# Bayesian Graphical Models for Multivariate Functional Data

arXiv: https://arxiv.org/abs/1411.4158 · HTML: https://mlsanity.com/paper/1411.4158/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2014.

## Built on by (most cited first, 8 of 8)

- [High-dimensional Functional Graphical Model Structure Learning via Neighborhood Selection Approach](https://mlsanity.com/paper/2105.02487/) (2021)
- [Directed Cyclic Graph for Causal Discovery from Multivariate Functional Data](https://mlsanity.com/paper/2310.20537/) (2023)
- [On Sufficient Graphical Models](https://mlsanity.com/paper/2307.04353/) (2023)
- [Interpretable and Scalable Graphical Models for Complex Spatio-temporal Processes](https://mlsanity.com/paper/2301.06021/) (2023)
- [Bayesian Regularization for Functional Graphical Models with Applications to Neuroimaging](https://mlsanity.com/paper/2110.05575/) (2021)
- [Functional-Edged Network Modeling](https://mlsanity.com/paper/2404.00218/) (2024)
- [Learning Functional Graphs with Nonlinear Sufficient Dimension Reduction](https://mlsanity.com/paper/2601.15696/) (2026)
- [Functional Causal Discovery via Conditional Covariance Ordering](https://mlsanity.com/paper/2609.27256/) (2026)

## Abstract (arXiv)

Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional independence between random functions, and construct a framework for Bayesian inference of undirected, decomposable graphs in the multivariate functional data context. This framework is based on extending Markov distributions and hyper Markov laws from random variables to random processes, providing a principled alternative to naive application of multivariate methods to discretized functional data. Markov properties facilitate the composition of likelihoods and priors according to the decomposition of a graph. Our focus is on Gaussian process graphical models using orthogonal basis expansions. We propose a hyper-inverse-Wishart-process prior for the covariance kernels of the infinite coefficient sequences of the basis expansion, establish existence, uniqueness, strong hyper Markov property, and conjugacy. Stochastic search Markov chain Monte Carlo algorithms are developed for posterior inference, assessed through simulations, and applied to a study of brain activity and alcoholism.