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

计算和统计遗传学领域关注的是进化关系的建模和推断。近年来，由于测序技术的重要进展，这些领域迅速发展。然而，仍然存在许多挑战。一个这样的例子出现在癌症遗传学领域，涉及癌症肿瘤内进化动力学的表征。更具体地说，挑战来自于需要表征单个癌细胞的演变，其中研究人员面临着获得不同突变集的多个癌细胞亚群的混合物。 目前，遗传学的核心挑战是计算和统计性质的。这不仅在刚才提到的癌症遗传学的例子中是正确的，而且在许多其他情况下，系统发育模型是基于复杂的数据库，如序列比对或基因树。遗传学目前面临的计算和统计挑战的一个统一特征是，它们需要复杂和细致入微的方法，将模型的构建和对组合结构进行推理的任务结合起来。 我的研究旨在解决遗传学中的这一重要挑战。更具体地说，我的研究旨在创建有效的方法，对组合结构的统计推断，重点是在系统发育分析中出现的模型。我的研究计划强调了癌症遗传学领域的模型，但也考虑了其他系统发育背景下的应用，如联合树和比对推断。从这项研究提案中开发的许多方法也将适用于机器学习的其他几个分支（如自然语言处理，计算机视觉和计算生物学）中遇到的数据分析情况。 我的研究计划由三个相互关联的目标组成： 1.开发实用的贝叶斯非参数化（BNP）：BNP提供了一个有效的框架来处理组合空间上的潜在变量，然而，BNP仍然存在显着的局限性，特别是计算的可扩展性，以及用户的陡峭学习曲线。我将开发解决这些问题的方法。 2.为难以处理的进化模型开发可扩展的推理方法：传统的系统发育模型通常假设给定一个假设树，数据的可能性可以在多项式时间内计算。我将开发可扩展的系统发育方法，放松这一假设。 3.部分观测随机微分方程（SDEs）的概率推理：我的目标是开发新的方法，使从业者更容易以声明方式开发模型，同时保持低计算成本。

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.