Path Imputation Strategies for Signature Models of Irregular Time Series

The signature transform is a 'universal nonlinearity' on the space of continuous vector-valued paths, and has received attention for use in machine learning on time series. However, real-world temporal data is typically observed at discrete points in time, and must first be transformed into a continuous path before signature techniques can be applied. We make this step explicit by characterising it as an imputation problem, and empirically assess the impact of various imputation strategies when applying signature-based neural nets to irregular time series data. For one of these strategies, Gaussian process (GP) adapters, we propose an extension~(GP-PoM) that makes uncertainty information directly available to the subsequent classifier while at the same time preventing costly Monte-Carlo (MC) sampling. In our experiments, we find that the choice of imputation drastically affects shallow signature models, whereas deeper architectures are more robust. Next, we observe that uncertainty-aware predictions (based on GP-PoM or indicator imputations) are beneficial for predictive performance, even compared to the uncertainty-aware training of conventional GP adapters. In conclusion, we have demonstrated that the path construction is indeed crucial for signature models and that our proposed strategy leads to competitive performance in general, while improving robustness of signature models in particular

Interpolation-Prediction Networks for Irregularly Sampled Time Series

In this paper, we present a new deep learning architecture for addressing the problem of supervised learning with sparse and irregularly sampled multivariate time series. The architecture is based on the use of a semi-parametric interpolation network followed by the application of a prediction network. The interpolation network allows for information to be shared across multiple dimensions of a multivariate time series during the interpolation stage, while any standard deep learning model can be used for the prediction network. This work is motivated by the analysis of physiological time series data in electronic health records, which are sparse, irregularly sampled, and multivariate. We investigate the performance of this architecture on both classification and regression tasks, showing that our approach outperforms a range of baseline and recently proposed models.Comment: International Conference on Learning Representations. arXiv admin note: substantial text overlap with arXiv:1812.0053

Learning to Detect Sepsis with a Multitask Gaussian Process RNN Classifier

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.Comment: Presented at 34th International Conference on Machine Learning (ICML 2017), Sydney, Australi

Scalable Joint Models for Reliable Uncertainty-Aware Event Prediction

Missing data and noisy observations pose significant challenges for reliably predicting events from irregularly sampled multivariate time series (longitudinal) data. Imputation methods, which are typically used for completing the data prior to event prediction, lack a principled mechanism to account for the uncertainty due to missingness. Alternatively, state-of-the-art joint modeling techniques can be used for jointly modeling the longitudinal and event data and compute event probabilities conditioned on the longitudinal observations. These approaches, however, make strong parametric assumptions and do not easily scale to multivariate signals with many observations. Our proposed approach consists of several key innovations. First, we develop a flexible and scalable joint model based upon sparse multiple-output Gaussian processes. Unlike state-of-the-art joint models, the proposed model can explain highly challenging structure including non-Gaussian noise while scaling to large data. Second, we derive an optimal policy for predicting events using the distribution of the event occurrence estimated by the joint model. The derived policy trades-off the cost of a delayed detection versus incorrect assessments and abstains from making decisions when the estimated event probability does not satisfy the derived confidence criteria. Experiments on a large dataset show that the proposed framework significantly outperforms state-of-the-art techniques in event prediction.Comment: To appear in IEEE Transaction on Pattern Analysis and Machine Intelligenc

Modeling Irregularly Sampled Clinical Time Series

While the volume of electronic health records (EHR) data continues to grow, it remains rare for hospital systems to capture dense physiological data streams, even in the data-rich intensive care unit setting. Instead, typical EHR records consist of sparse and irregularly observed multivariate time series, which are well understood to present particularly challenging problems for machine learning methods. In this paper, we present a new deep learning architecture for addressing this problem based on the use of a semi-parametric interpolation network followed by the application of a prediction network. The interpolation network allows for information to be shared across multiple dimensions during the interpolation stage, while any standard deep learning model can be used for the prediction network. We investigate the performance of this architecture on the problems of mortality and length of stay prediction.Comment: Machine Learning for Health (ML4H) Workshop at NeurIPS 2018 arXiv:cs/010120

