Graph-Guided Networks For Irregular & Complex Time Series

In many domains, including healthcare, biology, and climate science, time series are irregularly sampled with varying time intervals between successive readouts and different subsets of variables (sensors) observed at different time points. Practical issues often exist in collecting sensor measurements that lead to various types of irregularities caused by missing observations, such as cost saving, sensor failures, external forces in physical scenarios, medical interventions, to name a few.

While machine learning methods for time series usually assume fully observable and fixed-size inputs, irregularly sampled time series raise considerable challenges. For example, sensors' observations might not be aligned, time intervals among adjacent readouts can vary across sensors, different samples can have varying numbers of readouts recorded at different times.

We introduce Raindrop, a graph neural network that learns to embed irregularly sampled and multivariate time series while simultaneously learning the dynamics of sensors purely from observational data. Raindrop can handle misaligned observations, varying time gaps, arbitrary numbers of observations, thus producing fixed-dimensional embeddings via neural message passing and temporal self-attention.

Multivariate time series are prevalent in various domains, including healthcare, space science, cyber security, biology, and finance. Practical issues often exist in collecting sensor measurements that lead to various types of irregularities caused by missing observations, such as saving costs, sensor failures, external forces in physical systems, medical interventions, to name a few.

Prior methods for dealing with irregularly sampled time series involve filling in missing values using interpolation, kernel methods, and probabilistic approaches. However, the absence of observations can be informative on its own, and thus imputing missing observations is not necessarily beneficial. While modern techniques involve recurrent neural network architectures (e.g., RNN, LSTM, GRU) and transformers, they are restricted to regular sampling or assume aligned measurements across modalities. For misaligned measurements, existing methods rely on a two-stage approach that first imputes missing values to produce a regularly-sampled dataset and then optimizes a model of choice for downstream performance. This decoupled approach does not fully exploit informative missingness patterns or deal with irregular sampling, thus producing suboptimal performance. Therefore, recent methods circumvent the imputation stage and directly model irregularly sampled time series.

To address the characteristics of irregularly sampled time series, we propose to model temporal dynamics of sensor dependencies and how those relationships evolve over time. Our intuitive assumption is that the observed sensors can indicate how the unobserved sensors currently behave, further improving the representation learning of irregular multivariate time series. We develop Raindrop, a graph neural network that leverages relational structure to embed and classify irregularly sampled multivariate time series. Raindrop can handle misaligned observations, varying time gaps, arbitrary numbers of observations, and produce multi-scale embeddings via a novel hierarchical attention.

Motivation for Raindrop

Raindrop takes samples as input, every sample containing multiple sensors and each sensor consisting of irregularly recorded observations (e.g., in clinical data, an individual patient’s state of health is recorded at irregular time intervals with different subsets of sensors observed at different times). Every observation is a real-value scalar (sensor readout).

Raindrop is inspired by how raindrops hit a surface at varying time intervals and create ripple effects that propagate throughout the surface (as shown in the following figure). Mathematically, in Raindrop, observations (i.e., raindrops) hit the sensor graph (i.e., the surface) asynchronously and at irregular time intervals; each observation is processed by passing messages to neighboring sensors (i.e., creating ripples), taking into account the learned sensor dependencies.

The key idea of Raindrop is that the observed sensors can indicate how the unobserved sensors currently behave, which can further improve the representation learning of irregular multivariate time series. Taking advantage of the inter-sensor dependencies and temporal attention, Raindrop leans a fixed-dimensional embedding for irregularly sampled time series.

Raindrop approach

Raindrop learns sample embeddings in a hierarchical architecture that processes individual observations, combines them into sensors, which, in turn, are aggregated to produce sample embeddings:

  1. We first construct a graph for each sample where nodes represent sensors and edges indicate relations between sensors.
  2. Raindrop generates observation embedding based on observed value, passes messages to neighbor sensors, and generates observation embedding through inter-sensor dependencies (as shown in panel a).
  3. We apply the message passing to all timestamps and produce corresponding observation embeddings. We aggregate an arbitrary number of observation embeddings into a fixed-length sensor embedding, while paying distinctive attention to different observations (as shown in panel b) through temporal self-attention. We independently apply the sensor-level processing procedure to all sensors.
  4. At last, we use a readout function to merge all sensor embeddings to obtain a sample embedding. The learned sampled embedding can be fed into a downstream task such as classification.

