High-Dimensional Undirected Graphical Models for Arbitrary Mixed Data

• URL: http://arxiv.org/abs/2211.11700v2
• Date: Wed, 14 Feb 2024 15:03:18 GMT
• Title: High-Dimensional Undirected Graphical Models for Arbitrary Mixed Data
• Authors: Konstantin G\"obler and Anne Miloschewski and Mathias Drton and Sach Mukherjee
• Abstract summary: In many applications data span variables of different types, whose principled joint analysis is nontrivial. Recent advances have shown how the binary-continuous case can be tackled, but the general mixed variable type regime remains challenging. We propose flexible and scalable methodology for data with variables of entirely general mixed type.
• Score: 2.2871867623460207
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graphical models are an important tool in exploring relationships between variables in complex, multivariate data. Methods for learning such graphical models are well developed in the case where all variables are either continuous or discrete, including in high-dimensions. However, in many applications data span variables of different types (e.g. continuous, count, binary, ordinal, etc.), whose principled joint analysis is nontrivial. Latent Gaussian copula models, in which all variables are modeled as transformations of underlying jointly Gaussian variables, represent a useful approach. Recent advances have shown how the binary-continuous case can be tackled, but the general mixed variable type regime remains challenging. In this work, we make the simple yet useful observation that classical ideas concerning polychoric and polyserial correlations can be leveraged in a latent Gaussian copula framework. Building on this observation we propose flexible and scalable methodology for data with variables of entirely general mixed type. We study the key properties of the approaches theoretically and empirically, via extensive simulations as well an illustrative application to data from the UK Biobank concerning COVID-19 risk factors.

Related papers

• Learning Divergence Fields for Shift-Robust Graph Representations [73.11818515795761]
  In this work, we propose a geometric diffusion model with learnable divergence fields for the challenging problem with interdependent data. We derive a new learning objective through causal inference, which can guide the model to learn generalizable patterns of interdependence that are insensitive across domains.
  arXiv  Detail & Related papers  (2024-06-07T14:29:21Z)
• Shape Arithmetic Expressions: Advancing Scientific Discovery Beyond Closed-Form Equations [56.78271181959529]
  Generalized Additive Models (GAMs) can capture non-linear relationships between variables and targets, but they cannot capture intricate feature interactions. We propose Shape Expressions Arithmetic ( SHAREs) that fuses GAM's flexible shape functions with the complex feature interactions found in mathematical expressions. We also design a set of rules for constructing SHAREs that guarantee transparency of the found expressions beyond the standard constraints.
  arXiv  Detail & Related papers  (2024-04-15T13:44:01Z)
• Conformal inference for regression on Riemannian Manifolds [49.7719149179179]
  We investigate prediction sets for regression scenarios when the response variable, denoted by $Y$, resides in a manifold, and the covariable, denoted by X, lies in Euclidean space. We prove the almost sure convergence of the empirical version of these regions on the manifold to their population counterparts.
  arXiv  Detail & Related papers  (2023-10-12T10:56:25Z)
• A Graphical Model for Fusing Diverse Microbiome Data [2.385985842958366]
  We introduce a flexible multinomial-Gaussian generative model for jointly modeling such count data. We present a computationally scalable variational Expectation-Maximization (EM) algorithm for inferring the latent variables and the parameters of the model.
  arXiv  Detail & Related papers  (2022-08-21T17:54:39Z)
• On the Strong Correlation Between Model Invariance and Generalization [54.812786542023325]
  Generalization captures a model's ability to classify unseen data. Invariance measures consistency of model predictions on transformations of the data. From a dataset-centric view, we find a certain model's accuracy and invariance linearly correlated on different test sets.
  arXiv  Detail & Related papers  (2022-07-14T17:08:25Z)
• Inference of Multiscale Gaussian Graphical Model [0.0]
  We propose a new method allowing to simultaneously infer a hierarchical clustering structure and the graphs describing the structure of independence at each level of the hierarchy. Results on real and synthetic data are presented.
  arXiv  Detail & Related papers  (2022-02-11T17:11:20Z)
• Linear Discriminant Analysis with High-dimensional Mixed Variables [10.774094462083843]
  This paper develops a novel approach for classifying high-dimensional observations with mixed variables. We overcome the challenge of having to split data into exponentially many cells. Results on the estimation accuracy and the misclassification rates are established.
  arXiv  Detail & Related papers  (2021-12-14T03:57:56Z)
• Multimodal Data Fusion in High-Dimensional Heterogeneous Datasets via Generative Models [16.436293069942312]
  We are interested in learning probabilistic generative models from high-dimensional heterogeneous data in an unsupervised fashion. We propose a general framework that combines disparate data types through the exponential family of distributions. The proposed algorithm is presented in detail for the commonly encountered heterogeneous datasets with real-valued (Gaussian) and categorical (multinomial) features.
  arXiv  Detail & Related papers  (2021-08-27T18:10:31Z)
• Generalized Matrix Factorization: efficient algorithms for fitting generalized linear latent variable models to large data arrays [62.997667081978825]
  Generalized Linear Latent Variable models (GLLVMs) generalize such factor models to non-Gaussian responses. Current algorithms for estimating model parameters in GLLVMs require intensive computation and do not scale to large datasets. We propose a new approach for fitting GLLVMs to high-dimensional datasets, based on approximating the model using penalized quasi-likelihood.
  arXiv  Detail & Related papers  (2020-10-06T04:28:19Z)
• Bayesian Sparse Factor Analysis with Kernelized Observations [67.60224656603823]
  Multi-view problems can be faced with latent variable models. High-dimensionality and non-linear issues are traditionally handled by kernel methods. We propose merging both approaches into single model.
  arXiv  Detail & Related papers  (2020-06-01T14:25:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.