# Joint and Individual Component Regression

arXiv: https://arxiv.org/abs/2209.12388 · HTML: https://mlsanity.com/paper/2209.12388/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2022.

## Built on by (most cited first, 5 of 5)

- [Representation Retrieval Learning for Heterogeneous Data Integration](https://mlsanity.com/paper/2503.09494/) (2025)
- [Multi-task Learning for Heterogeneous Multi-source Block-Wise Missing Data](https://mlsanity.com/paper/2505.24413/) (2025)
- [A Machine Learning-Based Study on the Synergistic Optimization of Supply Chain Management and Financial Supply Chains from an Economic Perspective](https://mlsanity.com/paper/2509.03673/) (2025)
- [Study on Supply Chain Finance Decision-Making Model and Enterprise Economic Performance Prediction Based on Deep Reinforcement Learning](https://mlsanity.com/paper/2511.00166/) (2025)
- [Unveiling Invariant and Transferable Latent Factors Across Heterogeneous Environments via ATLAS](https://mlsanity.com/paper/2607.18209/) (2026)

## Abstract (arXiv)

Multi-group data are commonly seen in practice. Such data structure consists of data from multiple groups and can be challenging to analyze due to data heterogeneity. We propose a novel Joint and Individual Component Regression (JICO) model to analyze multi-group data. In particular, our proposed model decomposes the response into shared and group-specific components, which are driven by low-rank approximations of joint and individual structures from the predictors respectively. The joint structure has the same regression coefficients across multiple groups, whereas individual structures have group-specific regression coefficients. Moreover, the choice of global and individual ranks allows our model to cover global and group-specific models as special cases. For model estimation, we formulate this framework under the representation of latent components and propose an iterative algorithm to solve for the joint and individual scores under the new representation. To construct the latent scores, we utilize the Continuum Regression (CR), which provides a unified framework that covers the Ordinary Least Squares (OLS), the Partial Least Squares (PLS), and the Principal Component Regression (PCR) as its special cases. We show that JICO attains a good balance between global and group-specific models and remains flexible due to the usage of CR. Finally, we conduct simulation studies and analysis of an Alzheimer's disease dataset to further demonstrate the effectiveness of JICO. R implementation of JICO is available online at https://github.com/peiyaow/JICO.