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

May 2022:   George Named the 2022 Wojcicki Troper Fellow

May 2022:   New preprint on PrimeKG

New preprint on building knowledge graphs to enable precision medicine applications.

Apr 2022:   Webster on the Cover of Cell Systems

Webster is on the cover of April issue of Cell Systems. Webster uses cell viability changes following gene perturbation to automatically learn cellular functions and pathways from data.

Apr 2022:   NASA Space Biology

Dr. Zitnik will serve on the Science Working Group at NASA Space Biology.

Mar 2022:   Yasha's Graduate Research Fellowship

Yasha won the National Defense Science and Engineering Graduate (NDSEG) Fellowship. Congratulations!

Mar 2022:   AI4Science at ICML 2022

We are excited to be selected to organize the AI4Science meeting at ICML 2022. Stay tuned for details. http://www.ai4science.net/icml22

Mar 2022:   Graph Algorithms in Biomedicine at PSB 2023

Excited to be organizing a session on Graph Algorithms at PSB 2023. Stay tuned for details.

Mar 2022:   Multimodal Learning on Graphs

New preprint! We introduce REMAP, a multimodal AI approach for disease relation extraction and classification. Project website.

Feb 2022:   Explainable Graph AI on the Capitol Hill

Owen has been selected to present our research on explainable biomedical AI to members of the US Congress at the “Posters on the Hill” symposium. Congrats Owen!

Feb 2022:   Graph Neural Networks for Time Series

Hot off the press at ICLR 2022. Check out Raindrop, our graph neural network with unique predictive capability to learn from irregular time series. Project website.

Feb 2022:   Biomedical Graph ML Tutorial Accepted to ISMB

Excited to present a tutorial at ISMB 2022 on graph representation learning for precision medicine. Congratulations, Michelle!

Feb 2022:   Marissa Won the Gates Cambridge Scholarship

Marissa Sumathipala is among the 23 outstanding US scholars selected be part of the 2022 class of Gates Cambridge Scholars at the University of Cambridge. Congratulations, Marissa!

Jan 2022:   Inferring Gene Multifunctionality

Jan 2022:   Deep Graph AI for Time Series Accepted to ICLR

Paper on graph representation learning for time series accepted to ICLR. Congratulations, Xiang!

Jan 2022:   Probing GNN Explainers Accepted to AISTATS

Jan 2022:   Marissa Sumathipala selected as Churchill Scholar

Marissa Sumathipala is selected for the prestigious Churchill Scholarship. Congratulations, Marissa!

Jan 2022:   Therapeutics Data Commons User Meetup

We invite you to join the growing open-science community at the User Group Meetup of Therapeutics Data Commons! Register for the first live user group meeting on Tuesday, January 25 at 11:00 AM EST.

Jan 2022:   Workshop on Graph Learning Benchmarks

Dec 2021:   NASA: Precision Space Health System

Human space exploration beyond low Earth orbit will involve missions of significant distance and duration. To effectively mitigate myriad space health hazards, paradigm shifts in data and space health systems are necessary to enable Earth independence. Delighted to be working with NASA and can share our recommendations!

Zitnik Lab  ·  Harvard  ·  Department of Biomedical Informatics