[Paper Review] Simultaneous Missing Value Imputation and Structure Learning with Groups

Pablo Morales-Álvarez, Wenbo Gong+6 more|arXiv (Cornell University)|Oct 15, 2021

Advanced Graph Neural Networks8 citations

TL;DR

This paper proposes VISL, a deep generative model that simultaneously performs missing value imputation and group-wise structure learning in partially observed data using variational inference and a graph neural network (GNN)-based decoder. It models group-level relationships through a structured latent space and achieves state-of-the-art performance on both imputation and structure learning tasks across synthetic, semi-synthetic, and real-world education datasets.

ABSTRACT

Learning structures between groups of variables from data with missing values is an important task in the real world, yet difficult to solve. One typical scenario is discovering the structure among topics in the education domain to identify learning pathways. Here, the observations are student performances for questions under each topic which contain missing values. However, most existing methods focus on learning structures between a few individual variables from the complete data. In this work, we propose VISL, a novel scalable structure learning approach that can simultaneously infer structures between groups of variables under missing data and perform missing value imputations with deep learning. Particularly, we propose a generative model with a structured latent space and a graph neural network-based architecture, scaling to a large number of variables. Empirically, we conduct extensive experiments on synthetic, semi-synthetic, and real-world education data sets. We show improved performances on both imputation and structure learning accuracy compared to popular and recent approaches.

Motivation & Objective

• To address the challenge of learning structural relationships between groups of variables in data with missing values, particularly in real-world applications like education.
• To develop a scalable method that jointly performs missing value imputation and group-level structure learning without requiring complete data.
• To model complex dependencies between variable groups using a structured latent space and a GNN-based decoder.
• To evaluate the method on real-world education data, where student responses to questions (grouped by topic) are sparse and incomplete.
• To demonstrate improved performance over existing methods in both imputation accuracy and structure learning fidelity.

Proposed method

• VISL employs a variational autoencoder framework with a global latent variable representing the structure (adjacency matrix) and local latent variables for each group of variables.
• It uses a GNN-based decoder to model interactions between group-level latent representations, where the GNN's message-passing mechanism depends on the inferred structure.
• The model leverages variational inference to jointly optimize the posterior over the structure and latent variables, enabling end-to-end training under missing data.
• A structured latent space is introduced, where each group is embedded in a shared subspace, and inter-group relationships are regulated by the GNN architecture.
• The method naturally handles missing data by modeling observed values as conditionals on latent variables and the global structure, avoiding explicit imputation steps.
• The framework is scalable to large numbers of variables and groups, making it suitable for high-dimensional real-world data such as educational assessment data.

Experimental results

Research questions

• RQ1 Can a deep generative model jointly perform missing value imputation and group-wise structure learning in high-dimensional, partially observed data?
• RQ2 How does the integration of a GNN-based decoder with a structured latent space improve structure learning and imputation accuracy compared to existing methods?
• RQ3 To what extent does VISL outperform state-of-the-art baselines in both imputation and structure learning tasks on real-world education data?
• RQ4 How robust is VISL to varying levels of missingness and group size heterogeneity in synthetic and semi-synthetic datasets?
• RQ5 Can the learned structures from VISL be interpreted meaningfully by domain experts in the education domain?

Key findings

• VISL achieved the highest F1-score of 0.615 ± 0.074 in causal structure learning on the Eedi education dataset, significantly outperforming all baselines including MMHC (0.471 ± 0.061) and DAG-GNN (0.257 ± 0.066).
• In structure learning, VISL achieved a precision of 0.588 ± 0.042 and recall of 0.698 ± 0.052, demonstrating strong balance between precision and recall on the real-world education data.
• On the extended synthetic experiment, VISL achieved an F1-score of 0.635 ± 0.049 for adjacency prediction, outperforming all baselines, including the strong MMHC baseline.
• VISL showed superior imputation performance on real-world education data, with high accuracy in predicting un-answered student responses to questions across topics.
• Domain experts validated the learned topic relationships, confirming that VISL discovered meaningful and interpretable learning pathways, such as foundational topics preceding advanced ones.
• The model demonstrated scalability and robustness across varying group sizes and missingness levels, with consistent performance gains in both structure learning and imputation tasks.