# Integrative Factor Regression and Its Inference for Multimodal Data Analysis

arXiv: https://arxiv.org/abs/1911.04056 · HTML: https://mlsanity.com/paper/1911.04056/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2019.

## Built on by (most cited first, 11 of 11)

- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)
- [Are Latent Factor Regression and Sparse Regression Adequate?](https://mlsanity.com/paper/2203.01219/) (2022)
- [Bayesian Joint Additive Factor Models for Multiview Learning](https://mlsanity.com/paper/2406.00778/) (2024)
- [Orthogonalized Kernel Debiased Machine Learning for Multimodal Data Analysis](https://mlsanity.com/paper/2103.07088/) (2021)
- [FragmGAN: Generative Adversarial Nets for Fragmentary Data Imputation and Prediction](https://mlsanity.com/paper/2203.04692/) (2022)
- [Bayesian Simultaneous Factorization and Prediction Using Multi-Omic Data](https://mlsanity.com/paper/2211.16403/) (2022)
- [Latent Multimodal Functional Graphical Model Estimation](https://mlsanity.com/paper/2210.17237/) (2022)
- [Multi-task Learning for Heterogeneous Multi-source Block-Wise Missing Data](https://mlsanity.com/paper/2505.24413/) (2025)
- [Coupled Support Tensor Machine Classification for Multimodal Neuroimaging Data](https://mlsanity.com/paper/2201.07683/) (2022)
- [Adaptive Multi-task Learning for Multi-sector Portfolio Optimization](https://mlsanity.com/paper/2507.16433/) (2025)
- [PEARL: Performance-Enhanced Aggregated Representation Learning](https://mlsanity.com/paper/2509.24312/) (2025)

## Abstract (arXiv)

Multimodal data, where different types of data are collected from the same subjects, are fast emerging in a large variety of scientific applications. Factor analysis is commonly used in integrative analysis of multimodal data, and is particularly useful to overcome the curse of high dimensionality and high correlations. However, there is little work on statistical inference for factor analysis based supervised modeling of multimodal data. In this article, we consider an integrative linear regression model that is built upon the latent factors extracted from multimodal data. We address three important questions: how to infer the significance of one data modality given the other modalities in the model; how to infer the significance of a combination of variables from one modality or across different modalities; and how to quantify the contribution, measured by the goodness-of-fit, of one data modality given the others. When answering each question, we explicitly characterize both the benefit and the extra cost of factor analysis. Those questions, to our knowledge, have not yet been addressed despite wide use of factor analysis in integrative multimodal analysis, and our proposal bridges an important gap. We study the empirical performance of our methods through simulations, and further illustrate with a multimodal neuroimaging analysis.