phylogenetic models are based on complex datatypes such as sequence alignments or gene trees. A unifying feature of the computational and statistical challenges presently facing phylogenetics are that they require complex and nuanced approaches that incorporate the building of models and the task of performing inference over combinatorial structures. My research aims to address this important challenge in phylogenetics. More specifically, my research aims to create efficient methods for statistical inference over combinatorial structures, with a focus on models that arise in phylogenetic analysis. My research proposal emphasizes models from the field of cancer phylogenetics, but also considers applications to other phylogenetic contexts, such as joint tree and alignment inference. Many of the methods developed from this research proposal will also be applicable to data analysis situations encountered in several other branches of machine learning (such as natural language processing, computer vision, and computational biology). My research proposal is composed of three inter-related goals: 1. To develop practical Bayesian Non-Parametrics (BNP): BNP provides an effective framework to approach latent variables over combinatorial spaces, however, significant limitations remain with BNP, in particular, computational scalability, and a steep learning curve for users. I will develop methods that address these issues. 2. To develop scalable inference methods for intractable evolutionary models: Traditional phylogenetic models typically assume that given a hypothesized tree, the likelihood of the data can be computed in polynomial time. I will develop scalable phylogenetic methods that relax this assumption. 3. Probabilistic inference over partially observed stochastic differential equations (SDEs): My goal is to develop new methodologies that make it easier for practitioners to develop models declaratively while keeping computational costs low.