[Paper Review] Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks

Andrea Cini, Ivan Marisca+1 more|arXiv (Cornell University)|Jul 31, 2021

Functional Brain Connectivity Studies40 citations

TL;DR

GRIN is a graph neural network based bidirectional recurrent architecture for multivariate time series imputation that leverages relational information among channels to reconstruct missing values, achieving state-of-the-art results on multiple benchmarks.

ABSTRACT

Dealing with missing values and incomplete time series is a labor-intensive, tedious, inevitable task when handling data coming from real-world applications. Effective spatio-temporal representations would allow imputation methods to reconstruct missing temporal data by exploiting information coming from sensors at different locations. However, standard methods fall short in capturing the nonlinear time and space dependencies existing within networks of interconnected sensors and do not take full advantage of the available - and often strong - relational information. Notably, most state-of-the-art imputation methods based on deep learning do not explicitly model relational aspects and, in any case, do not exploit processing frameworks able to adequately represent structured spatio-temporal data. Conversely, graph neural networks have recently surged in popularity as both expressive and scalable tools for processing sequential data with relational inductive biases. In this work, we present the first assessment of graph neural networks in the context of multivariate time series imputation. In particular, we introduce a novel graph neural network architecture, named GRIN, which aims at reconstructing missing data in the different channels of a multivariate time series by learning spatio-temporal representations through message passing. Empirical results show that our model outperforms state-of-the-art methods in the imputation task on relevant real-world benchmarks with mean absolute error improvements often higher than 20%.

Motivation & Objective

• Motivate imputation of missing values in interconnected sensor networks by exploiting relational information.
• Introduce a graph-based recurrent architecture (GRIN) for MTSI that uses message passing to model spatio-temporal dependencies.
• Demonstrate state-of-the-art imputation performance on diverse real-world benchmarks.
• Show that GRIN handles variable input dimensionality and disconnected nodes.
• Provide ablation studies to highlight the importance of spatial decoding and bidirectionality.

Proposed method

• Model input multivariate time series as sequences of graphs with fixed topology.
• Develop a bidirectional GRIN with two stages: spatio-temporal encoder and spatial decoder per direction.
• Use MPNNs to implement GRU gates within the spatio-temporal encoder.
• Apply a filler operator to merge one-step-ahead predictions with observed values for imputations.
• Incorporate a second imputation stage using imputation representations aggregated via neighbor messages.
• Combine forward and backward representations through an MLP to produce final imputations.

Experimental results

Research questions

• RQ1 Can graph neural networks effectively capture nonlinear spatio-temporal dependencies for MTSI?
• RQ2 Does a bidirectional GRIN improve imputation by leveraging both past and future context?
• RQ3 How does GRIN compare to state-of-the-art baselines across diverse real-world datasets with varying relational structures?

Key findings

• GRIN achieves state-of-the-art imputation performance on multiple benchmarks, with mean absolute error improvements often higher than 20%.
• In traffic and smart-grid datasets, GRIN substantially outperforms BRITS and other baselines, reducing MAE by approximately 29% on average in traffic datasets.
• GRIN remains effective even for isolated nodes and when relational information is less explicit.
• Ablation studies show that removing the spatial decoder or bidirectionality degrades performance, highlighting the importance of spatial and bidirectional components.