Toward the Identifiability of Comparative Deep Generative Models.

Area of Science:

• Machine Learning
• Computational Biology
• Data Science

Background:

• Deep Generative Models (DGMs) are used for data representation and comparing datasets.
• Interpretable latent representations are crucial but challenging in practice.
• Existing methods for comparative DGMs lack theoretical grounding.

Approach:

• Propose a theory of identifiability for comparative DGMs by extending non-linear independent component analysis.
• Investigate identifiability for piece-wise affine mixing functions (e.g., ReLU networks).
• Analyze the impact of model misspecification and existing regularization techniques.

Key Points:

• Comparative DGMs lack general identifiability but gain it with piece-wise affine mixing functions.
• Regularization techniques aid identifiability, especially with an unknown number of latent variables.
• A novel methodology using multi-objective and constrained optimization is introduced for fitting comparative DGMs.

Conclusions:

• The study provides theoretical grounding for comparative DGMs' identifiability.
• The novel methodology enhances multi-source data handling and hyperparameter tuning.
• Empirical validation on simulated and single-cell RNA sequencing data supports the findings.