Diverse Influence Component Analysis: A Geometric Approach to Nonlinear Mixture Identifiability
This work addresses a foundational problem in machine learning for researchers and practitioners in fields like representation learning and causal inference, offering a novel geometric approach that relaxes key assumptions, though it appears incremental as it builds on prior nonlinear ICA methods.
The paper tackles the challenge of identifying latent components from unknown nonlinear mixtures, a problem in machine learning for tasks like disentangled representation learning and causal inference, by introducing Diverse Influence Component Analysis (DICA) with a Jacobian Volume Maximization criterion, which achieves identifiability without auxiliary information, independence, or sparsity assumptions.
Latent component identification from unknown nonlinear mixtures is a foundational challenge in machine learning, with applications in tasks such as disentangled representation learning and causal inference. Prior work in nonlinear independent component analysis (nICA) has shown that auxiliary signals -- such as weak supervision -- can support identifiability of conditionally independent latent components. More recent approaches explore structural assumptions, e.g., sparsity in the Jacobian of the mixing function, to relax such requirements. In this work, we introduce Diverse Influence Component Analysis (DICA), a framework that exploits the convex geometry of the mixing function's Jacobian. We propose a Jacobian Volume Maximization (J-VolMax) criterion, which enables latent component identification by encouraging diversity in their influence on the observed variables. Under reasonable conditions, this approach achieves identifiability without relying on auxiliary information, latent component independence, or Jacobian sparsity assumptions. These results extend the scope of identifiability analysis and offer a complementary perspective to existing methods.