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Register a new userScalable Linear Causal Inference for Irregularly Sampled Time Series with Long Range Dependencies
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Linear causal analysis is central to a wide range of important application spanning finance, the physical sciences, and engineering. Much of the existing literature in linear causal analysis operates in the time domain. Unfortunately, the direct application of time domain linear causal analysis to many real-world time series presents three critical challenges: irregular temporal sampling, long range dependencies, and scale. Moreover, real-world data is often collected at irregular time intervals across vast arrays of decentralized sensors and with long range dependencies which make naive time domain correlation estimators spurious. In this paper we present a frequency domain based estimation framework which naturally handles irregularly sampled data and long range dependencies while enabled memory and communication efficient distributed processing of time series data. By operating in the frequency domain we eliminate the need to interpolate and help mitigate the effects of long range dependencies. We implement and evaluate our new work-flow in the distributed setting using Apache Spark and demonstrate on both Monte Carlo simulations and high-frequency financial trading that we can accurately recover causal structure at scale.
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Recurrent neural networks (RNNs) with continuous-time hidden states are a natural fit for modeling irregularly-sampled time series. These models, however, face difficulties when the input data possess long-term dependencies. We prove that similar to standard RNNs, the underlying reason for this issue is the vanishing or exploding of the gradient during training. This phenomenon is expressed by the ordinary differential equation (ODE) representation of the hidden state, regardless of the ODE solvers choice. We provide a solution by designing a new algorithm based on the long short-term memory (LSTM) that separates its memory from its time-continuous state. This way, we encode a continuous-time dynamical flow within the RNN, allowing it to respond to inputs arriving at arbitrary time-lags while ensuring a constant error propagation through the memory path. We call these RNN models ODE-LSTMs. We experimentally show that ODE-LSTMs outperform advanced RNN-based counterparts on non-uniformly sampled data with long-term dependencies. All code and data is available at https://github.com/mlech26l/ode-lstms.
Continuous, automated surveillance systems that incorporate machine learning models are becoming increasingly more common in healthcare environments. These models can capture temporally dependent changes across multiple patient variables and can enhance a clinicians situational awareness by providing an early warning alarm of an impending adverse event such as sepsis. However, most commonly used methods, e.g., XGBoost, fail to provide an interpretable mechanism for understanding why a model produced a sepsis alarm at a given time. The black-box nature of many models is a severe limitation as it prevents clinicians from independently corroborating those physiologic features that have contributed to the sepsis alarm. To overcome this limitation, we propose a generalized linear model (GLM) approach to fit a Granger causal graph based on the physiology of several major sepsis-associated derangements (SADs). We adopt a recently developed stochastic monotone variational inequality-based estimator coupled with forwarding feature selection to learn the graph structure from both continuous and discrete-valued as well as regularly and irregularly sampled time series. Most importantly, we develop a non-asymptotic upper bound on the estimation error for any monotone link function in the GLM. We conduct real-data experiments and demonstrate that our proposed method can achieve comparable performance to popular and powerful prediction methods such as XGBoost while simultaneously maintaining a high level of interpretability.
Electronic health record (EHR) data is sparse and irregular as it is recorded at irregular time intervals, and different clinical variables are measured at each observation point. In this work, we propose a multi-view features integration learning from irregular multivariate time series data by self-attention mechanism in an imputation-free manner. Specifically, we devise a novel multi-integration attention module (MIAM) to extract complex information inherent in irregular time series data. In particular, we explicitly learn the relationships among the observed values, missing indicators, and time interval between the consecutive observations, simultaneously. The rationale behind our approach is the use of human knowledge such as what to measure and when to measure in different situations, which are indirectly represented in the data. In addition, we build an attention-based decoder as a missing value imputer that helps empower the representation learning of the inter-relations among multi-view observations for the prediction task, which operates at the training phase only. We validated the effectiveness of our method over the public MIMIC-III and PhysioNet challenge 2012 datasets by comparing with and outperforming the state-of-the-art methods for in-hospital mortality prediction.
Multivariate time series (MTS) data are becoming increasingly ubiquitous in diverse domains, e.g., IoT systems, health informatics, and 5G networks. To obtain an effective representation of MTS data, it is not only essential to consider unpredictable dynamics and highly variable lengths of these data but also important to address the irregularities in the sampling rates of MTS. Existing parametric approaches rely on manual hyperparameter tuning and may cost a huge amount of labor effort. Therefore, it is desirable to learn the representation automatically and efficiently. To this end, we propose an autonomous representation learning approach for multivariate time series (TimeAutoML) with irregular sampling rates and variable lengths. As opposed to previous works, we first present a representation learning pipeline in which the configuration and hyperparameter optimization are fully automatic and can be tailored for various tasks, e.g., anomaly detection, clustering, etc. Next, a negative sample generation approach and an auxiliary classification task are developed and integrated within TimeAutoML to enhance its representation capability. Extensive empirical studies on real-world datasets demonstrate that the proposed TimeAutoML outperforms competing approaches on various tasks by a large margin. In fact, it achieves the best anomaly detection performance among all comparison algorithms on 78 out of all 85 UCR datasets, acquiring up to 20% performance improvement in terms of AUC score.
We introduce new quantities for exploratory causal inference between bivariate time series. The quantities, called penchants and leanings, are computationally straightforward to apply, follow directly from assumptions of probabilistic causality, do not depend on any assumed models for the time series generating process, and do not rely on any embedding procedures; these features may provide a clearer interpretation of the results than those from existing time series causality tools. The penchant and leaning are computed based on a structured method for computing probabilities.
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