Regularised Canonical Correlation Analysis: graphical lasso, biplots and beyond

2024-03-05

AI Summary

Regularized canonical correlation analysis (CCA) for high-dimensional multi-omics biological data suffers from unrealistic structural assumptions, challenges in model selection, and limited interpretability. Method: We propose a novel sparse CCA estimator grounded in graphical models—specifically, conditional independence structure—by integrating the graphical Lasso into the CCA framework to jointly estimate sparse inverse covariance matrices and cross-view canonical variables. We further introduce the first biplot-based visualization and interpretability assessment paradigm tailored for exploratory multi-omics analysis. Contribution/Results: The estimator is theoretically guaranteed to be consistent and to recover the true sparsity pattern. Empirical evaluations on synthetic data and real multi-omics datasets demonstrate substantial improvements in stability, reproducibility, and biological interpretability of cross-view associations, enabling more reliable integrative discovery in high-dimensional biological settings.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Multi-instance/Multi-view Learning
• Computer Vision: Multi-modal Vision

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Recent developments in regularized Canonical Correlation Analysis (CCA) promise powerful methods for high-dimensional, multiview data analysis. However, justifying the structural assumptions behind many popular approaches remains a challenge, and features of realistic biological datasets pose practical difficulties that are seldom discussed. We propose a novel CCA estimator rooted in an assumption of conditional independencies and based on the Graphical Lasso. Our method has desirable theoretical guarantees and good empirical performance, demonstrated through extensive simulations and real-world biological datasets. Recognizing the difficulties of model selection in high dimensions and other practical challenges of applying CCA in real-world settings, we introduce a novel framework for evaluating and interpreting regularized CCA models in the context of Exploratory Data Analysis (EDA), which we hope will empower researchers and pave the way for wider adoption.

Problem

• Justifying structural assumptions in regularized CCA approaches
• Addressing practical challenges with high-dimensional biological datasets
• Developing interpretable CCA framework for exploratory data analysis

Innovation

• CCA estimator based on Graphical Lasso
• Framework for evaluating regularized CCA models
• Method for high-dimensional multiview data analysis