We present a scalable end-to-end classifier that uses streaming physiological and medication data to accurately predict the onset of sepsis, a life-threatening complication from infections that has high mortality and morbidity. Our proposed framework models the multivariate trajectories of continuous-valued physiological time series using multitask Gaussian processes, seamlessly accounting for the high uncertainty, frequent missingness, and irregular sampling rates typically associated with real clinical data. The Gaussian process is directly connected to a black-box classifier that predicts whether a patient will become septic, chosen in our case to be a recurrent neural network to account for the extreme variability in the length of patient encounters. We show how to scale the computations associated with the Gaussian process in a manner so that the entire system can be discriminatively trained end-to-end using backpropagation. In a large cohort of heterogeneous inpatient encounters at our university health system we find that it outperforms several baselines at predicting sepsis, and yields 19.4 and 55.5 improved areas under the Receiver Operating Characteristic and Precision Recall curves as compared to the NEWS score currently used by our hospital.
There are several related works that also utilized multitask Gaussian processes in modeling multivariate physiological time series. For instance @cite_3 and @cite_10 used a similar model to ours, but instead focused more on forecasting of vitals to predict clinical instability, whereas our task is a binary classification to identify sepsis early. Finally, our end-to-end technique to discriminatively learn both the MGP and classifier parameters builds off of @cite_25 . However, our focus is more applied and the setting is more involved, as our time series are multivariate, of highly variable length, and may contain large amounts of missingness.
@cite_10 @cite_25 @cite_3
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Gaussian process (GP) models are a flexible means of performing nonparametric Bayesian regression. However, GP models in healthcare are often only used to model a single univariate output time series, denoted as single-task GPs (STGP). Due to an increasing prevalence of sensors in healthcare settings, there is an urgent need for robust multivariate time-series tools. Here, we propose a method using multitask GPs (MTGPs) which can model multiple correlated multivariate physiological time series simultaneously. The flexible MTGP framework can learn the correlation between multiple signals even though they might be sampled at different frequencies and have training sets available for different intervals. Furthermore, prior knowledge of any relationship between the time series such as delays and temporal behavior can be easily integrated. A novel normalization is proposed to allow interpretation of the various hyperparameters used in the MTGP. We investigate MTGPs for physiological monitoring with synthetic data sets and two real-world problems from the field of patient monitoring and radiotherapy. The results are compared with standard Gaussian processes and other existing methods in the respective biomedical application areas. In both cases, we show that our framework learned the correlation between physiological time series efficiently, outperforming the existing state of the art. The ability to determine patient acuity (or severity of illness) has immediate practical use for clinicians. We evaluate the use of multivariate timeseries modeling with the multi-task Gaussian process (GP) models using noisy, incomplete, sparse, heterogeneous and unevenly-sampled clinical data, including both physiological signals and clinical notes. The learned multi-task GP (MTGP) hyperparameters are then used to assess and forecast patient acuity. Experiments were conducted with two real clinical data sets acquired from ICU patients: firstly, estimating cerebrovascular pressure reactivity, an important indicator of secondary damage for traumatic brain injury patients, by learning the interactions between intracranial pressure and mean arterial blood pressure signals, and secondly, mortality prediction using clinical progress notes. In both cases, MTGPs provided improved results: an MTGP model provided better results than single-task GP models for signal interpolation and forecasting (0.91 vs 0.69 RMSE), and the use of MTGP hyperparameters obtained improved results when used as additional classification features (0.812 vs 0.788 AUC). Multivariate time series (MTS) classification has gained importance with the increase in the number of temporal datasets in different domains (such as medicine, finance, multimedia, etc.). Similarity-based approaches, such as nearest-neighbor classifiers, are often used for univariate time series, but MTS are characterized not only by individual attributes, but also by their relationships. Here we provide a classifier based on a new symbolic representation for MTS (denoted as SMTS) with several important elements. SMTS considers all attributes of MTS simultaneously, rather than separately, to extract information contained in the relationships. Symbols are learned from a supervised algorithm that does not require pre-defined intervals, nor features. An elementary representation is used that consists of the time index, and the values (and first differences for numerical attributes) of the individual time series as columns. That is, there is essentially no feature extraction (aside from first differences) and the local series values are fused to time position through the time index. The initial representation of raw data is quite simple conceptually and operationally. Still, a tree-based ensemble can detect interactions in the space of the time index and time values and this is exploited to generate a high-dimensional codebook from the terminal nodes of the trees. Because the time index is included as an attribute, each MTS is learned to be segmented by time, or by the value of one of its attributes. The codebook is processed with a second ensemble where now implicit feature selection is exploited to handle the high-dimensional input. The constituent properties produce a distinctly different algorithm. Moreover, MTS with nominal and missing values are handled efficiently with tree learners. Experiments demonstrate the effectiveness of the proposed approach in terms of accuracy and computation times in a large collection multivariate (and univariate) datasets. We propose a Bayesian nonparametric approach to the problem of jointly modeling multiple related time series. Our model discovers a latent set of dynamical behaviors shared among the sequences, and segments each time series into regions defined by a subset of these behaviors. Using a beta process prior, the size of the behavior set and the sharing pattern are both inferred from data. We develop Markov chain Monte Carlo (MCMC) methods based on the Indian buffet process representation of the predictive distribution of the beta process. Our MCMC inference algorithm efficiently adds and removes behaviors via novel split-merge moves as well as data-driven birth and death proposals, avoiding the need to consider a truncated model. We demonstrate promising results on unsupervised segmentation of human motion capture data. 1. Introduction. Classical time series analysis has generally focused on the study of a single (potentially multivariate) time series. Instead, we consider analyzing collections of related time series, motivated by the increasing abundance of such data in many domains. In this work we explore this problem by considering time series produced by motion capture sensors on the joints of people performing exercise routines. An individual recording provides a multivariate time series that can be segmented into types of exercises (e.g., jumping jacks, arm-circles, and twists). Each exercise type describes locally coherent and simple dynamics that persist over a segment of time. We have such motion capture recordings from multiple individuals, each of whom performs some subset of a global set of exercises, as shown in Figure1. Our goal is to discover the set of global exercise types (“behaviors”) and their occurrences in each individual’s data stream. We would like to take advantage of the overlap between individuals: if a jumping-jack behavior is discovered in one sequence, then it can be used to model data for other individuals.