Progressive Growing of Neural ODEs

Neural Ordinary Differential Equations (NODEs) have proven to be a powerful modeling tool for approximating (interpolation) and forecasting (extrapolation) irregularly sampled time series data. However, their performance degrades substantially when applied to real-world data, especially long-term data with complex behaviors (e.g., long-term trend across years, mid-term seasonality across months, and short-term local variation across days). To address the modeling of such complex data with different behaviors at different frequencies (time spans), we propose a novel progressive learning paradigm of NODEs for long-term time series forecasting. Specifically, following the principle of curriculum learning, we gradually increase the complexity of data and network capacity as training progresses. Our experiments with both synthetic data and real traffic data (PeMS Bay Area traffic data) show that our training methodology consistently improves the performance of vanilla NODEs by over 64%

Integrating Physiological Time Series and Clinical Notes with Deep Learning for Improved ICU Mortality Prediction

Intensive Care Unit Electronic Health Records (ICU EHRs) store multimodal data about patients including clinical notes, sparse and irregularly sampled physiological time series, lab results, and more. To date, most methods designed to learn predictive models from ICU EHR data have focused on a single modality. In this paper, we leverage the recently proposed interpolation-prediction deep learning architecture(Shukla and Marlin 2019) as a basis for exploring how physiological time series data and clinical notes can be integrated into a unified mortality prediction model. We study both early and late fusion approaches and demonstrate how the relative predictive value of clinical text and physiological data change over time. Our results show that a late fusion approach can provide a statistically significant improvement in mortality prediction performance over using individual modalities in isolation.Comment: Presented at ACM Conference on Health, Inference and Learning (Workshop Track), 202

Unsupervised Online Anomaly Detection On Irregularly Sampled Or Missing Valued Time-Series Data Using LSTM Networks

We study anomaly detection and introduce an algorithm that processes variable length, irregularly sampled sequences or sequences with missing values. Our algorithm is fully unsupervised, however, can be readily extended to supervised or semisupervised cases when the anomaly labels are present as remarked throughout the paper. Our approach uses the Long Short Term Memory (LSTM) networks in order to extract temporal features and find the most relevant feature vectors for anomaly detection. We incorporate the sampling time information to our model by modulating the standard LSTM model with time modulation gates. After obtaining the most relevant features from the LSTM, we label the sequences using a Support Vector Data Descriptor (SVDD) model. We introduce a loss function and then jointly optimize the feature extraction and sequence processing mechanisms in an end-to-end manner. Through this joint optimization, the LSTM extracts the most relevant features for anomaly detection later to be used in the SVDD, hence completely removes the need for feature selection by expert knowledge. Furthermore, we provide a training algorithm for the online setup, where we optimize our model parameters with individual sequences as the new data arrives. Finally, on real-life datasets, we show that our model significantly outperforms the standard approaches thanks to its combination of LSTM with SVDD and joint optimization.Comment: 11 page

Set Functions for Time Series

Despite the eminent successes of deep neural networks, many architectures are often hard to transfer to irregularly-sampled and asynchronous time series that commonly occur in real-world datasets, especially in healthcare applications. This paper proposes a novel approach for classifying irregularly-sampled time series with unaligned measurements, focusing on high scalability and data efficiency. Our method SeFT (Set Functions for Time Series) is based on recent advances in differentiable set function learning, extremely parallelizable with a beneficial memory footprint, thus scaling well to large datasets of long time series and online monitoring scenarios. Furthermore, our approach permits quantifying per-observation contributions to the classification outcome. We extensively compare our method with existing algorithms on multiple healthcare time series datasets and demonstrate that it performs competitively whilst significantly reducing runtime.Comment: Accepted at the International Conference on Machine Learning (ICML) 202

A Survey on Principles, Models and Methods for Learning from Irregularly Sampled Time Series

Irregularly sampled time series data arise naturally in many application domains including biology, ecology, climate science, astronomy, and health. Such data represent fundamental challenges to many classical models from machine learning and statistics due to the presence of non-uniform intervals between observations. However, there has been significant progress within the machine learning community over the last decade on developing specialized models and architectures for learning from irregularly sampled univariate and multivariate time series data. In this survey, we first describe several axes along which approaches to learning from irregularly sampled time series differ including what data representations they are based on, what modeling primitives they leverage to deal with the fundamental problem of irregular sampling, and what inference tasks they are designed to perform. We then survey the recent literature organized primarily along the axis of modeling primitives. We describe approaches based on temporal discretization, interpolation, recurrence, attention and structural invariance. We discuss similarities and differences between approaches and highlight primary strengths and weaknesses.Comment: Presented at NeurIPS 2020 Workshop: ML Retrospectives, Surveys & Meta-Analyses (ML-RSA