III: Small: A New Approach to Latent Space Learning with Diversity-Inducing Regularization and Applications to Healthcare Data Analytics

潜在变量模型（lvm）从原始数据中提取隐藏信息，如主题、主题或疾病模式，在电子健康记录（EHR）管理和应用程序中发挥着重要作用。随着电子病历数据量和复杂性的急剧增加，当前的lvm面临着一些新的挑战，包括无法捕获人群中少数患者存在的罕见模式（也称为长尾模式），发现的模式之间存在冗余，计算效率低下，这些都严重影响了电子病历数据在推动高质量个性化医疗中的价值。迫切需要开发新方法，将传统lvm转换为能够规避此类限制的lvm，以便更有效、更可靠地将EHR数据用于医疗保健应用程序。该项目解决了这一需求，并开发了一种被称为“多样性诱导机器学习模型”的新技术，该技术以高计算效率促进稀有模式和浓缩冗余模式，从而从复杂和异构（例如文本、图像和时间序列）的电子病历数据中实现更有效的模式发现和知识提取。具体而言，本项目包含以下研究组成部分：1。开发一个新的正则化LVM学习框架，允许潜在空间的基础倾向于更多的多样性诱导几何和更少的冗余，从而实现长尾模式覆盖和更好的欧几里得和希尔伯特空间设置的可解释性。2. 开发一个促进多样性的贝叶斯LVM学习框架，能够有效地推断后验概率分布，以促进不确定性的量化和缓解过度拟合。3. 从理论上分析1和2中提出的多样性诱导技术，了解这些技术如何影响有监督lvm的泛化误差、无监督lvm的后验收缩率以及lvm诱导的分布的信息几何形状。4. 将各种lvm应用于医疗保健应用程序。该项目还为本科生、研究生和专业水平的多学科教育和研究培训提供了丰富的机会。

Latent variable models (LVMs), which extract hidden information, such as topics, themes, or disease patterns, from raw data, play an important role in electronic health record (EHR) management and applications. With the dramatic increase of the volume and complexity of EHR data, current LVMs face several new challenges, including inadequacy in capturing rare patterns existing in only small number of patients in a population (also known as long tail patterns), redundancy amongst patterns being discovered, and low computational efficiency, which all seriously impair the value of EHR data in driving high-quality personalized medicine. There is a critical need in developing new methods to transform conventional LVMs to ones that can circumvent such limitations so that the EHR data can be more effectively and reliably used for healthcare applications. This project addresses this need and develops a new technique known as "diversity-inducing machine learning models", which promote rare patterns and condense redundant patterns, at high computational efficiency, to enable more effective pattern discovery and knowledge extraction from complex and heterogeneous (e.g., textual, image, and time series) EHR data. Specifically, this project contains the following research components: 1. Develop a new regularized LVM learning framework that allows the basis of the latent space to favor a more diversity-inducing geometry and less redundancy, thereby accomplish long-tail pattern coverage and better interpretability for both Euclidean and Hilbert space settings. 2. Develop a diversity-promoting Bayesian LVM learning framework that enables efficient inference of posteriors probability distributions to facilitate quantization of uncertainty and alleviate over fitting. 3. Theoretically analyze the diversity-inducing techniques proposed in 1 and 2 to understand how these techniques affect the generalization errors in supervised LVMs, posterior contraction rate in unsupervised LVMs, and the information geometry of the distributions induced by LVMs. 4. Apply the diversified LVMs to healthcare applications. This project also provides rich opportunities for multi-disciplinary education and research training, at both undergraduate, graduate, and professional levels.