Networks: Estimation in Protein Molecules, Modeling of Transactional Data, and Application to Ensemble Learning

我将继续探索一些关于网络的令人兴奋的问题，我开始研究我以前的NSERC发现加速器补充资金。 首先，我将研究蛋白质分子中的网络估计。蛋白质分子是由一系列氨基酸残基组成的。与一个学生和一个同事，我已经开始研究有关表征蛋白质分子的3D结构的各种计算问题，其中之一是任何两个残基之间的直接耦合强度的量化。这种类型的分析通常会产生一个残基-残基网络，其中每个节点对应一个残基，如果两个节点的直接耦合强度很高，则在两个节点之间绘制一条边。这对于变构的研究是重要的，变构是一个残基位点的构象变化影响另一个残基位点构象的过程。在处理这个问题时，我们开创了一种新的分析范式，这将使我们能够在统计学中做许多有趣的事情。 接下来，我将研究事务数据的网络建模。网络数据分析是统计学的一个新兴领域。通常，网络中的每个节点可以属于许多不同社区中的一个。研究人员使用所谓的随机块模型（SBM）来检测这些社区。早期的作品通常不考虑时间，并将网络视为静态的。最近，研究人员开始考虑网络随时间的动态变化，但他们通常以离散的方式处理时间变量。与一个学生和一个合作者一起，我一直在研究SBM的连续时间扩展，它可以用于对事务数据建模，例如，在一段时间内，许多人之间发送的信息，但我想进一步扩展我们的模型，以纳入空间信息。由此产生的时空SBM可用于研究任何在空间和时间上旅行时相互通信的实体集合;它对许多科学分支都非常有用。 最后，我将把网络分析的思想应用到集成学习中。据我所知，朱和奇普曼（2006，Technometrics 48：491-502）是第一个使用集合方法进行变量选择（而不是预测）的人。从那时起，我继续研究这个问题，并进一步明确了变量选择集合的概念，但一个悬而未决的问题是什么构成了一个好的生成机制。有趣的是，我和一个学生发现了一种基于网络分析的新机制。到目前为止，这种新机制在我们之前考虑的几乎所有模拟设置中都表现出了出色的性能。我对这个新发现很感兴趣，想更深入地研究它。 参加这项研究计划的学员将能够培养当今经济所急需的计算技能，并了解科学和工程中一些非常具有挑战性的问题。

I will continue to explore a few exciting problems about networks, which I started to investigate with my previous NSERC Discovery Accelerator Supplement grant. First, I will work on network estimation in protein molecules. A protein molecule is made up of a sequence of amino acid residues. With a student and a colleague, I have started to study various computational problems about characterizing the 3D structures of protein molecules, one of which is the quantification of direct-coupling strengths between any two residues. This type of analysis often results in a residue-residue network, in which each node corresponds to a residue, and an edge is drawn between two nodes if their direct-coupling strength is high. This is important for the study of allostery, the process by which conformational changes at one residue site affect the conformation of another. In dealing with this problem, we have pioneered a new analytic paradigm, which will allow us to do many interesting things in statistics. Next, I will work on network modeling of transactional data. Network data analysis is an emerging area of statistics. Often, each node in a network can belong to one of many different communities. Researchers have used a so-called stochastic block model (SBM) to detect these communities. Early works often do not account for time and treat the network as if it were static. Recently, researchers have started to consider network dynamics over time, but they often treat the time variable in a discrete manner. With a student and a collaborator, I have been studying a continuous-time extension of the SBM, which can be used to model transactional data, e.g., messages sent over a period of time among many individuals, but I would like to further extend our model to incorporate spatial information. The resulting spatial-temporal SBM can be used to study any collection of entities that communicate with each other while travelling over space and time; it can be very useful for many branches of science. Finally, I will apply ideas from network analysis to ensemble learning. As far as I am aware, Zhu & Chipman (2006, Technometrics 48:491-502) were the first ones to use the ensemble approach for variable selection (as opposed to prediction). Since then, I have continued to work on this problem and further crystallized the notion of variable-selection ensembles, but an open question is what constitutes a good generating mechanism. Interestingly, a student and I have discovered a new mechanism based on network analysis. So far, this new mechanism has shown outstanding performance in almost all the simulation settings we have previously considered. I am intrigued by this new discovery, and want to dig much deeper into it. Trainees participating in this research program will be able to cultivate computational skills that are much needed in today’s economy, and acquire a taste of some very challenging problems in science and engineering.