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. Background Early classification of time series is beneficial for biomedical informatics problems such including, but not limited to, disease change detection. Early classification can be of tremendous help by identifying the onset of a disease before it has time to fully take hold. In addition, extracting patterns from the original time series helps domain experts to gain insights into the classification results. This problem has been studied recently using time series segments called shapelets. In this paper, we present a method, which we call Multivariate Shapelets Detection (MSD), that allows for early and patient-specific classification of multivariate time series. The method extracts time series patterns, called multivariate shapelets, from all dimensions of the time series that distinctly manifest the target class locally. The time series were classified by searching for the earliest closest patterns. Predicated on the increasing abundance of electronic health records, we investigate the problem of inferring individualized treatment effects using observational data. Stemming from the potential outcomes model, we propose a novel multi-task learning framework in which factual and counterfactual outcomes are modeled as the outputs of a function in a vector-valued reproducing kernel Hilbert space (vvRKHS). We develop a nonparametric Bayesian method for learning the treatment effects using a multi-task Gaussian process (GP) with a linear coregionalization kernel as a prior over the vvRKHS. The Bayesian approach allows us to compute individualized measures of confidence in our estimates via pointwise credible intervals, which are crucial for realizing the full potential of precision medicine. The impact of selection bias is alleviated via a risk-based empirical Bayes method for adapting the multi-task GP prior, which jointly minimizes the empirical error in factual outcomes and the uncertainty in (unobserved) counterfactual outcomes. We conduct experiments on observational datasets for an interventional social program applied to premature infants, and a left ventricular assist device applied to cardiac patients wait-listed for a heart transplant. In both experiments, we show that our method significantly outperforms the state-of-the-art. Abstract Over the past decade, multivariate time series classification has received great attention. We propose transforming the existing univariate time series classification models, the Long Short Term Memory Fully Convolutional Network (LSTM-FCN) and Attention LSTM-FCN (ALSTM-FCN), into a multivariate time series classification model by augmenting the fully convolutional block with a squeeze-and-excitation block to further improve accuracy. Our proposed models outperform most state-of-the-art models while requiring minimum preprocessing. The proposed models work efficiently on various complex multivariate time series classification tasks such as activity recognition or action recognition. Furthermore, the proposed models are highly efficient at test time and small enough to deploy on memory constrained systems. Many machine learning and pattern classification methods have been applied to the diagnosis of Alzheimer’s disease (AD) and its prodromal stage, i.e., mild cognitive impairment (MCI). Recently, rather than predicting categorical variables as in classification, several pattern regression methods have also been used to estimate continuous clinical variables from brain images. However, most existing regression methods focus on estimating multiple clinical variables separately and thus cannot utilize the intrinsic useful correlation information among different clinical variables. On the other hand, in those regression methods, only a single modality of data (usually only the structural MRI) is often used, without considering the complementary information that can be provided by different modalities. In this paper, we propose a general methodology, namely Multi-Modal Multi-Task (M3T) learning, to jointly predict multiple variables from multi-modal data. Here, the variables include not only the clinical variables used for regression but also the categorical variable used for classification, with different tasks corresponding to prediction of different variables. Specifically, our method contains two key components, i.e., (1) a multi-task feature selection which selects the common subset of relevant features for multiple variables from each modality, and (2) a multi-modal support vector machine which fuses the above-selected features from all modalities to predict multiple (regression and classification) variables. To validate our method, we perform two sets of experiments on ADNI baseline MRI, FDG-PET, and cerebrospinal fluid (CSF) data from 45 AD patients, 91 MCI patients, and 50 healthy controls (HC). In the first set of experiments, we estimate two clinical variables such as Mini Mental State Examination (MMSE) and Alzheimer’s Disease Assessment Scale - Cognitive Subscale (ADAS-Cog), as well as one categorical variable (with value of ‘AD’, ‘MCI’ or ‘HC’), from the baseline MRI, FDG-PET, and CSF data. In the second set of experiments, we predict the 2-year changes of MMSE and ADAS-Cog scores and also the conversion of MCI to AD from the baseline MRI, FDG-PET, and CSF data. The results on both sets of experiments