PaperlayerView exact revision on arXiv

Source-linked AI summary

Graph-Guided Network for Irregularly Sampled Multivariate Time Series

Xiang Zhang, Marko Zeman, Theodoros Tsiligkaridis, Marinka Zitnik

arXiv:2110.05357v2cs.LGcs.AI

TL;DR

Irregularly sampled multivariate time series contain varying time gaps and differently observed sensors, challenging methods that assume regular or aligned inputs. RAINDROP learns sample-specific sensor graphs and propagates messages to model time-varying dependencies, outperforming baselines across datasets and difficult leave-sensor-out settings.

  • Problem

    Irregular time series have varying time intervals and misaligned sensor observations, while many existing models assume regular or aligned inputs.

  • Method

    RAINDROP represents each sample with a latent sensor dependency graph and uses neural message passing and attention to model evolving inter-sensor relationships.

  • Results

    RAINDROP outperforms baselines across three datasets and settings, achieving a 3.5% average absolute AUROC improvement and 9.3% absolute accuracy improvement with malfunctioning sensors.

  • Takeaways & Limitations

    Graph structure enables RAINDROP to handle misaligned observations, non-uniform time intervals, and sensors with varying numbers of recorded observations.

  • Takeaways & Limitations

    In healthcare applications, RAINDROP should be used cautiously because data-driven predictions may be biased, including through demographic attributes correlated with protected attributes.

Abstract

from arXiv · show

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. Here, we introduce RAINDROP, a graph neural network that embeds irregularly sampled and multivariate time series while also learning the dynamics of sensors purely from observational data. RAINDROP represents every sample as a separate sensor graph and models time-varying dependencies between sensors with a novel message passing operator. It estimates the latent sensor graph structure and leverages the structure together with nearby observations to predict misaligned readouts. This model can be interpreted as a graph neural network that sends messages over graphs that are optimized for capturing time-varying dependencies among sensors. We use RAINDROP to classify time series and interpret temporal dynamics on three healthcare and human activity datasets. RAINDROP outperforms state-of-the-art methods by up to 11.4% (absolute F1-score points), including techniques that deal with irregular sampling using fixed discretization and set functions. RAINDROP shows superiority in diverse setups, including challenging leave-sensor-out settings.

1 INTRODUCTION

RAINDROP addresses irregular, misaligned multivariate time series by learning sample-specific sensor dependencies and propagating messages over time-varying graphs. It outperforms baseline methods across datasets and challenging missing-sensor settings.

  • Motivation: Irregular sampling creates missing, misaligned, and non-uniform observations that challenge models designed for fully observed, fixed-size inputs.Different sensors may be observed at different times, and missingness can arise from sensor failures, cost constraints, or interventions.
  • Limitations of prior work: Existing approaches often impute missing values or require regular, aligned measurements, limiting their ability to exploit informative missingness patterns.Two-stage imputation-and-prediction pipelines decouple missing-data handling from downstream optimization.
  • Approach: RAINDROP learns latent inter-sensor structure and models time-varying dependencies through neural message passing over sample-specific sensor graphs.The approach integrates graph neural networks to capture sample-varying and time-varying relational structure from observational time series.
  • Approach: RAINDROP estimates observations using neighboring temporal readouts and similar sensors identified by optimized graph connectivity.It handles misaligned observations, varying time gaps, arbitrary observation counts, and multi-scale embeddings through hierarchical attention.
  • Results: 3.5% average absolute AUROC improvement across classification tasks accompanies RAINDROP’s better performance than baselines on all evaluated datasets.The evaluation covers two healthcare datasets and one activity-recognition dataset across three experimental settings.
  • Results: 9.3% absolute accuracy improvement over prior work occurs when varying subsets of sensors malfunction.This setting removes all readouts from selected sensors in test samples.

2 RELATED WORK

Related work covers irregular multivariate time series, graph-based learning, and neural message passing. RAINDROP connects these areas by specifying message passing over sensor graphs for misaligned readouts.

  • Irregularly sampled time series: Irregular multivariate time series involve varying intervals, misaligned sensor observations, and differing numbers of observations across samples.These properties complicate downstream time-series analysis.
  • Irregularly sampled time series: Prior work on irregular time series includes representation-learning approaches for classification and other downstream tasks.The related-work discussion situates irregular sampling as a distinct modeling setting.
  • Graphs and message passing: Graph embeddings, graph neural networks, and message passing neural networks provide established tools for learning from relational structures.These methods motivate the graph-based formulation used by RAINDROP.
  • Graphs and message passing: RAINDROP specifies a message-passing strategy that exchanges neural messages along sensor-graph edges to address misaligned sensor readouts.This links graph neural network methodology with irregular time-series modeling.

3 RAINDROP

RAINDROP represents irregular multivariate time series hierarchically, learning sample-specific sensor dependencies and using message passing and attention to form fixed-length sample embeddings.

  • Each sample contains multiple sensors with irregularly timed observations and may include only a subset of active sensors.
  • RAINDROP maps each irregular time series sample to a fixed-length representation suitable for downstream classification.
  • It constructs a separate directed, weighted sensor dependency graph for every sample, with edge weights learned from observational time series.
  • When one sensor is observed, message passing uses learned inter-sensor relationships to generate observation embeddings for neighboring sensors without direct measurements.
  • Temporal attention aggregates arbitrarily many observation embeddings into fixed-length sensor embeddings while emphasizing more informative observations.
  • RAINDROP updates graph edge weights using aggregated inter-sensor attention across timestamps and regularizes similar samples toward similar dependency graphs.

4 EXPERIMENTS

RAINDROP is evaluated against established baselines on irregularly sampled healthcare and activity datasets across standard classification and missing-sensor settings. It achieves the strongest reported performance, with larger gains as sensor observations become more incomplete.

