# High Dimensional Semiparametric Latent Graphical Model for Mixed Data

arXiv: https://arxiv.org/abs/1404.7236 · HTML: https://mlsanity.com/paper/1404.7236/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Apr 2014.

## Built on by (most cited first, 10 of 10)

- [Gene Regulatory Network Inference in the Presence of Dropouts: a Causal View](https://mlsanity.com/paper/2403.15500/) (2024)
- [Permutation-Based Rank Test in the Presence of Discretization and Application in Causal Discovery with Mixed Data](https://mlsanity.com/paper/2501.18990/) (2025)
- [A Conditional Independence Test in the Presence of Discretization](https://mlsanity.com/paper/2404.17644/) (2024)
- [Asymptotically Exact and Fast Gaussian Copula Models for Imputation of Mixed Data Types](https://mlsanity.com/paper/2102.02642/) (2021)
- [Scalable Regularised Joint Mixture Models](https://mlsanity.com/paper/2205.01486/) (2022)
- [Structure Learning in Graphical Models from Indirect Observations](https://mlsanity.com/paper/2205.03454/) (2022)
- [High-Dimensional Undirected Graphical Models for Arbitrary Mixed Data](https://mlsanity.com/paper/2211.11700/) (2022)
- [Causal Discovery on Dependent Binary Data](https://mlsanity.com/paper/2412.20289/) (2024)
- [An Integrated Deep Learning and Statistical Framework for Whole-Network Gene--Environment Association with Leaf Vascular Architecture](https://mlsanity.com/paper/2607.22763/) (2026)
- [MIND: Marginal-Invariant Neural Dependency Diffusion for Mixed-Type Tabular Generation](https://mlsanity.com/paper/2609.39628/) (2026)

## Abstract (arXiv)

Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete variables or a combination of both continuous and discrete variables poses new challenges in statistical modeling. In this paper, we propose a semiparametric model named latent Gaussian copula model for binary and mixed data. The observed binary data are assumed to be obtained by dichotomizing a latent variable satisfying the Gaussian copula distribution or the nonparanormal distribution. The latent Gaussian model with the assumption that the latent variables are multivariate Gaussian is a special case of the proposed model. A novel rank-based approach is proposed for both latent graph estimation and latent principal component analysis. Theoretically, the proposed methods achieve the same rates of convergence for both precision matrix estimation and eigenvector estimation, as if the latent variables were observed. Under similar conditions, the consistency of graph structure recovery and feature selection for leading eigenvectors is established. The performance of the proposed methods is numerically assessed through simulation studies, and the usage of our methods is illustrated by a genetic dataset.