demonstrate that our proposed M3T learning scheme can achieve better performance on both regression and classification tasks than the conventional learning methods. In the scenario of real-time monitoring of hospital patients, high-quality inference of patients' health status using all information available from clinical covariates and lab tests is essential to enable successful medical interventions and improve patient outcomes. Developing a computational framework that can learn from observational large-scale electronic health records (EHRs) and make accurate real-time predictions is a critical step. In this work, we develop and explore a Bayesian nonparametric model based on Gaussian process (GP) regression for hospital patient monitoring. We propose MedGP, a statistical framework that incorporates 24 clinical and lab covariates and supports a rich reference data set from which relationships between observed covariates may be inferred and exploited for high-quality inference of patient state over time. To do this, we develop a highly structured sparse GP kernel to enable tractable computation over tens of thousands of time points while estimating correlations among clinical covariates, patients, and periodicity in patient observations. MedGP has a number of benefits over current methods, including (i) not requiring an alignment of the time series data, (ii) quantifying confidence regions in the predictions, (iii) exploiting a vast and rich database of patients, and (iv) inferring interpretable relationships among clinical covariates. We evaluate and compare results from MedGP on the task of online prediction for three patient subgroups from two medical data sets across 8,043 patients. We found MedGP improves online prediction over baseline methods for nearly all covariates across different disease subgroups and studies. The publicly available code is at this https URL. In this paper we develop a framework for a sequential decision making under budget constraints for multi-class classification. In many classification systems, such as medical diagnosis and homeland security, sequential decisions are often warranted. For each instance, a sensor is first chosen for acquiring measurements and then based on the available information one decides (rejects) to seek more measurements from a new sensor modality or to terminate by classifying the example based on the available information. Different sensors have varying costs for acquisition, and these costs account for delay, throughput or monetary value. Consequently, we seek methods for maximizing performance of the system subject to budget constraints. We formulate a multi-stage multi-class empirical risk objective and learn sequential decision functions from training data. We show that reject decision at each stage can be posed as supervised binary classification. We derive bounds for the VC dimension of the multi-stage system to quantify the generalization error. We compare our approach to alternative strategies on several multi-class real world datasets. We demonstrate a simple strategy to cope with missing data in sequential inputs, addressing the task of multilabel classification of diagnoses given clinical time series. Collected from the pediatric intensive care unit (PICU) at Children's Hospital Los Angeles, our data consists of multivariate time series of observations. The measurements are irregularly spaced, leading to missingness patterns in temporally discretized sequences. While these artifacts are typically handled by imputation, we achieve superior predictive performance by treating the artifacts as features. Unlike linear models, recurrent neural networks can realize this improvement using only simple binary indicators of missingness. For linear models, we show an alternative strategy to capture this signal. Training models on missingness patterns only, we show that for some diseases, what tests are run can be as predictive as the results themselves. In this paper we investigate multi-task learning in the context of Gaussian Processes (GP). We propose a model that learns a shared covariance function on input-dependent features and a "free-form" covariance matrix over tasks. This allows for good flexibility when modelling inter-task dependencies while avoiding the need for large amounts of data for training. We show that under the assumption of noise-free observations and a block design, predictions for a given task only depend on its target values and therefore a cancellation of inter-task transfer occurs. We evaluate the benefits of our model on two practical applications: a compiler performance prediction problem and an exam score prediction task. Additionally, we make use of GP approximations and properties of our model in order to provide scalability to large data sets. Machine learning research has, to a great extent, ignored an important aspect of many real world applications: time. Existing concept learners predominantly operate on a static set of attributes; for example, classifying flowers described by leaf size, pet al colour and pet al count. However, many real datasets are not static; they cannot sensibly be represented as a fixed set of attributes. Rather, the examples are expressed as features that vary temporally, and it is the temporal variation itself that is used for classification. Consider a simple gesture recognition domain, in which