Gaussian Graphical Learning via PSD Constraint for Blockwise Missing Multimodal Data

Joseph L. Graves, Yufeng Liu, Elio Zhang, Seong-Tae Kim,  for the Alzheimer’s Disease Neuroimaging Initiative
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:1748-1768, 2026.

Abstract

{Gaussian} graphical models, estimated via precision matrices, are popular for uncovering underlying conditional dependencies among variables, yet the case of multimodal data with blockwise missing remains unaddressed. We propose a novel method, Direct Sparse Graphical Learning for Multimodal Data ({DSGL}), to handle this issue using only observed data. The {DSGL} consists of two stages: constructing a pilot estimator for the covariance matrix without imputation as an admissible input for {GLASSO}; and estimating the {DSGL} precision matrix via {GLASSO} with repeated cross-validation tuning. We further propose a thresholded variant to address false-positive edges, a common issue in high-dimensional data. We establish theoretical properties for {DSGL} with respect to element-wise deviation and its ability to recover the true graphical structure. In simulations and an Alzheimer’s Disease Neuroimaging Initiative ({ADNI}) application, {DSGL} outperforms imputation-based and other competing approaches, yielding more accurate graph estimation and lower Frobenius-norm error.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-graves26a, title = {{Gaussian} Graphical Learning via {PSD} Constraint for Blockwise Missing Multimodal Data}, author = {Graves, Joseph L. and Liu, Yufeng and Zhang, Elio and Kim, Seong-Tae and {for the Alzheimer's Disease Neuroimaging Initiative}}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {1748--1768}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/graves26a/graves26a.pdf}, url = {https://proceedings.mlr.press/v337/graves26a.html}, abstract = {{Gaussian} graphical models, estimated via precision matrices, are popular for uncovering underlying conditional dependencies among variables, yet the case of multimodal data with blockwise missing remains unaddressed. We propose a novel method, Direct Sparse Graphical Learning for Multimodal Data ({DSGL}), to handle this issue using only observed data. The {DSGL} consists of two stages: constructing a pilot estimator for the covariance matrix without imputation as an admissible input for {GLASSO}; and estimating the {DSGL} precision matrix via {GLASSO} with repeated cross-validation tuning. We further propose a thresholded variant to address false-positive edges, a common issue in high-dimensional data. We establish theoretical properties for {DSGL} with respect to element-wise deviation and its ability to recover the true graphical structure. In simulations and an Alzheimer’s Disease Neuroimaging Initiative ({ADNI}) application, {DSGL} outperforms imputation-based and other competing approaches, yielding more accurate graph estimation and lower Frobenius-norm error.} }
Endnote
%0 Conference Paper %T Gaussian Graphical Learning via PSD Constraint for Blockwise Missing Multimodal Data %A Joseph L. Graves %A Yufeng Liu %A Elio Zhang %A Seong-Tae Kim %A for the Alzheimer’s Disease Neuroimaging Initiative %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-graves26a %I PMLR %P 1748--1768 %U https://proceedings.mlr.press/v337/graves26a.html %V 337 %X {Gaussian} graphical models, estimated via precision matrices, are popular for uncovering underlying conditional dependencies among variables, yet the case of multimodal data with blockwise missing remains unaddressed. We propose a novel method, Direct Sparse Graphical Learning for Multimodal Data ({DSGL}), to handle this issue using only observed data. The {DSGL} consists of two stages: constructing a pilot estimator for the covariance matrix without imputation as an admissible input for {GLASSO}; and estimating the {DSGL} precision matrix via {GLASSO} with repeated cross-validation tuning. We further propose a thresholded variant to address false-positive edges, a common issue in high-dimensional data. We establish theoretical properties for {DSGL} with respect to element-wise deviation and its ability to recover the true graphical structure. In simulations and an Alzheimer’s Disease Neuroimaging Initiative ({ADNI}) application, {DSGL} outperforms imputation-based and other competing approaches, yielding more accurate graph estimation and lower Frobenius-norm error.
APA
Graves, J.L., Liu, Y., Zhang, E., Kim, S. & for the Alzheimer’s Disease Neuroimaging Initiative, . (2026). Gaussian Graphical Learning via PSD Constraint for Blockwise Missing Multimodal Data. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:1748-1768 Available from https://proceedings.mlr.press/v337/graves26a.html.

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