  • Experimental setup: RAINDROP is compared with five state-of-the-art baselines on two healthcare datasets and one activity-recognition dataset.The baselines include Transformer, Trans-mean, GRU-D, SeFT, and mTAND.
  • Setting 1: Classic time series classification: RAINDROP obtains the best performance across all three benchmark datasets in classic time-series classification.For binary classification, it exceeds the strongest baselines by 5.3% in AUROC and 4.8% in AUPRC on average; for PAM 8-way classification, gains are 5.7% in accuracy and 5.5% in F1 score.
  • Setting 2: Leave-fixed-sensors-out: RAINDROP outperforms baselines by up to 24.9% in accuracy, 50.3% in precision, 29.3% in recall, and 42.8% in F1 score when fixed sensor sets are left out.The performance improvements increase with the amount of missing data.
  • Setting 3: Leave-random-sensors-out: RAINDROP achieves better performance than baselines in 16 out of 20 random-sensor-missing settings on PAM.Trans-mean and GRU-D are the strongest competitors in this setting.
  • Ablation study: Ablation results show that all examined model components are necessary, while regularization Lr contributes positively to performance.The study evaluates inter-sensor dependencies, temporal attention, and sensor-level concatenation.
  • Visualizing sensor dependency graphs: Visualized dependency graphs display distinguishable patterns between negative and positive samples, indicating label-specific extracted relationships.The analysis uses P19 under Setting 1.

5 CONCLUSION

RAINDROP learns a distinct sensor dependency graph for each sample to capture time-varying sensor relationships. This graph structure supports irregular observations, non-uniform intervals, and sensors with different numbers of recorded observations.

  • 5 CONCLUSION: RAINDROP learns a distinct sensor dependency graph for every sample, capturing time-varying dependencies between sensors.The authors frame message passing as a way to leverage relational information in multivariate time series.
  • 5 CONCLUSION: Graph structure enables RAINDROP to handle misaligned observations, non-uniform time intervals, and sensors with varying numbers of recorded observations.

REPRODUCIBILITY STATEMENT

The work supports reproducibility by releasing code, raw-data links, processed datasets, and detailed training information.

  • REPRODUCIBILITY STATEMENT: The authors provide publicly accessible code and data, including raw sources and ready-to-run processed datasets.Training details cover preprocessing, data splits, hyperparameters, and sensor selection.

ETHICS STATEMENT

The paper notes that RAINDROP should be used cautiously because data-driven biomedical predictions may be biased. The datasets are publicly available and anonymized, with PhysioNet privacy guidelines followed for P12 and P19.

  • ETHICS STATEMENT: RAINDROP may produce biased predictions, including biases arising from demographic attributes correlated with protected or regulated attributes.The caution is stated especially for healthcare applications.
  • ETHICS STATEMENT: All datasets are public and anonymized, and the experiments using P12 and P19 followed PhysioNet privacy policies and guidelines.

A.1 ENCODING TIMESTAMPS

RAINDROP encodes each continuous timestamp with trigonometric functions to produce a time representation, rather than encoding discrete observation positions.

  • Each timestamp t is passed to trigonometric functions with frequency 10,000 to generate a time representation p_t.The representation has expected dimension ξ.
  • The model uses ξ = 16 for time representations in all experimental settings and for all models.
  • RAINDROP encodes continuous timestamps rather than discrete integers representing observation order.

A.2 ADDITIONAL INFORMATION ON THE CALCULATION OF TEMPORAL ATTENTION WEIGHT

RAINDROP converts self-attention relationships among observations from each sensor into a temporal attention vector that weights observations when forming the sensor embedding.

  • RAINDROP generates a temporal attention weight vector β_i,v for each sensor instead of a standard self-attention matrix.The vector is sufficient for aggregating observation embeddings into one sensor embedding through a weighted sum.
  • Each self-attention matrix row represents one observation’s dependencies on all observations from the same sensor.
  • A learnable weight vector s aggregates each row’s cross-time correlations into a scalar temporal importance weight.The resulting scalars are concatenated into the temporal attention vector.
  • Each temporal importance weight β_i,v represents the corresponding observation’s importance to the complete sensor embedding.

A.3 ADDITIONAL INFORMATION ON SAMPLE EMBEDDING

RAINDROP forms each sample embedding by concatenating all sensor embeddings, while offering dimensionality-reduction and alternative readout options for settings with many sensors.

  • Concatenating all sensor embeddings produces the sample embedding but can create long vectors when many sensors are present.
  • A neural layer can reduce the sample-embedding dimension after concatenation, while averaging can replace concatenation for very large sensor sets.
  • Concatenation outperforms averaging, improving AUROC by 0.6% in P19, Setting 1.

A.4 ADDITIONAL INFORMATION ON SAMPLE SIMILARITIES

The study examines sample similarities and evaluates RAINDROP across standard, challenging, and group-wise settings. Results connect sample-specific dependency graphs with strong performance and interpretable inter-sensor structure.

  • RAINDROP assumes samples share common characteristics rather than forming distinct latent groups with different within-group similarities.
  • The experiments benchmark irregular time-series classification in a standard setup and additional settings informed by selected data attributes.
  • RAINDROP achieves the best results across four P19 cross-group scenarios, including 4.8% AUROC and 13.1% AUPRC absolute improvements over the second-best model.
  • Sample-specific dependency graphs support transfer across groups because they learn inter-sensor dependencies from each test sample’s observations.
  • Removing inter-sensor dependencies reduces performance substantially, leaving RAINDROP on par with other baselines.
  • Excluding attention weights decreases accuracy by 3.9%, while excluding dependency-graph edge weights decreases accuracy by 7.1%.
Loading 2110.05357v2…