ContiFormer: Continuous-Time Transformer for Irregular Time Series Modeling

Modeling continuous-time dynamics on irregular time series is critical to account for data evolution and correlations that occur continuously. Traditional methods including recurrent neural networks or Transformer models leverage inductive bias via powerful neural architectures to capture complex patterns. However, due to their discrete characteristic, they have limitations in generalizing to continuous-time data paradigms. Though neural ordinary differential equations (Neural ODEs) and their variants have shown promising results in dealing with irregular time series, they often fail to capture the intricate correlations within these sequences. It is challenging yet demanding to concurrently model the relationship between input data points and capture the dynamic changes of the continuous-time system. To tackle this problem, we propose ContiFormer that extends the relation modeling of vanilla Transformer to the continuous-time domain, which explicitly incorporates the modeling abilities of continuous dynamics of Neural ODEs with the attention mechanism of Transformers. We mathematically characterize the expressive power of ContiFormer and illustrate that, by curated designs of function hypothesis, many Transformer variants specialized in irregular time series modeling can be covered as a special case of ContiFormer. A wide range of experiments on both synthetic and real-world datasets have illustrated the superior modeling capacities and prediction performance of ContiFormer on irregular time series data. The project link is https://seqml.github.io/contiformer/.

Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Data

Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an alternative approach, utilizing neural networks combined with ODE solvers to learn continuous latent representations through parameterized vector fields. Neural Stochastic Differential Equations (Neural SDEs) extend Neural ODEs by incorporating a diffusion term, although this addition is not trivial, particularly when addressing irregular intervals and missing values. Consequently, careful design of drift and diffusion functions is crucial for maintaining stability and enhancing performance, while incautious choices can result in adverse properties such as the absence of strong solutions, stochastic destabilization, or unstable Euler discretizations, significantly affecting Neural SDEs' performance. In this study, we propose three stable classes of Neural SDEs: Langevin-type SDE, Linear Noise SDE, and Geometric SDE. Then, we rigorously demonstrate their robustness in maintaining excellent performance under distribution shift, while effectively preventing overfitting. To assess the effectiveness of our approach, we conduct extensive experiments on four benchmark datasets for interpolation, forecasting, and classification tasks, and analyze the robustness of our methods with 30 public datasets under different missing rates. Our results demonstrate the efficacy of the proposed method in handling real-world irregular time series data.

Global Contrastive Training for Multimodal Electronic Health Records with Language Supervision

Modern electronic health records (EHRs) hold immense promise in tracking personalized patient health trajectories through sequential deep learning, owing to their extensive breadth, scale, and temporal granularity. Nonetheless, how to effectively leverage multiple modalities from EHRs poses significant challenges, given its complex characteristics such as high dimensionality, multimodality, sparsity, varied recording frequencies, and temporal irregularities. To this end, this paper introduces a novel multimodal contrastive learning framework, specifically focusing on medical time series and clinical notes. To tackle the challenge of sparsity and irregular time intervals in medical time series, the framework integrates temporal cross-attention transformers with a dynamic embedding and tokenization scheme for learning multimodal feature representations. To harness the interconnected relationships between medical time series and clinical notes, the framework equips a global contrastive loss, aligning a patient's multimodal feature representations with the corresponding discharge summaries. Since discharge summaries uniquely pertain to individual patients and represent a holistic view of the patient's hospital stay, machine learning models are led to learn discriminative multimodal features via global contrasting. Extensive experiments with a real-world EHR dataset demonstrated that our framework outperformed state-of-the-art approaches on the exemplar task of predicting the occurrence of nine postoperative complications for more than 120,000 major inpatient surgeries using multimodal data from UF health system split among three hospitals (UF Health Gainesville, UF Health Jacksonville, and UF Health Jacksonville-North).

Probabilistic Forecasting of Irregular Time Series via Conditional Flows

Probabilistic forecasting of irregularly sampled multivariate time series with missing values is an important problem in many fields, including health care, astronomy, and climate. State-of-the-art methods for the task estimate only marginal distributions of observations in single channels and at single timepoints, assuming a fixed-shape parametric distribution. In this work, we propose a novel model, ProFITi, for probabilistic forecasting of irregularly sampled time series with missing values using conditional normalizing flows. The model learns joint distributions over the future values of the time series conditioned on past observations and queried channels and times, without assuming any fixed shape of the underlying distribution. As model components, we introduce a novel invertible triangular attention layer and an invertible non-linear activation function on and onto the whole real line. We conduct extensive experiments on four datasets and demonstrate that the proposed model provides $4$ times higher likelihood over the previously best model.

Spatiotemporal Representation Learning for Short and Long Medical Image Time Series

Analyzing temporal developments is crucial for the accurate prognosis of many medical conditions. Temporal changes that occur over short time scales are key to assessing the health of physiological functions, such as the cardiac cycle. Moreover, tracking longer term developments that occur over months or years in evolving processes, such as age-related macular degeneration (AMD), is essential for accurate prognosis. Despite the importance of both short and long term analysis to clinical decision making, they remain understudied in medical deep learning. State of the art methods for spatiotemporal representation learning, developed for short natural videos, prioritize the detection of temporal constants rather than temporal developments. Moreover, they do not account for varying time intervals between acquisitions, which are essential for contextualizing observed changes. To address these issues, we propose two approaches. First, we combine clip-level contrastive learning with a novel temporal embedding to adapt to irregular time series. Second, we propose masking and predicting latent frame representations of the temporal sequence. Our two approaches outperform all prior methods on temporally-dependent tasks including cardiac output estimation and three prognostic AMD tasks. Overall, this enables the automated analysis of temporal patterns which are typically overlooked in applications of deep learning to medicine.

