Inference Methods & Examples

VBI provides multiple approaches for parameter inference, each with different strengths and use cases.

Inference Method Overview

Inference Methods Comparison

Method	Dependencies	Performance	Best For
CDE (Conditional Density Estimation)	NumPy + autograd	Fast, lightweight	Quick inference, limited resources
SBI (Simulation-Based Inference)	PyTorch + sbi	State-of-the-art	Complex problems, research

CDE-Based Inference (Lightweight)

Conditional Density Estimation using pure NumPy implementation - no PyTorch required.

Key Features:

• ✅ Lightweight: Only requires NumPy and autograd

• ✅ Fast: Efficient implementation for moderate-scale problems

• ✅ Transparent: Clear mathematical foundation

• ✅ Flexible: Easy to customize and extend

Documentation & Tutorials

Quick Start:

• CDE Quick Start: Mixture Density Networks (MDN) - Quick Start Guide for MDN (5-minute read)

Complete Reference:

• CDE API Guide: Conditional Density Estimation - Comprehensive API Documentation for MDN and MAF (includes theory, usage, and best practices)

Example Notebooks

Complete examples demonstrating CDE inference on various brain models:

• Damped Oscillator - CDE
• Jansen-Rit whole brain (NUMBA)
• Virtual Epileptic Patient
• VEP SDE CDE Example (84 Regions)
• Montbrió–Pazó–Roxin (MPR) SDE — Simulation & Likelihood-Free Inference
• Wilson-Cowan SDE model in Numba
• Wong–Wang full model (Numba implementation)

When to use CDE:

• Limited computational resources

• Want to avoid heavy PyTorch dependency

• Need transparent, interpretable inference

SBI-Based Inference (Advanced)

Simulation-Based Inference using PyTorch and the sbi library - state-of-the-art methods.

Key Features:

• 🚀 State-of-the-art: Latest neural density estimation techniques

• 🧠 Scalable: Handles high-dimensional problems efficiently

• 🔧 Comprehensive: Multiple inference algorithms (SNPE, SNLE, SNRE)

Current Examples:

Note: Most simulation examples currently use SBI for inference. We’re working on separating these into dedicated inference tutorials.

When to use SBI:

• Working with high-dimensional parameter spaces (> 10 parameters)

• Need state-of-the-art performance

• Complex, multimodal posterior distributions

Getting Started

For CDE Inference:

1. Start with CDE Quick Start: Mixture Density Networks (MDN) - Quick start with MDN

2. Read CDE API Guide: Conditional Density Estimation - Comprehensive API guide for MDN and MAF

3. Try example notebooks:

   • Damped Oscillator - CDE - Simple damped oscillator

   • Jansen-Rit whole brain (NUMBA) - Jansen-Rit neural mass model

   • Wilson-Cowan SDE model in Numba - Wilson-Cowan model

4. Apply to your brain model of choice

For SBI Inference:

1. Install full VBI: pip install vbi[inference]

2. Check existing simulation examples that include SBI

3. Adapt to your specific use case

Upcoming Examples

We’re working on expanding the inference examples:

• CDE + Brain Models: Direct application to Jansen-Rit, Wilson-Cowan models

• SBI Tutorials: Dedicated SBI workflow examples

• Method Comparisons: Side-by-side CDE vs SBI comparisons

• Real Data Examples: Using experimental neuroimaging data

Performance Guidelines

CDE Performance Tips:

• Use appropriate number of mixture components (MDN) or layers (MAF)

• Monitor training convergence carefully

• Consider data preprocessing/normalization

SBI Performance Tips:

• Use GPU acceleration when available

• Tune simulation budget vs accuracy trade-off

• Consider sequential vs single-round inference

Memory and Speed:

• CDE: Lower memory usage, faster setup

• SBI: Higher memory usage, potentially faster inference for complex problems

Contributing

We welcome contributions of new inference examples! See our CONTRIBUTING.md for guidelines on adding new tutorials and examples.