Flexible latent variable models on graphs: Laplace approximated inference for multiview network data
Abstract
We propose a novel and flexible nonlinear approach for dimensionality reduction of large-scale multiview network data and derive its theory. The (linear) predictor incorporates observed covariates (edge-specific, layer-specific, and global) and Gaussian latent factors. Inference is conducted via the graph Laplace approximated maximum likelihood estimator. Letting K denote the number of network layers and nV the number of nodes, we derive asymptotic theory under two regimes: (i) K → ∞ with fixed nV, and (ii) double asymptotics K, nV → ∞, establishing consistency and asymptotic normality for local and global parameters, with distinct convergence rates. In an application to the gravity model for commodity trades, we use a zero-adjusted Gamma distribution with latent factors and observable covariates (e.g.\ distance, tariffs, common language) to capture excess zeros, skewness, and unobserved heterogeneity. Synthetic and real-data exercises show that our approach outperforms the routinely applied Poisson pseudo-maximum likelihood estimator with fixed effects. We complement our theoretical and empirical contributions with open-source R/C++ routines and a novel strategy for starting values selection.
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BibTeX
@misc{es2026flexible,
title = {{Flexible latent variable models on graphs: Laplace approximated inference for multiview network data}},
author = {Anna van Es and Eva Cantoni and Davide La Vecchia},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26495},
eprint = {2609.26495},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26495},
}
RIS
TY - UNPB
TI - Flexible latent variable models on graphs: Laplace approximated inference for multiview network data
AU - Anna van Es
AU - Eva Cantoni
AU - Davide La Vecchia
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26495
UR - https://arxiv.org/abs/2609.26495
AB - We propose a novel and flexible nonlinear approach for dimensionality reduction of large-scale multiview network data and derive its theory. The (linear) predictor incorporates observed covariates (edge-specific, layer-specific, and global) and Gaussian latent factors. Inference is conducted via the graph Laplace approximated maximum likelihood estimator. Letting K denote the number of network layers and n_V the number of nodes, we derive asymptotic theory under two regimes: (i) K → ∞ with fixed n_V, and (ii) double asymptotics K, n_V → ∞, establishing consistency and asymptotic normality for local and global parameters, with distinct convergence rates. In an application to the gravity model for commodity trades, we use a zero-adjusted Gamma distribution with latent factors and observable covariates (e.g.\ distance, tariffs, common language) to capture excess zeros, skewness, and unobserved heterogeneity. Synthetic and real-data exercises show that our approach outperforms the routinely applied Poisson pseudo-maximum likelihood estimator with fixed effects. We complement our theoretical and empirical contributions with open-source R/C++ routines and a novel strategy for starting values selection.
ER -