Time Series Modeling of Irregularly Sampled Multivariate Clinical Data

Building of an accurate predictive model of clinical time series for a patient is critical for understanding of the patient condition, its dynamics, and optimal patient management. Unfortunately, this process is challenging because of: (1) multivariate behaviors: the real-world dynamics is multivariate and it is better described by multivariate time series (MTS); (2) irregular samples: sequential observations are collected at different times, and the time elapsed between two consecutive observations may vary; and (3) patient variability: clinical MTS vary from patient to patient and an individual patient may exhibit short-term variability reflecting the different events affecting the care and patient state. In this dissertation, we investigate the different ways of developing and refining forecasting models from the irregularly sampled clinical MTS data collection. First, we focus on the refinements of a popular model for MTS analysis: the linear dynamical system (LDS) (a.k.a Kalman filter) and its application to MTS forecasting. We propose (1) a regularized LDS learning framework which automatically shuts down LDSs' spurious and unnecessary dimensions, and consequently, prevents the overfitting problem given a small amount of data; and (2) a generalized LDS learning framework via matrix factorization, which allows various constraints can be easily incorporated to guide the learning process. Second, we study ways of modeling irregularly sampled univariate clinical time series. We develop a new two-layer hierarchical dynamical system model for irregularly sampled clinical time series prediction. We demonstrate that our new system adapts better to irregular samples and it supports more accurate predictions. Finally, we propose, develop and experiment with two personalized forecasting frameworks for modeling and predicting clinical MTS of an individual patient. The first approach relies on model adaptation techniques. It calibrates the population based model's predictions with patient specific residual models, which are learned from the difference between the patient observations and the population based model's predictions. The second framework relies on adaptive model selection strategies to combine advantages of the population based, patient specific and short-term individualized predictive models. We demonstrate the benefits and advantages of the aforementioned frameworks on synthetic data sets, public time series data sets and clinical data extracted from EHRs