the temporal features are the position of the hands, finger bends, and so on. Looking at the position of the hand at one point in time is not likely to lead to a successful classification; it is only by analysing changes in position that recognition is possible. This thesis presents a new technique for temporal classification. By extracting sub-events from the training instances and parameterising them to allow feature construction for a subsequent learning process, it is able to employ background knowledge and express learnt concepts in terms of the background knowledge. The novel results of the thesis are: a temporal learner capable of producing comprehensible and accurate classifiers for multivariate time series that can learn from a small number of instances and can integrate non-temporal features; a feature construction technique that parameterises sub-events of the training set and clusters them to construct features for a propositional learner; and a technique for post-processing classification rules produced by the learner to give a comprehensible description expressed in the same form as the original background knowledge. The thesis discusses the implementation of TClass, a temporal learner. Results show rules that are comprehensible in many cases and accuracy results close to or better than existing technique—over 98 per cent for sign language and 72 per cent for ECGs (equivalent to the accuracy of a human cardiologist). One further surprising result is that a small set of very primitive sub-events proves to be functional, avoiding the need for labour-intensive background knowledge if it is not available. Multi-task learning (MTL) aims to improve generalization performance by learning multiple related tasks simultaneously. While sometimes the underlying task relationship structure is known, often the structure needs to be estimated from data at hand. In this paper, we present a novel family of models for MTL, applicable to regression and classification problems, capable of learning the structure of tasks relationship. In particular, we consider a joint estimation problem of the tasks relationship structure and the individual task parameters, which is solved using alternating minimization. The task relationship revealed by structure learning is founded on recent advances in Gaussian graphical models endowed with sparse estimators of the precision (inverse covariance) matrix. An extension to include exible Gaussian copula models that relaxes the Gaussian marginal assumption is also proposed. We illustrate the effectiveness of the proposed model on a variety of synthetic and benchmark data sets for regression and classification. We also consider the problem of combining Earth System Model (ESM) outputs for better projections of future climate, with focus on projections of temperature by combining ESMs in South and North America, and show that the proposed model outperforms several existing methods for the problem. In this paper, we propose a Gaussian process (GP) model for analysis of nonlinear time series. Formulation of our model is based on the consideration that the observed data are functions of latent variables, with the associated mapping between observations and latent representations modeled through GP priors. In addition, to capture the temporal dynamics in the modeled data, we assume that subsequent latent representations depend on each other on the basis of a hidden Markov prior imposed over them. Derivation of our model is performed by marginalizing out the model parameters in closed form using GP priors for observation mappings, and appropriate stick-breaking priors for the latent variable (Markovian) dynamics. This way, we eventually obtain a nonparametric Bayesian model for dynamical systems that accounts for uncertainty in the modeled data. We provide efficient inference algorithms for our model on the basis of a truncated variational Bayesian approximation. We demonstrate the efficacy of our approach considering a number of applications dealing with real-world data, and compare it with the related state-of-the-art approaches. Gaussian process (GP) models are very popular for machine learning and regression and they are widely used to account for spatial or temporal relationships between multivariate random variables. In this paper, we propose a general formulation of underdetermined source separation as a problem involving GP regression. The advantage of the proposed unified view is first to describe the different underdetermined source separation problems as particular cases of a more general framework. Second, it provides a flexible means to include a variety of prior information concerning the sources such as smoothness, local stationarity or periodicity through the use of adequate covariance functions. Third, given the model, it provides an optimal solution in the minimum mean squared error (MMSE) sense to the source separation problem. In order to make the GP models tractable for very large signals, we introduce framing as a GP approximation and we show that computations for regularly sampled and locally stationary GPs can be done very efficiently in the frequency domain. These findings establish a deep connection between GP and nonnegative tensor factorizations (NTF) with the Itakura-Saito distance and lead to effective methods to learn GP hyperparameters for very large and