Multi-scale Spatio-temporal Transformer-based Imbalanced Longitudinal Learning for Glaucoma Forecasting from Irregular Time Series Images

Glaucoma is one of the major eye diseases that leads to progressive optic nerve fiber damage and irreversible blindness, afflicting millions of individuals. Glaucoma forecast is a good solution to early screening and intervention of potential patients, which is helpful to prevent further deterioration of the disease. It leverages a series of historical fundus images of an eye and forecasts the likelihood of glaucoma occurrence in the future. However, the irregular sampling nature and the imbalanced class distribution are two challenges in the development of disease forecasting approaches. To this end, we introduce the Multi-scale Spatio-temporal Transformer Network (MST-former) based on the transformer architecture tailored for sequential image inputs, which can effectively learn representative semantic information from sequential images on both temporal and spatial dimensions. Specifically, we employ a multi-scale structure to extract features at various resolutions, which can largely exploit rich spatial information encoded in each image. Besides, we design a time distance matrix to scale time attention in a non-linear manner, which could effectively deal with the irregularly sampled data. Furthermore, we introduce a temperature-controlled Balanced Softmax Cross-entropy loss to address the class imbalance issue. Extensive experiments on the Sequential fundus Images for Glaucoma Forecast (SIGF) dataset demonstrate the superiority of the proposed MST-former method, achieving an AUC of 98.6% for glaucoma forecasting. Besides, our method shows excellent generalization capability on the Alzheimer's Disease Neuroimaging Initiative (ADNI) MRI dataset, with an accuracy of 90.3% for mild cognitive impairment and Alzheimer's disease prediction, outperforming the compared method by a large margin.

Continuous Time Evidential Distributions for Irregular Time Series

Prevalent in many real-world settings such as healthcare, irregular time series are challenging to formulate predictions from. It is difficult to infer the value of a feature at any given time when observations are sporadic, as it could take on a range of values depending on when it was last observed. To characterize this uncertainty we present EDICT, a strategy that learns an evidential distribution over irregular time series in continuous time. This distribution enables well-calibrated and flexible inference of partially observed features at any time of interest, while expanding uncertainty temporally for sparse, irregular observations. We demonstrate that EDICT attains competitive performance on challenging time series classification tasks and enabling uncertainty-guided inference when encountering noisy data.

Continuous-time Autoencoders for Regular and Irregular Time Series Imputation

Time series imputation is one of the most fundamental tasks for time series. Real-world time series datasets are frequently incomplete (or irregular with missing observations), in which case imputation is strongly required. Many different time series imputation methods have been proposed. Recent self-attention-based methods show the state-of-the-art imputation performance. However, it has been overlooked for a long time to design an imputation method based on continuous-time recurrent neural networks (RNNs), i.e., neural controlled differential equations (NCDEs). To this end, we redesign time series (variational) autoencoders based on NCDEs. Our method, called continuous-time autoencoder (CTA), encodes an input time series sample into a continuous hidden path (rather than a hidden vector) and decodes it to reconstruct and impute the input. In our experiments with 4 datasets and 19 baselines, our method shows the best imputation performance in almost all cases.

Invertible Solution of Neural Differential Equations for Analysis of Irregularly-Sampled Time Series

To handle the complexities of irregular and incomplete time series data, we propose an invertible solution of Neural Differential Equations (NDE)-based method. While NDE-based methods are a powerful method for analyzing irregularly-sampled time series, they typically do not guarantee reversible transformations in their standard form. Our method suggests the variation of Neural Controlled Differential Equations (Neural CDEs) with Neural Flow, which ensures invertibility while maintaining a lower computational burden. Additionally, it enables the training of a dual latent space, enhancing the modeling of dynamic temporal dynamics. Our research presents an advanced framework that excels in both classification and interpolation tasks. At the core of our approach is an enhanced dual latent states architecture, carefully designed for high precision across various time series tasks. Empirical analysis demonstrates that our method significantly outperforms existing models. This work significantly advances irregular time series analysis, introducing innovative techniques and offering a versatile tool for diverse practical applications.

Imputation with Inter-Series Information from Prototypes for Irregular Sampled Time Series

Irregularly sampled time series are ubiquitous, presenting significant challenges for analysis due to missing values. Despite existing methods address imputation, they predominantly focus on leveraging intra-series information, neglecting the potential benefits that inter-series information could provide, such as reducing uncertainty and memorization effect. To bridge this gap, we propose PRIME, a Prototype Recurrent Imputation ModEl, which integrates both intra-series and inter-series information for imputing missing values in irregularly sampled time series. Our framework comprises a prototype memory module for learning inter-series information, a bidirectional gated recurrent unit utilizing prototype information for imputation, and an attentive prototypical refinement module for adjusting imputations. We conducted extensive experiments on three datasets, and the results underscore PRIME's superiority over the state-of-the-art models by up to 26% relative improvement on mean square error.