# Multi-Platform Multivariate Regression with Group Sparsity for High-Dimensional Data Integration

## TL;DR

This paper introduces a new regression model that integrates data from multiple platforms to improve prediction accuracy and interpretability in high-dimensional settings.

## Contribution

The novel MM-HLR model combines Lasso and group Lasso penalties to handle multivariate responses and cross-platform data integration.

## Key findings

- The MM-HLR model achieves low bias and small variance in simulations.
- The method is robust across various data dimensions and performs well on real financial data.
- Theoretical guarantees include oracle bounds on prediction error and support recovery.

## Abstract

High-dimensional regression with multivariate responses poses significant challenges when data are collected across multiple platforms, each with potentially correlated outcomes. In this paper, we introduce a multi-platform multivariate high-dimensional linear regression (MM-HLR) model for simultaneously modeling within-platform correlation and cross-platform information fusion. Our approach incorporates a mixture of Lasso and group Lasso penalties to promote both individual predictor sparsity and cross-platform group sparsity, thereby enhancing interpretability and estimation stability. We develop an efficient computational algorithm based on iteratively reweighted least squares and block coordinate descent to solve the resulting regularized optimization problem. We establish theoretical guarantees for our estimator, including oracle bounds on prediction error, estimation accuracy, and support recovery under mild conditions. Our simulation studies confirm the method’s strong empirical performance, demonstrating low bias, small variance, and robustness across various dimensions. The analysis of real financial data further validates the performance gains achieved by incorporating multivariate responses and integrating data across multiple platforms.