regularly sampled signals. Consider the problem of learning logistic-regression models for multiple classification tasks, where the training data set for each task is not drawn from the same statistical distribution. In such a multi-task learning (MTL) scenario, it is necessary to identify groups of similar tasks that should be learned jointly. Relying on a Dirichlet process (DP) based statistical model to learn the extent of similarity between classification tasks, we develop computationally efficient algorithms for two different forms of the MTL problem. First, we consider a symmetric multi-task learning (SMTL) situation in which classifiers for multiple tasks are learned jointly using a variational Bayesian (VB) algorithm. Second, we consider an asymmetric multi-task learning (AMTL) formulation in which the posterior density function from the SMTL model parameters (from previous tasks) is used as a prior for a new task: this approach has the significant advantage of not requiring storage and use of all previous data from prior tasks. The AMTL formulation is solved with a simple Markov Chain Monte Carlo (MCMC) construction. Experimental results on two real life MTL problems indicate that the proposed algorithms: (a) automatically identify subgroups of related tasks whose training data appear to be drawn from similar distributions; and (b) are more accurate than simpler approaches such as single-task learning, pooling of data across all tasks, and simplified approximations to DP. Clinical medical data, especially in the intensive care unit (ICU), consist of multivariate time series of observations. For each patient visit (or episode), sensor data and lab test results are recorded in the patient's Electronic Health Record (EHR). While potentially containing a wealth of insights, the data is difficult to mine effectively, owing to varying length, irregular sampling and missing data. Recurrent Neural Networks (RNNs), particularly those using Long Short-Term Memory (LSTM) hidden units, are powerful and increasingly popular models for learning from sequence data. They effectively model varying length sequences and capture long range dependencies. We present the first study to empirically evaluate the ability of LSTMs to recognize patterns in multivariate time series of clinical measurements. Specifically, we consider multilabel classification of diagnoses, training a model to classify 128 diagnoses given 13 frequently but irregularly sampled clinical measurements. First, we establish the effectiveness of a simple LSTM network for modeling clinical data. Then we demonstrate a straightforward and effective training strategy in which we replicate targets at each sequence step. Trained only on raw time series, our models outperform several strong baselines, including a multilayer perceptron trained on hand-engineered features. Multivariate time series data in practical applications, such as health care, geoscience, and biology, are characterized by a variety of missing values. In time series prediction and other related tasks, it has been noted that missing values and their missing patterns are often correlated with the target labels, a.k.a., informative missingness. There is very limited work on exploiting the missing patterns for effective imputation and improving prediction performance. In this paper, we develop novel deep learning models, namely GRU-D, as one of the early attempts. GRU-D is based on Gated Recurrent Units (GRU), a state-of-the-art recurrent neural network. It takes two representations of missing patterns, i.e., masking and time interval, and effectively incorporates them into a deep model architecture so that it not only captures the long-term temporal dependencies in time series, but also utilizes the missing patterns to achieve better prediction results. Experiments of time series classification tasks on real-world clinical datasets (MIMIC-III, PhysioNet) and synthetic datasets demonstrate that our models achieve state-of-the-art performance and provides useful insights for better understanding and utilization of missing values in time series analysis. Multivariate time series data in practical applications, such as health care, geoscience, and biology, are characterized by a variety of missing values. In time series prediction and other related tasks, it has been noted that missing values and their missing patterns are often correlated with the target labels, a.k.a., informative missingness. There is very limited work on exploiting the missing patterns for effective imputation and improving prediction performance. In this paper, we develop novel deep learning models, namely GRU-D, as one of the early attempts. GRU-D is based on Gated Recurrent Unit (GRU), a state-of-the-art recurrent neural network. It takes two representations of missing patterns, i.e., masking and time interval, and effectively incorporates them into a deep model architecture so that it not only captures the long-term temporal dependencies in time series, but also utilizes the missing patterns to achieve better prediction results. Experiments of time series classification tasks on real-world clinical datasets (MIMIC-III, PhysioNet) and synthetic datasets demonstrate that our models achieve state-of-the-art performance and provides useful insights for better understanding and utilization of missing values in time series analysis.