Non-Gaussian latent variable mixture models

申请人拟开发新型潜在变量混合模型，该模型可用于联合建模混合类型（二元，分类和连续）数据，并探索已知在这些类型模型拟合中出现的问题的潜在解决方案。重要的是，这些解决方案可能适用于广泛的统计模型。对于所提议的研究的每一个方面，申请人都打算发布免费的、开源的、多平台的软件，供其他研究人员和公众使用。本研究的主要目的是推动潜变量混合模型的方法论，从而形成一套在真实数据集上具有更广泛适用性的模型。目前使用的统计模型通常基于正态分布数据的假设。现实世界的数据并不总是，甚至通常不符合这个假设。放宽这一假设将为各种科学领域和工业领域的研究人员带来更好的见解。学生将在这些方法的研究中发挥不可或缺的作用，为他们提供理论和实践培训，为他们未来的学习和就业机会做好准备。方法本文的研究重点是对上述模型进行数学推导。这需要在选定的参数估计框架下严格使用微积分和线性代数。正在开发的模型的性质使它们需要大量的计算；也就是说，它们需要极其大量的计算。因此，申请人在他的研究中大量使用计算机，依靠算法对他开发的模型进行参数估计。这些算法有时会导致无法直接求解的方程。拟议研究的一部分是研究处理这些困难方程的替代方法。本摘要中提到的模型通常用于对数据集中出现的组进行分类。作为这种方法重要性的一个具体例子，在医学领域经常获得关于患有某种疾病的病人和健康的病人的数据。申请人介绍的技术可以为这些研究人员提供一种额外的工具，以确定其数据中的“健康”和“生病”群体。具体来说，拟议中的研究将允许研究人员将分类信息（如性别、血统、吸烟习惯等）与数字信息（如体重、身高、血细胞计数等）结合起来，以帮助估计患者可能是“生病”还是“健康”。

INTRODUCTION The applicant is proposing to develop novel latent variable mixture models, which can be used to jointly model mixed-type (binary, categorical, and continuous) data, and explore potential solutions to problems that are known to arise in the fitting of these types of models. Importantly, these solutions are likely to be applicable to a broad base of statistical models. For each aspect of the proposed research, it is the intention of the applicant to release free, open source, multi-platform software for fellow researchers and the public to access. OBJECTIVE The main objective of the proposed research is to push forward the methodology of latent variable mixture models, which will lead to a set of models with a wider range of applicability on real data sets. The current statistical models used are often based on the assumption of normally distributed data. Real world data does not always, or even commonly, conform to this assumption. Relaxing this assumption will lead to better insights for researchers across a variety of scientific fields and in industry. Students will play an integral role in the research of these methods, providing them with theoretical and practical training that will prepare them for future studies and employment opportunities. METHODS The focus of the proposed research is the mathematical development of the aforementioned models. This requires rigorous usage of calculus and linear algebra, under the chosen parameter estimation framework. The nature of the models being developed makes them computationally intensive; that is, they require an extremely large number of calculations. As such, the applicant makes heavy use of computers in his research, relying on algorithms to perform parameter estimation for the models he develops. These algorithms occasionally result in equations that cannot be solved directly. Part of the proposed research is to investigate alternate ways to approach these difficult equations. IMPACT The models alluded to in this summary are often used to classify groups that arise in data sets. As a concrete example of the importance of such methods, data is often obtained in medical fields on patients who have a particular disease and those who are healthy. The techniques introduced by the applicant may provide these researchers with an additional tool to determine `healthy' and `sick' groups within their data. Specifically, the proposed research would allow researchers to include categorical information (such as gender, ancestry, smoking habits, etc.) combined with numeric information (such as weight, height, blood cell counts, etc.) to aid in the estimation of whether a patient is likely to be `sick' or `healthy'.