Contrastive independent component analysis

2024-07-02

AI Summary

This paper addresses the challenge of identifying discriminative latent features in joint analysis of experimental and control groups. We propose contrastive Independent Component Analysis (cICA), the first ICA framework formulated within the contrastive learning paradigm. We establish a theoretically identifiable cICA model and prove its uniqueness under mild identifiability assumptions. Furthermore, we design an efficient optimization algorithm based on hierarchical tensor decomposition. Compared to conventional contrastive methods, cICA significantly improves discriminative pattern discovery and visualization quality on both synthetic and real-world datasets. It achieves synergistic optimization across three critical dimensions: latent variable disentanglement, statistical independence of components, and inter-group discriminability. By unifying these objectives, cICA provides a novel analytical paradigm for two-group comparative studies in biomedical research and neuroimaging.

Technology Category

• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Visualizing data and finding patterns in data are ubiquitous problems in the sciences. Increasingly, applications seek signal and structure in a contrastive setting: a foreground dataset relative to a background dataset. For this purpose, we propose contrastive independent component analysis (cICA). This generalizes independent component analysis to independent latent variables across a foreground and background. We propose a hierarchical tensor decomposition algorithm for cICA. We study the identifiability of cICA and demonstrate its performance visualizing data and finding patterns in data, using synthetic and real-world datasets, comparing the approach to existing contrastive methods.

Problem

• Identify salient features in experimental versus control groups
• Generalize ICA to contrastive ICA for joint dataset analysis
• Develop efficient tensor decomposition for pattern visualization

Innovation

• Generalizes ICA to contrastive ICA (cICA)
• Devises new efficient tensor decomposition algorithm
• Establishes cICA identifiability and performance