Scalable Bayesian Inference for Interpretable Time-Series Models

从医疗保健到零售，从政府到教育，我们都在收集和存储数据。这些数据源提供了前所未有的机遇：最初用于计费目的的医疗保健数据存储可以被挖掘以更好地了解疾病并改进治疗；政府数据存储，最初收集的目的是报告，可以挖掘，以提高国家福利和安全；最初为会计目的收集的零售数据存储可用于检测复杂的欺诈行为并改善客户体验。特别是，这些大型数据存储使我们能够了解患者、客户、公民和学生随时间变化的模式。用于时间序列分析的概率模型可以恢复疾病轨迹和购买需求等模式。然而，由于以下几个原因，使用这些数据来更好地理解这些模式（通常是为其他目的收集和存储的）是具有挑战性的。这些数据通常存储在标准的关系数据库中，并受到复杂的安全保护。它们也常常是有偏见和不完整的；人们可以使用它们来发现有趣的模式，但必须谨慎使用结果。这项建议为解决这些核心问题采取了步骤。特别是，我们建议创建分析时间序列的方法，这些方法可以在现有的数据管理架构上有效地运行，并提供可解释的结果，这些结果可以由领域专家进行准确性审查。我们将这些方法应用于通过分析电子健康记录来了解糖尿病和精神疾病的疾病进展。从技术角度来看，这项工作侧重于一个特定的概率时间序列模型，即层次狄利克雷过程隐马尔可夫模型（HDP-HMM）。该模型的推理通常在数值计算环境中使用马尔可夫链蒙特卡罗（MCMC）进行。我们工作的第一部分涉及调整MCMC步骤，以便它们可以在传统数据库体系结构中有效地运行。具体来说，我们将开发不需要从数据库中删除数据的方法，方法是将推理分为直接操作数据的计算（将在数据库中执行）和操作派生统计数据的计算（将在数值计算环境中执行）。我们工作的第二部分涉及使从稀疏、高维数据中学习的模型更具可解释性。这里我们将利用这样一个事实：虽然这些数据存储通常是高维的（成千上万个维度），但这些维度并不都是独立的；事实上，在大多数实际应用程序中都存在关于这些数据如何结构化的知识。我们将应用这些知识库来创建稀疏模型，使领域专家更容易解释。虽然我们将重点放在医疗保健应用程序上，但这些技术与涉及具有高维稀疏采样数据的时间序列的各种应用程序相关。

From healthcare to retail, from governments to education, we are collecting and storing data. These data sources provide unprecedented opportunities: healthcare data stores, originally collected for billing purposes, can be mined to better understand diseases and improve treatments; government data stores, originally collected for reporting purposes, can be mined to improve national welfare and security; retail data stores, originally collected for accounting purposes, can be used to detect complex fraud and improve the customer experience. In particular, these large data stores allow us to understand the patterns of patients, customers, citizens, and students over time. Probabilistic models for time-series analysis can recover patterns such as disease trajectories and purchasing needs. However, using these data to better understand these patterns---generally collected and stored for other purposes---is challenging for several reasons. These data are typically stored in standard relational databases and subject to complex security protections. They are also often biased and incomplete; one can use them to discover interesting patterns but the results must be used with caution. This proposal makes steps toward addressing these core problems. In particular, we propose to create methods for analyzing time-series that can run efficiently on existing data management architectures and provide interpretable results that can be vetted by a domain expert for accuracy. We apply these approaches to understanding disease progression in diabetes and psychiatric diseases through the analysis of electronic health records. From a technical point of view, this work focuses on a particular probabilistic time-series model, the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM). Inference in this model is typically performed in a numerical computing environment using Markov Chain Monte Carlo (MCMC). The first part of our work involves adapting the MCMC steps so that they can be run efficiently with a traditional database architectures. Specifically, we will develop methods that do not require the data to be removed from the database by splitting the inference into computations that operate directly on the data---to be performed within the database---and computations that operate on derived statistics---to be performed in a numerical computing environment. The second part of our work involves making models learned from sparse, high-dimensional data more interpretable. Here we will leverage the fact that while these data stores are typically high-dimensional (tens of thousands of dimensions), these dimensions are not all independent; in fact, in most real applications there exists knowledge about how these data are structured. We will apply these knowledge bases to create sparse models that are easier for domain experts to interpret. While we focus on our healthcare application for this work, these techniques are relevant to a variety of applications involving time-series with high-dimensional, sparsely sampled data.