CDE Inference with MAF (Masked Autoregressive Flows)

This notebook demonstrates parameter inference using Masked Autoregressive Flows (MAF) from the CDE module. MAF provides a more sophisticated approach to density estimation compared to MDN.

Note

This is a placeholder for the full tutorial. The complete interactive notebook will be available in the examples directory.

Overview

MAF vs MDN:

  • MAF: Uses autoregressive flows for flexible density modeling

  • MDN: Uses mixture of Gaussians for density approximation

  • Trade-off: MAF is more expressive but computationally more intensive

Key Advantages:

  • Expressive: Can model complex, multimodal distributions

  • Autoregressive: Captures parameter dependencies naturally

  • Scalable: Efficient for moderate to high-dimensional problems

Tutorial Content

The full tutorial demonstrates:

  1. Complex Data Generation: Multi-dimensional nonlinear relationships

  2. MAF Architecture: Configure autoregressive flow layers

  3. Advanced Training: Monitor convergence and performance

  4. 3D Visualization: Comprehensive posterior analysis

  5. Robustness Testing: Multiple test cases and evaluation metrics

When to Choose MAF vs MDN

Use MAF when:

  • Complex dependencies between parameters

  • Multimodal posterior distributions

  • Higher-dimensional parameter spaces

  • Need maximum expressiveness

Use MDN when:

  • Simpler parameter relationships

  • Faster inference required

  • Better interpretability needed

  • Lower computational resources

Performance Comparison

The tutorial includes comprehensive comparison:

  • Accuracy: Posterior approximation quality

  • Speed: Training and inference time

  • Robustness: Performance across multiple test cases

  • Scalability: Behavior with increasing dimensionality

Next Steps

  • Download the complete notebook from examples directory

  • Apply to real brain models (Jansen-Rit, Wilson-Cowan, etc.)

  • Compare computational efficiency with SBI methods

  • Explore different MAF architectures and hyperparameters