Forward Operator Estimation in Generative Models with Kernel Transfer Operators.

Area of Science:

• Machine Learning
• Computational Statistics

Background:

• Generative models like VAEs, flow-based models, and GANs map known distributions to unknown data distributions.
• Deep neural networks are commonly used for this mapping, but can be computationally expensive.

Purpose of the Study:

• To propose a computationally cheaper and simpler strategy for distribution approximation and sampling.
• To adapt existing kernel transfer operator methods for generative modeling.

Main Methods:

• Leveraging kernel transfer operators to estimate the mapping between distributions.
• Exploring a class of non-linear functions for distribution approximation.

Main Results:

• The proposed method enables highly efficient distribution approximation and sampling.
• Empirical performance favorably compares with powerful baseline models.
• Reduced runtime and memory costs compared to traditional deep learning approaches.

Conclusions:

• The kernel transfer operator approach offers a viable, efficient alternative for generative modeling.
• Accepting minor compromises in functionality and scalability yields significant computational benefits.