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

计算和统计系统发育学领域涉及进化关系的建模和推断。近年来，由于测序技术的重要进步，这些领域发展迅速。然而，许多挑战依然存在。一个这样的例子出现在癌症系统发生学领域，涉及癌症肿瘤内进化动力学的特征。更具体地说，挑战来自于描述单个癌细胞进化的需要，在这种情况下，研究人员看到的是获得不同突变集的多个癌细胞亚群的混合物。 目前，系统发育学的核心挑战本质上是计算和统计。这不仅在刚才提到的癌症系统发育学例子中是正确的，而且在许多其他情况下也是如此，其中系统发育模型基于复杂的数据类型，例如序列比对或基因树。目前系统发育学面临的计算和统计挑战的一个统一特征是，它们需要复杂和微妙的方法，其中包括建立模型和对组合结构进行推理的任务。 我的研究旨在解决系统发育学中的这一重要挑战。更具体地说，我的研究旨在为组合结构创造有效的统计推断方法，重点放在系统发育分析中出现的模型上。我的研究方案强调癌症系统发生学领域的模型，但也考虑应用于其他系统发生学背景，如联合树和比对推理。从这项研究建议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。 我的研究提案由三个相互关联的目标组成： 1.开发实用的贝叶斯非参数方法(BNP)：BNP提供了一个有效的框架来逼近组合空间上的潜在变量，但BNP仍然存在显著的限制，特别是计算的可扩展性，以及用户学习曲线的陡峭。我将开发解决这些问题的方法。 2.为棘手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棵假想的树，数据的可能性可以在多项式时间内计算出来。我将开发可扩展的系统发育方法来放松这一假设。 3.部分观测随机微分方程的概率推理：我的目标是开发新的方法，使实践者更容易以声明的方式开发模型，同时保持较低的计算成本。

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.