# Simultaneous Missing Value Imputation and Structure Learning with Groups

arXiv: https://arxiv.org/abs/2110.08223 · HTML: https://mlsanity.com/paper/2110.08223/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 75 references that are in the map.
- First posted on arXiv 15 Oct 2021.

## Builds on (most cited first, 30 of 31)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [SLAPS: Self-Supervision Improves Structure Learning for Graph Neural Networks](https://mlsanity.com/paper/2102.05034/) (2021)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [Implicit Graph Neural Networks](https://mlsanity.com/paper/2009.06211/) (2020)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [EDDI: Efficient Dynamic Discovery of High-Value Information with Partial VAE](https://mlsanity.com/paper/1809.11142/) (2018)
- [Variational Autoencoder with Arbitrary Conditioning](https://mlsanity.com/paper/1806.02382/) (2018)
- [Causal Discovery in the Presence of Missing Data](https://mlsanity.com/paper/1807.04010/) (2018)
- [Unsuitability of NOTEARS for Causal Graph Discovery](https://mlsanity.com/paper/2104.05441/) (2021)
- [Knowledge Tracing Machines: Factorization Machines for Knowledge Tracing](https://mlsanity.com/paper/1811.03388/) (2018)
- [CASTLE: Regularization via Auxiliary Causal Graph Discovery](https://mlsanity.com/paper/2009.13180/) (2020)
- [Towards Scalable Bayesian Learning of Causal DAGs](https://mlsanity.com/paper/2010.00684/) (2020)
- [Neuropathic Pain Diagnosis Simulator for Causal Discovery Algorithm Evaluation](https://mlsanity.com/paper/1906.01732/) (2019)
- [Concave Penalized Estimation of Sparse Gaussian Bayesian Networks](https://mlsanity.com/paper/1401.0852/) (2014)
- [Fast Causal Inference with Non-Random Missingness by Test-Wise Deletion](https://mlsanity.com/paper/1705.09031/) (2017)
- [Results and Insights from Diagnostic Questions: The NeurIPS 2020 Education Challenge](https://mlsanity.com/paper/2104.04034/) (2021)
- [Zero Shot Learning for Code Education: Rubric Sampling with Deep Learning Inference](https://mlsanity.com/paper/1809.01357/) (2018)
- [Penalized Estimation of Directed Acyclic Graphs From Discrete Data](https://mlsanity.com/paper/1403.2310/) (2014)
- [Time-varying Learning and Content Analytics via Sparse Factor Analysis](https://mlsanity.com/paper/1312.5734/) (2013)
- [Conditional Inference in Pre-trained Variational Autoencoders via Cross-coding](https://mlsanity.com/paper/1805.07785/) (2018)

## Built on by (most cited first, 16 of 16)

- [CUTS+: High-dimensional Causal Discovery from Irregular Time-series](https://mlsanity.com/paper/2305.05890/) (2023)
- [CUTS: Neural Causal Discovery from Irregular Time-Series Data](https://mlsanity.com/paper/2302.07458/) (2023)
- [Transformed Distribution Matching for Missing Value Imputation](https://mlsanity.com/paper/2302.10363/) (2023)
- [Causal Deep Learning](https://mlsanity.com/paper/2303.02186/) (2023)
- [Causal Reasoning in the Presence of Latent Confounders via Neural ADMG Learning](https://mlsanity.com/paper/2303.12703/) (2023)
- [RedCore: Relative Advantage Aware Cross-modal Representation Learning for Missing Modalities with Imbalanced Missing Rates](https://mlsanity.com/paper/2312.10386/) (2023)
- [Causality for Tabular Data Synthesis: A High-Order Structure Causal Benchmark Framework](https://mlsanity.com/paper/2406.08311/) (2024)
- [Predictive Coding beyond Correlations](https://mlsanity.com/paper/2306.15479/) (2023)
- [Optimal Transport for Structure Learning Under Missing Data](https://mlsanity.com/paper/2402.15255/) (2024)
- [A Context-Aware Approach for Enhancing Data Imputation with Pre-trained Language Models](https://mlsanity.com/paper/2405.17712/) (2024)
- [Knowledge Guided Representation Learning and Causal Structure Learning in Soil Science](https://mlsanity.com/paper/2306.09302/) (2023)
- [Data Augmentation for Sparse Multidimensional Learning Performance Data Using Generative AI](https://mlsanity.com/paper/2409.15631/) (2024)
- [Incomplete Graph Learning: A Comprehensive Survey](https://mlsanity.com/paper/2502.12412/) (2025)
- [Generative Adversarial Networks for Imputing Sparse Learning Performance](https://mlsanity.com/paper/2407.18875/) (2024)
- [GLACIAL: Granger and Learning-based Causality Analysis for Longitudinal Imaging Studies](https://mlsanity.com/paper/2210.07416/) (2022)
- [Generative Data Imputation for Sparse Learner Performance Data Using Generative Adversarial Imputation Networks](https://mlsanity.com/paper/2503.18982/) (2025)

## Abstract (arXiv)

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.