Attractive properties of Raindrop

  • Unique capability to model irregularly sampled time series: Raindrop can learn fixed-dimensional embedding for irregularly sampled multivariate time series while addressing challenges including misaligned observations, varying time gaps, and arbitrary numbers of observations.
  • Modeling of inter-sensor structure: To the best of our knowledge, Raindrop is the first model adopting neural message passing to model inter-sensor dependencies in irregular time series.
  • Excellent performance on leave-sensor-out scenarios: Raindrop outperforms five state-of-the-art methods across three datasets and four experimental settings, including a setup where a subset of sensors in the test set have malfunctioned (i.e., have no readouts at all).

Publication

Graph-Guided Network For Irregularly Sampled Multivariate Time Series
Xiang Zhang, Marko Zeman, Theodoros Tsiligkaridis, and Marinka Zitnik
International Conference on Learning Representations, ICLR 2022

@inproceedings{zhang2022graph,
title = {Graph-Guided Network For Irregularly Sampled Multivariate Time Series},
author = {Zhang, Xiang and Zeman, Marko and Tsiligkaridis, Theodoros and Zitnik, Marinka},
booktitle = {International Conference on Learning Representations, ICLR},
year      = {2022}
}

Code

Pytorch implementation of Raindrop are available in the GitHub repository.

Physical activity monitoring dataset is deposited in the Figshare.

Slides

Slides describing Raindrop are available here.

Authors

Latest News

Mar 2023:   New Paper in Nature Machine Intelligence

New paper with NASA in Nature Machine Intelligence on biomonitoring and precision health in deep space supported by artificial intelligence.

Mar 2023:   New Paper in Nature Machine Intelligence

Mar 2023:   TxGNN - Zero-shot prediction of therapeutic use

Mar 2023:   GraphXAI published in Scientific Data

Feb 2023:   Welcoming New Postdoctoral Fellows

A warm welcome to postdoctoral fellows Ruth Johnson and Wanxiang Shen. We are thrilled to have them joining us soon and look forward to working together.

Feb 2023:   New Preprint on Distribution Shifts

Feb 2023:   PrimeKG published in Scientific Data

Jan 2023:   GNNDelete published at ICLR 2023

Jan 2023:   New Network Principle for Molecular Phenotypes

Dec 2022:   Can we shorten rare disease diagnostic odyssey?

New preprint! Geometric deep learning for diagnosing patients with rare genetic diseases. Implications for using deep learning on sparsely-labeled medical datasets. Thankful for this collaboration with Zak Lab. Project website.

Nov 2022:   Can AI transform the way we discover new drugs?

Our conversation with Harvard Medicine News highlights recent developments and new features in Therapeutics Data Commons.

Oct 2022:   New Paper in Nature Biomedical Engineering

New paper on graph representation learning in biomedicine and healthcare published in Nature Biomedical Engineering.

Sep 2022:   New Paper in Nature Chemical Biology

Our paper on artificial intelligence foundation for therapeutic science is published in Nature Chemical Biology.

Sep 2022:   Self-Supervised Pre-Training at NeurIPS 2022

New paper on self-supervised contrastive pre-training accepted at NeurIPS 2022. Project page. Thankful for this collaboration with the Lincoln National Laboratory.

Sep 2022:   Best Paper Honorable Mention Award at IEEE VIS

Our paper on user-centric AI of drug repurposing received the Best Paper Honorable Mention Award at IEEE VIS 2022. Thankful for this collaboration with Gehlenborg Lab.

Sep 2022:   Multimodal Representation Learning with Graphs

Aug 2022:   On Graph AI for Precision Medicine

The recording of our tutorial on using graph AI to advance precision medicine is available. Tune into four hours of interactive lectures about state-of-the-art graph AI methods and applications in precision medicine.

Aug 2022:   Evaluating Explainability for GNNs

New preprint! We introduce a resource for broad evaluation of the quality and reliability of GNN explanations, addressing challenges and providing solutions for GNN explainability. Project website.

Jul 2022:   New Frontiers in Graph Learning at NeurIPS

Excited to organize the New Frontiers in Graph Learning workshop at NeurIPS.

Jul 2022:   AI4Science at NeurIPS

We are excited to host the AI4Science meeting at NeurIPS discussing AI-driven scientific discovery, implementation and verification of AI in science, the influence AI has on the conduct of science, and more.

Zitnik Lab  ·  Artificial Intelligence in Medicine and Science  ·  Harvard  ·  Department of Biomedical Informatics